Colleges’ SAT Score Percentiles and Acceptance Rates

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The SAT exam has around 5 to 7 SAT Geometry and Trigonometry content domain questions out of 44 SAT Math questions. This makes up around 15% of the SAT Math. Note that, SAT Geometry and Trigonometry is the content domain where many SAT exam students wobble. Having a solid SAT Geometry and Trigonometry background and solving as many SAT Geometry and Trigonometry Practice questions as possible is key to having a high SAT Math score.

📌 Hint: Do not skip this article, you will find FREE SAT Math Prep resources throughout the article.

We’ve listed the most important and frequently occurring concepts in this SAT Geometry and Trigonometry post. You will see SAT Geometry and Trigonometry practice test questions and exercises, in total 8 Geometry and Trigonometry questions with rationales all for FREE. 

💡You might be interested in reading the Digital SAT Math Prep post.

SAT Geometry and Trigonometry Content Domain

Geometry is the study of different shapes, sizes, and positions of different shapes based on the number of sides, angles, and so on. Whereas trigonometry is the subset of geometry that deals with the properties of one of the shapes in geometry called “triangle”. In the SAT Geometry and Trigonometry domain, the College Board assesses the abilities of students in solving problems that focus on area and volume; angles, triangles, trigonometry; and circles.

💡You might be interested in reading the Digital SAT Math Ultimate Guide post. We have provided further details about the SAT Math structure, examples of easy, medium, and hard questions, answers, rationales, and frequently asked questions about the SAT Math.

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

SAT Geometry and Trigonometry Skills and Knowledge Testing Points

Geometry and Trigonometry is the fourth and last content domain in SAT Math. The SAT exam will have around 5 to 7 questions from the Geometry and Trigonometry content domain. There are 4 skills and knowledge testing points in the SAT Geometry and Trigonometry content domain:

1. 1. Area and Volume
   2. Lines, angles, and triangles
   3. Right triangles and trigonometry
   4. Circles

👉 Take our full-length FREE SAT Practice Test, see where you stand!

Let’s review the important points you should know for each of the SAT Geometry and Trigonometry skills and knowledge below.

🗎 Download the 15-page Digital SAT Math Formula Sheet.

SAT Geometry Topic 1: Area and Volume – Important Points

Area measures the amount of space inside a two-dimensional shape, while volume measures the space a three-dimensional object occupies. Both concepts are fundamental in SAT geometry and have numerous real-world applications, such as calculating the amount of paint needed to cover a wall or the volume of water a container can hold.

Calculating Area of Basic Shapes

Rectangles and Squares:

• Formula for Rectangle: Area = Length . Width
• Formula for Square: Area =

Triangles:

• Formula: Area =

Parallelograms:

• Formula: Area = Base . Height

Trapezoids:

• Formula: Area =

Circles:

• Formula: Area =

Memorize these formulas for solving SAT Geometry questions correctly.

Calculating Volume of Basic Solids

Cubes and Rectangular Prisms:

Formula for Cube:
Formula for Rectangular Prism: Volume = Length . Width . Height

Cylinders:

Formula: Volume=

Cones:

Formula: Volume =

Spheres:

Formula: Volume =

Composite Shapes and Solids

For composite shapes, break them down into simpler shapes, calculate the area or volume of each part, and then add them together.

Example: To find the area of a shape made from a rectangle and a semicircle:

1. Calculate the area of the rectangle.
2. Calculate the area of the semicircle.
3. Add the two areas together.

Surface Area of Solids

Surface Area of Cubes and Rectangular Prisms:

• Cube: Surface Area =
• Rectangular Prism: Surface Area = 2lw + 2lh + 2wh

Cylinders:

• Formula: Surface Area= (top and bottom circles + lateral area)

Cones:

• Formula: Surface Area = (base area + lateral area, where l is the slant height)

Spheres:

• Formula: Surface Area =

Note that, some of these formulas are provided on the SAT exam as follows. However, memorizing them will save you time when solving SAT Geometry problems in the SAT Exam.

💡We’ve prepared a 7-Step Digital SAT Math Study Guide helping students to prepare their unique SAT Math Study Guide.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Geometry Topic 2: Lines, Angles and Triangles

Understanding the properties and relationships between lines, angles, and triangles is fundamental to mastering SAT Geometry questions. This lecture will cover essential concepts and formulas to help solve these types of problems efficiently.

Lines and Angles

Definitions:

• Point: An exact location in space.
• Line: A collection of points extending infinitely in both directions.
• Line Segment: A part of a line with two endpoints.
• Ray: A part of a line that starts at a point and extends infinitely in one direction.

Types of Angles:

• Acute Angle: Less than 90°.
• Right Angle: Exactly 90°.
• Obtuse Angle: Greater than 90° but less than 180°.
• Straight Angle: Exactly 180°.
• Reflex Angle: Greater than 180° but less than 360°.

Angle Relationships:

• Complementary Angles: Two angles whose measures add up to 90°.
• Supplementary Angles: Two angles whose measures add up to 180°.
• Vertical Angles: Opposite angles formed by two intersecting lines (always equal).
• Linear Pair: A pair of adjacent angles that form a straight line (supplementary).

Parallel and Perpendicular Lines

Definitions:

• Parallel Lines: Lines in a plane that never intersect and are always the same distance apart.
• Perpendicular Lines: Lines that intersect to form a right angle (90°).

Properties Involving Transversals:

• Corresponding Angles Postulate: If a transversal intersects two parallel lines, each pair of corresponding angles is equal.
• Alternate Interior Angles Theorem: If a transversal intersects two parallel lines, each pair of alternate interior angles is equal.
• Consecutive Interior Angles Theorem: If a transversal intersects two parallel lines, consecutive interior angles are supplementary.
• Alternate Exterior Angles Theorem: If a transversal intersects two parallel lines, each pair of alternate exterior angles is equal.

Triangles: Types and Properties

Classification by Sides:

• Equilateral Triangle: All sides and angles are equal (each angle is 60°).
• Isosceles Triangle: At least two sides are equal, and the angles opposite these sides are also equal.
• Scalene Triangle: All sides and angles are different.

Classification by Angles:

• Acute Triangle: All angles are less than 90°.
• Right Triangle: One angle is exactly 90°.
• Obtuse Triangle: One angle is greater than 90°.

Key Theorems:

• Triangle Sum Theorem: The sum of the angles in any triangle is 180°.
• Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Special Properties of Triangles

Isosceles Triangle Theorem: The angles opposite the equal sides of an isosceles triangle are equal.

Pythagorean Theorem: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Special Right Triangles:

• 30-60-90 Triangle: The sides are in the ratio 1 : √3 : 2.
• 45-45-90 Triangle: The sides are in the ratio 1 : 1 : √2.

Congruence and Similarity in Triangles

Triangle Congruence Criteria:

• SSS (Side-Side-Side): Three sides of one triangle are equal to three sides of another triangle.
• SAS (Side-Angle-Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• ASA (Angle-Side-Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.
• AAS (Angle-Angle-Side): Two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle.
• HL (Hypotenuse-Leg for Right Triangles): The hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle.

Triangle Similarity Criteria:

• AA (Angle-Angle): Two angles of one triangle are equal to two angles of another triangle.
• SSS (Side-Side-Side): The corresponding sides of two triangles are proportional.
• SAS (Side-Angle-Side): Two sides are proportional, and the included angle is equal.

📚 San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

SAT Geometry Topic 3: Right Triangles and Trigonometry

Trigonometry deals with the relationships between the angles and sides of triangles, especially right triangles. Understanding these relationships is crucial for solving many SAT Geometry and Trigonometry problems, including those involving angles, heights, distances, and more.

Properties of Right Triangles

A right triangle is a triangle in which one angle is a right angle (90°). The side opposite the right angle is called the hypotenuse, and the other two sides are known as the legs.

Pythagorean Theorem:

For any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides:

where c is the hypotenuse and a and b are the legs.

Special Right Triangles:

• 30-60-90 Triangle: The sides are in the ratio 1 : √3 : 2.
• 45-45-90 Triangle: The sides are in the ratio 1 : 1 : √2.

Basic Trigonometric Ratios

Trigonometric Ratios relate the angles of a right triangle to the lengths of its sides. The three basic trigonometric ratios are:

• Sine (sin):
  sin⁡θ=
• Cosine (cos):
  cos⁡θ=
• Tangent (tan):
  tan⁡θ=

These ratios are fundamental in solving right triangle SAT Geometry and Trigonometry problems.

Using Trigonometric Ratios to Solve Problems

To solve for missing sides or angles in right triangles:

• Finding Missing Sides: Use the trigonometric ratios to set up equations based on the given information.
  Example:
  If sin⁡θ=0.5 and the hypotenuse is 10, then the opposite side is:
  Opposite Side = sin⁡θ × Hypotenuse = 0.5 × 10 = 0.5 × 10 = 5.
• Finding Angles: Use the inverse trigonometric functions to determine the measure of an angle given two sides.

The Pythagorean Identity and Trigonometric Values

Pythagorean Identity:

If , and If

This identity is useful for finding one trigonometric value if another is known.

Key Trigonometric Values to Memorize for SAT Geometry and Trigonometry

sin, cos, tan for 0°, 30°, 45°, 60°, and 90°:

• sin⁡0° = Error: WPMathPub plugin shortcode cannot be empty, sin⁡30° = , sin⁡45° = , sin⁡60°=, sin90° =
• cos0° = , cos⁡30° = , cos⁡45° = , cos60°=, cos90° = Error: WPMathPub plugin shortcode cannot be empty
• tan0° = Error: WPMathPub plugin shortcode cannot be empty, tan30° = , tan⁡45° = , tan⁡60°= , tan90° = undefined

Applications of Right Triangle Trigonometry

• Word Problems: Trigonometry is often used in word problems involving heights, distances, and angles of elevation or depression.
• Coordinate Geometry: Trigonometry can be used to find slopes, distances, and angles between lines in coordinate planes.

Tips for SAT Geometry and Trigonometry Problems on Right Triangles and Trigonometry

• Remember the definitions of the trigonometric ratios and when to use them.
• Use the Pythagorean Theorem and trigonometric identities to simplify problems.
• Practice visualizing right triangles in different contexts, such as coordinate planes and word problems.

SAT Geometry & Trigonometry – Hack Points & Exercises – YouTube Video

You can view our SAT Geometry & Trigonometry YouTube video. We’ve gone through each of the 4 SAT Geometry & Trigonometry topics, provided the important points to know, and exercises for each as well.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Geometry Topic 4: Circles

A circle is a set of all points in a plane that are equidistant from a fixed point called the center. Understanding the properties and formulas related to circles is essential for solving many SAT Geometry problems on the SAT.

Properties of Circles

• Radius (r): The distance from the center of the circle to any point on the circle.
• Diameter (d): The distance across the circle through its center; d = 2r
• Circumference (C): The distance around the circle; C = 2πr.
• Chord: A line segment with both endpoints on the circle.
• Arc: A portion of the circumference of a circle.
• Sector: A region enclosed by two radii of a circle and their intercepted arc.
• Segment: A region enclosed by a chord and the arc it subtends.
• Central Angle: An angle whose vertex is at the center of the circle.
• Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords.

Formulas Related to Circles

Circumference and Area:

• Circumference:
  C=2πr
  or
  C=πd
• Area:
  A=

Length of an Arc:

Formula:
Arc Length =
where θ is the central angle in degrees.

Area of a Sector:

Formula:
Area of a Sector =

Equation of a Circle in the Coordinate Plane:

Standard Form:
where (h,k) is the center of the circle and r is the radius.

🖋️ Standard form of a circle is a frequently occurring SAT Geometry concept in SAT. 

Angles and Arcs in Circles

Central Angles and Arc Measures:

• A central angle is equal to the measure of its intercepted arc.

Inscribed Angles:

• An inscribed angle is half the measure of its intercepted arc.
• Angles inscribed in a semicircle are right angles (90°).

Angles Formed by Chords, Secants, and Tangents:

• The angle formed by two intersecting chords is half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
• The angle formed by a tangent and a chord through the point of contact is half the measure of the intercepted arc.

Tangents and Their Properties

Definition of a Tangent:
A tangent to a circle is a line that touches the circle at exactly one point.

Properties of Tangents:
A tangent is perpendicular to the radius drawn to the point of tangency.
Two tangents drawn to a circle from an external point are equal in length.

Tangent-Secant and Tangent-Tangent Angle Theorems:
The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

Solving SAT Geometry Problems Involving Circles

Common Problem Types:
Finding circumference, area, or arc length.
Solving for angles formed by tangents, chords, or secants.
Applying the properties of inscribed angles and central angles.
Word problems involving real-world applications of circles.

Strategies for SAT Geometry and Trigonometry Problems

We recommend the following tips and strategies for solving SAT Geometry and Trigonometry problems:

• Draw diagrams to visualize the problem.
• Use the appropriate formulas based on the given information.
• Check for relationships between angles, arcs, and chords.

Tips for SAT Geometry Problems on Circles

• Familiarize yourself with all circle formulas and properties.
• Pay attention to the specific details given in the problem (e.g., diameter vs. radius).
• Practice recognizing and applying the properties of tangents, chords, and arcs.

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

SAT Geometry and Trigonometry Exercises

There are four SAT Geometry and Trigonometry Exercises below, one for each skill and knowledge testing below. To improve your math skills, we do not recommend using a calculator when solving these SAT Geometry and Trigonometry Exercises.

Exercise I. One side of a rectangle and a square are common. The area of the rectangle is two times the area of the square. If the perimeter of the rectangle is 10 units greater than the perimeter of the square, what is the length of the rectangle in units?

Exercise II.

In the figure, line m is parallel to line n, and line k intersects both lines. What is the value of x + y ?

Exercise III. One leg of an isosceles right triangle A is common with the shortest leg of another right triangle B. The length of the longest side of the triangle B is 17, and longer leg length is 15. What is the length of the longest side of triangle A?

Exercise IV. The graph of in the xy-plane is a circle. What is the area of the circle?

💡You can see our Free SAT Math Exercises which has 50 exercises on all SAT Math domains. 

Note: You can use a calculator in this SAT Math Exercise

💡Do not forget to visit SAT Math Exercises which has 50 exercises on all SAT Math domains. It’s for free!

SAT Geometry and Trigonometry Practice Test

We’ve listed 4 hard SAT Geometry and Trigonometry practice test questions below. Note that this test does not resemble the typical question difficulty distribution on an SAT Geometry and Trigonometry domain. Instead, we wanted to show you the hardest SAT Math Geometry and Trigonometry questions you may see on the SAT.

Besides, since these are the hardest questions for the SAT Geometry and Trigonometry, it is very normal that you will spend longer than usual time to solve each question. It is also super normal that you may score lower than your previous SAT Geometry and Trigonometry Practice tests in this one. Because a typical Digital SAT Math Practice Test covers easy, medium, and hard questions. However, this one contains only the hardest questions.

Question 1

What is the area, in square units, of the triangle formed by connecting the three points shown?

Skill and Knowledge Testing Point: Area and volume

SAT Geometry and Trigonometry Practice – Question 2

In triangle RST, angle T is a right angle, point L lies on , point K lies on , and is parallel to . If the length of is 72 units, the length of is 24 units, and the area of triangle RST is 792 square units, what is the length of , in units?

Skill and Knowledge Testing Point: Lines, angles, and triangles

Question 3

Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. Angles C and F are right angles. If and DF = 125, what is the length of ?

A.

B.

C.

D.

Skill and Knowledge Testing Point: Right triangles and trigonometry

Question 4

A circle in the xy-plane, the graph of is a circle. What is the radius of the circle?

A. 5

B. 6.5

C.

D.

Skill and Knowledge Testing Point: Circles

SAT Geometry and Trigonometry Practice Test Answers and Rationales

We’ve created a comprehensive answers and rationales PDF file for these SAT Geometry and Practice questions. If you can fill in your name and email below, we can send it to your email in minutes. Note that, the PDF you will receive will have 19 questions from all SAT Math domains. The last 4 questions (Questions 16-19) are answers and rationales for this SAT Geometry and Trigonometry Practice Test.

Note that, the email may hit your junk or spam folders, please check your junk and spam folders and if you did not receive it, please email us at support@sanfranciscobs.com.

💡Do not forget to visit SAT Math Practice Test – Hardest Questions. Assess your SAT Math skills with the hardest questions you may see on SAT Math.

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There are 44 SAT Math questions in the SAT Exam. 13 to 15 of these 44 questions come from the SAT Algebra content domain. This makes the Algebra content domain 30-35% of the SAT Math. Therefore, having a solid SAT Algebra background and solving as many SAT Algebra Practice Tests as possible is crucial to having a high SAT Math score.

📌 Hint: Do not skip this article, you will find FREE Digital SAT Math Prep resources throughout the article.

We’ve listed the most important and frequently occurring concepts in this SAT Algebra post. You will see SAT Algebra practice test questions and exercises, in total 31 SAT Algebra questions with rationales all for FREE. 

💡You might be interested in reading the Digital SAT Math Prep post.

SAT Algebra Content Domain

Algebra is a branch of mathematics in which arithmetical operations and formal manipulations are applied to abstract symbols rather than specific numbers. Algebra is the first content domain in the SAT Math. In the SAT Algebra domain, the College Board assesses the abilities of students in solving and creating linear equations and inequalities as well as analyzing and fluently solving equations and systems of equations using multiple techniques.

💡You might be interested in reading the Digital SAT Math Ultimate Guide post. We have provided further details about the SAT Math structure, examples of easy, medium, and hard questions, answers, rationales, and frequently asked questions about the SAT Math.

👉 Take our full-length FREE SAT Practice Test, see where you stand!

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

SAT Algebra Skills and Knowledge Testing Points

The SAT exam will have around 13 to 15 questions from the Algebra content domain. There are 5 skills and knowledge testing points in the Algebra content domain:

1. Linear equations in one variable
2. Linear equations in two variables
3. Linear functions
4. Systems of two linear equations in two variables
5. Linear inequalities in one or two variables

Let’s review each skill and knowledge point and see some SAT Algebra Exercises for each.

🗎 Download the 15-page Digital SAT Math Formula Sheet.

1. Linear Equations in One Variable – Important Points

A linear equation in one variable is an equation that can be expressed in the form:

Where:

• and are constants and ≠ Error: WPMathPub plugin shortcode cannot be empty.
• is the variable.

The general solution to a linear equation in one variable will yield a single value for .

How to Solve SAT Algebra Linear Equations

There are three simple steps to solve linear equations:

1. Isolate the variable: Use addition, subtraction, multiplication, and division to get the variable by itself on one side of the equation.
2. Simplify: Combine like terms and simplify both sides if necessary.
3. Check your solution: Substitute the found value into the original equation to verify correctness.

💡We’ve prepared a 7-Step Digital SAT Math Study Guide helping students to prepare their unique SAT Math Study Guide.

SAT Math Algebra Exercises for Linear Equations in One Variable

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Algebra Exercises.

Exercise I. 

Exercise II. 

Exercise III. 

Exercise IV. 

Exercise V. 

Exercise VI.  Ethan has $15. He gets dollars from his grandfather. If Ethan has $35 now, what is the value of ?

💡You can see our Free SAT Math Exercises which has 50 exercises on all SAT Math domains. 

2. Linear Equations in Two Variables – Important Points

A linear equation in two variables can be expressed in the form:

Where:

• , and are constants.
• and are variables.

Graphing SAT Algebra Linear Equations

• The graph of a linear equation in two variables is a straight line.
• The coefficients and determine the slope of the line, while affects its position on the graph.

Slope-Intercept Form:

• A common way to express a linear equation is the slope-intercept form: where is the slope and is the y-intercept (the point where the line crosses the y-axis).

🖋️ Slope-intercept form is a frequently occurring concept in SAT Math. 

• Parallel Lines: Slopes of parallel lines are the same.
• Perpendicular Lines: The product of the perpendicular lines is (-1).

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Algebra Exercises for Linear Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.  . What is the y-intercept of this graph?

Exercise II.  . What is the x-intercept of this graph?

Exercise III.  . and are two possible solutions to the equation. What is the value of ?

Exercise IV.  . Grapf of line m is given. A line k is parallel to line m. What is the slope of line k?

Exercise V.  . If the line h is perpendicular to the given equation’s graph, what is the slope of line h?

Exercise VI. A line passes through (0, 4) and the slope of the line is 2. What is the equation of this line?

SAT Algebra Hack Points & Exercises YouTube Video

You can view our SAT Algebra YouTube video. We’ve gone through each of the 5 SAT Algebra topics, provided the important points to know, and exercises for each as well.

💡You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

3. Linear Functions – Important Points

A linear function is a function that creates a straight line when graphed on the xy-plane.

• The general form of a linear function is: where is the slope and is the y-intercept ((0, b), the value of f(x) when x = 0).
• The slope (m) of a linear function indicates the steepness of the line. It can be calculated as:

The slope can be positive, negative, zero, or undefined:

• • Positive slope: The line rises as it moves from left to right.
  • Negative slope: The line falls as it moves from left to right.
  • Zero slope: The line is horizontal.
  • Undefined slope: The line is vertical.

SFBS Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

SAT Algebra Exercises for Linear Functions

To improve your math skills, we do not recommend using a calculator when solving these SAT Algebra Exercises.

Exercise I.   The graph of y = f(x) passes through the points (1, 4) and (3, 10). What is the function f ?

Exercise II.  The function f is defined by the equation . What is the value of f(x) when ?

Exercise III. An electrician charges a $40 fixed fee plus $25 per hour. If the function h models the total fee for the electrician for t hours of work, write the function h.

Exercise IV. The function f is defined by . What is the y-intercept of the graph of in the xy-plane?

Exercise V. The graph of y = f(x) and y=h(x) are perpendicular to each other in the xy-plane. Function f is defined by . If , write the y=h(x) function.

Exercise VI. The function models the altitude of an airplane m minutes after takeoff. According to the model, what is the altitude of the airport where the airplane took off?

📚 San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

4. Systems of Two Linear Equations in Two Variables – Important Points

A system of two linear equations in two variables consists of two equations that can be represented in the form:

where x and y are variables, and , , , , , and are constants.

Graphical Interpretation: Each equation represents a straight line in the coordinate plane. The solution to the system is the point where the two lines intersect.

How to Solve SAT Algebra Systems of Equations

There are three main methods to solve a system of linear equations:

1. Graphing:
   • Rewrite both equations in slope-intercept form (y = mx + b).
   • Graph each line on the same coordinate plane.
   • Identify the intersection point, which is the solution.
     
2. Substitution
   • Solve one equation for one variable.
   • Substitute that expression into the other equation.
   • Solve for the remaining variable.
   • Substitute back to find the other variable.
3. Elimination
   • Align the equations.
   • Multiply one or both equations to make the coefficients of one variable opposite.
   • Add or subtract the equations to eliminate one variable.
   • Solve for the remaining variable.
   • Substitute back to find the other variable.

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Algebra Exercises for Systems of Two Linear Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Algebra Exercises.

Exercise I. 

The solution to the given system of equations is (x, y). What is the value of y)

Exercise II. 

For the given system of equations, what is the value of y ?

Exercise III. 

The solution to the given system of equations is (x, y). What is the value of x + y?

Exercise IV.   

In the given system of equations, k is a constant. If the system has no solution, what is the value of k?

💡You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

5. Linear Inequalities in One or Two Variables – Important Points

A linear inequality is similar to a linear equation but uses inequality signs (>, <, ≥, ≤) instead of the equals sign (=).

Example: Linear inequality: ( 2x + 3 < 7 )

Solving SAT Algebra Linear Inequalities in One Variable

You can apply the following basic steps to solve SAT Algebra Linear Inequalities in One Variable:

• Isolate the variable on one side of the inequality.
• Perform the same operations on both sides (addition, subtraction, multiplication, division).
• Important: If you multiply or divide by a negative number, reverse the inequality sign.

Example: Solve ( 3x – 5 ≥ 4 ).

• Step 1: Add 5 to both sides: ( 3x ≥ 9 )
• Step 2: Divide by 3: ( x ≥ 3 )
• Graphing the Solution: On a number line, you would represent ( x ≥ 3 ) with a closed circle at 3 shaded to the right.

SAT Algebra Compound Inequalities

These involve two inequalities connected by “and” or “or”. Types:

• Conjunction (And): True if both inequalities are true.
• Disjunction (Or): True if at least one inequality is true.

Example (Conjunction): Solve ( 1 < 2x + 1 < 7 ).

• Break it into two inequalities:
  • ( 1 < 2x + 1 )
    ( 2x + 1 < 7 )
• Solve both:
  • First: ( 0 < 2x  ->  x > 0 )
  • Second: ( 2x < 6  ->  x < 3 )
• Combined solution: ( 0 < x < 3 )
• Graphing: Represent this with an open interval on a number line from 0 to 3.

Linear Inequalities in Two Variables

Linear inequality uses two variables, represented in the form ( Ax + By < C ), ( Ax + By > C ), etc.

Example: Linear inequality: ( x + 2y ≤ 4 )

Systems of Linear Inequalities

A set of two or more inequalities that can be graphed on the same coordinate plane.

Example:
( y > x + 1 )
( y < -x + 3 )

SFBS Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

SAT Algebra Exercises for Linear Inequalities in One or Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. Ryan has $100 and wants to purchase balls. A store sells basketballs and baseballs. Basketballs are $15 each and baseballs are $20 each.  If x represents the number of basketballs and y represents the number of baseballs Ryan can purchase, what is the inequality representing this situation?

Exercise II. The maximum value of is 13 greater than another number k. What is the inequality for x in terms of k?

Exercise III. A High School has students whose height is between 160 cm to 186cm. If h represents the height of a student in this High School, what is the inequality representing the height of a student?

Exercise IV.

(2, p) is a solution to the given system of inequalities. What is the maximum integer value for p?

💡You can see our Free SAT Math Exercises which has 50 exercises on all SAT Math domains. 

SAT Algebra Practice Test

We’ve listed 5 hard SAT Algebra practice test questions below. Note that this test does not resemble the typical question difficulty distribution on a SAT Algebra domain. Instead, we wanted to show you the hardest SAT Math Algebra questions you may see on the SAT.

Besides, since these are the hardest questions for the SAT Algebra, it is very normal that you will spend longer than usual time to solve each question. It is also super normal that you may score lower than your previous SAT Algebra Practice tests in this one. Because a typical Digital SAT Math Practice Test covers easy, medium, and hard questions. However, this one contains only the hardest questions.

Question 1

The equation 9x + 5 =a(x+b), where a and b are constants, has no solutions. Which of the following must be true?

I. a = 9
II. b = 5
III. b ≠

A. None

B. I only

C. I and II only

D. I and III only

Skill and Knowledge Testing Point: Linear equations in one variable

Question 2

To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of s dollars for working at job B. In one week, Avery earned a total of s dollars for working at the two part-time jobs. The graph above represents all possible combinations of the number of hours Avery could have worked at the two jobs to earn s dollars. What is the value of s ?

A. 128

B. 160

C. 200

D. 320

Skill and Knowledge Testing Point: Linear equations in two variables

Question 3

An object hangs from a spring. The formula relates the length , in centimeters, of the spring to the weight , in newtons, of the object. Which of the following describes the meaning of the 2 in this context?

A. The length, in centimeters, of the spring with no weight attached

B. The weight, in newtons, of an object that will stretch the spring 30 centimeters

C. The increase in the weight, in newtons, of the object for each one-centimeter increase in the length of the spring

D. The increase in the length, in centimeters, of the spring for each one-newton increase in the weight of the object

Skill and Knowledge Testing Point: Linear functions

SAT Algebra Practice Test – Question 4

Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?

A. 4

B. 5

C. 8

D. 12

Skill and Knowledge Testing Point: Systems of two linear equations in two variables

Question 5

Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

A. 38

B. 33

C. 22

D. 16

Skill and Knowledge Testing Point: Linear inequalities in one or two variables

SAT Algebra Practice Test Answers and Rationales

We’ve created a comprehensive answers and rationales PDF file for these SAT Algebra Practice questions. If you can fill in your name and email below, we can send it to your email in minutes. Note that, the PDF you will receive will have 19 questions from SAT Math domains. The first 5 questions are answers and rationales for this SAT Algebra Practice Test.

Note that, the email may hit your junk or spam folders, please check your junk and spam folders and if you did not receive it, please email us at support@sanfranciscobs.com.

💡You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

The post SAT Algebra – Hack Points and FREE SAT Algebra Practice appeared first on San Francisco Business School.

After teaching thousands of SAT exam students, we’ve revealed that a high SAT Math score strongly depends on students’ practice on SAT Math exercises. We’ve seen many students increase their SAT Math scores by around 200 points. This is a huge increase, and it is only possible by doing as many SAT Math exercises and practices as possible.

📌 Hint: Do not skip this article, you will find FREE Digital SAT Math Prep resources throughout the article.

Ethan is one of our thousands of successful SAT students. He perfectly scored 1600 on the SAT, the highest score a student can get! We were with thousands of students, like Ethan, in their SAT Math Prep journey. We’ve witnessed how they approach SAT Math Exercises and practices and that is why created this SAT Math Exercices post to help many others!

💡You might be interested in reading the Digital SAT Math Prep post.

Digital SAT Math Structure

Before diving into SAT Math Exercises, you must understand the SAT Math structure, question types, and how to approach different types of questions.

The SAT exam consists of two modules, Module I and Module II. Each module consists of 22 questions, and there will be a total of 44 questions. You will have 35 minutes for each module. Going through comprehensive SAT Math Exercises will help you to get a higher score on SAT Math. We prepared the following table to summarize the structure of the  SAT Math sections.

👉 Take our full-length FREE SAT Practice Test, see where you stand!

The most critical aspect of the Digital SAT is being adaptive. In SAT Math Module I, you will be asked a broad mix of easy, medium, and hard questions. Then, the difficulty of the SAT Math Module II will depend on your score in the SAT Math Module I. This means that the test “adapts” to present questions that are more appropriate to a student’s performance level. Going through several SAT Math Exercises and Practices will improve your scores. The following figure depicts the Digital SAT adaptive testing model.

💡You might be interested in reading the Digital SAT Math Ultimate Guide post. We have provided further details about the SAT Math structure, examples of easy, medium, and hard questions, answers, rationales, and frequently asked questions about the SAT Math.

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

Now, let’s go through the SAT Math Exercises!

🗎 Download the 15-page Digital SAT Math Formula Sheet.

Digital SAT Math Exercises

We’ve created these SAT Math Exercises to provide exercises for the commonly tested concepts on the SAT exam. You can consider enrolling in our Online Digital SAT Math Prep Course for a comprehensive SAT Math Prep.

We’ve listed the SAT Math Exercises for each content domain and skills and knowledge testing points respectively. There are a total of 50 SAT Math Exercises in 10 sets. We do not recommend using a calculator for many of the questions. In case a question needs complex calculations, we mentioned as a note that you can use a calculator for that particular SAT Math Exercise.

💡We’ve prepared a 7-Step Digital SAT Math Study Guide helping students to prepare their unique SAT Math Study Guide.

SAT Math Exercises for Algebra

Algebra is the first content domain in the SAT Math. The SAT exam will have around 13 to 15 questions from the Algebra content domain. There are 5 skills and knowledge testing points in the Algebra content domain:

1. Linear equations in one variable
2. Linear equations in two variables
3. Linear functions
4. Systems of two linear equations in two variables
5. Linear inequalities in one or two variables

💡You might be interested in seeing our SAT Algebra post. It covers the hack points you should know and 31 SAT Algebra Practice Questions!

Let’s review each skill and knowledge point and see some SAT Math Exercises for each.

SAT Math Exercise Set 1: Linear Equations in One Variable

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. 

Exercise II. 

Exercise III. 

Exercise IV. 

Exercise V. 

Exercise VI.  Ethan has $15. He gets dollars from his grandfather. If Ethan has $35 now, what is the value of ?

💡You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

📚 San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Math Exercise Set 2: Linear Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.  . What is the y-intercept of this graph?

Exercise II.  . What is the x-intercept of this graph?

Exercise III.  . and are two possible solutions to the equation. What is the value of ?

Exercise IV.  . Grapf of line m is given. A line k is parallel to line m. What is the slope of line k?

Exercise V.  . If the line h is perpendicular to the given equation’s graph, what is the slope of line h?

Exercise VI. A line passes through (0, 4) and the slope of the line is 2. What is the equation of this line?

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

SAT Math Exercise Set 3: Linear Functions

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.   The graph of y = f(x) passes through the points (1, 4) and (3, 10). What is the function f ?

Exercise II.  The function f is defined by the equation . What is the value of f(x) when ?

Exercise III. An electrician charges a $40 fixed fee plus $25 per hour. If the function h models the total fee for the electrician for t hours of work, write the function h.

Exercise IV. The function f is defined by . What is the y-intercept of the graph of in the xy-plane?

Exercise V. The graph of y = f(x) and y=h(x) are perpendicular to each other in the xy-plane. Function f is defined by . If , write the y=h(x) function.

Exercise VI. The function models the altitude of an airplane m minutes after takeoff. According to the model, what is the altitude of the airport where the airplane took off?

SAT Math Exercise Set 4: Systems of Two Linear Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. 

The solution to the given system of equations is (x, y). What is the value of y)

Exercise II. 

For the given system of equations, what is the value of y ?

Exercise III. 

The solution to the given system of equations is (x, y). What is the value of x + y?

Exercise IV.   

In the given system of equations, k is a constant. If the system has no solution, what is the value of k?

SAT Math Exercise Set 5: Linear Inequalities in One or Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. Ryan has $100 and wants to purchase balls. A store sells basketballs and baseballs. Basketballs are $15 each and baseballs are $20 each.  If x represents the number of basketballs and y represents the number of baseballs Ryan can purchase, what is the inequality representing this situation?

Exercise II. The maximum value of is 13 greater than another number k. What is the inequality for x in terms of k?

Exercise III. A High School has students whose height is between 160 cm to 186cm. If h represents the height of a student in this High School, what is the inequality representing the height of a student?

Exercise IV.

(2, p) is a solution to the given system of inequalities. What is the maximum integer value for p?

SAT Math Exercises for Advanced Math

Advanced Math is the second content domain in SAT Math. In the SAT exam, there will be around 13 to 15 questions from the Advanced Math content domain. There are 3 skills and knowledge testing points in the Advanced Math content domain:

1. 1. Equivalent expressions
   2. Nonlinear equations in one variable and systems of equations in two variables
   3. Nonlinear functions

💡You might be interested in seeing our SAT Advanced Math post. It covers the hack points you should know and 27 SAT Advanced Math Practice Questions!

Let’s go through each skill and knowledge point and see some SAT Math Exercises for each one.

SAT Math Exercise Set 6: Equivalent Expressions

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.

The given equation relates the positive numbers p, x, and y. Write the p-value in terms of x and y.

Exercise II.

What is the value of ?

Exercise III.

What is the value of x?

Exercise IV. 

Simplify the given expression.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Math Exercise Set 7: Nonlinear Equations in One Variable and Systems of Equations in Two Variables

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I. Two variables, x, and y are related such that for each increase of 1 in the value of x, the value of y increases by a factor of 5. When x=0, y=10. Write the y in terms of x.

Exercise II. .

One solution to the given equation can be written as , where k is a constant. What is the value of k?

Exercise III. .

In the given equation, p is a constant. The equation has exactly one solution. What is the value of p?

Exercise IV.
.

A solution to the given system of equations is (x, y), where x>0. What is the value of x?

SAT Math Exercise Set 8: Nonlinear Functions

To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

Exercise I.

The given equation defines the function f. What is the minimum value of f(x)?

Exercise II. The function f is defined by . What is the value of f(6)?

Exercise III. The function gives a spring’s length, in feet, when an object of w kilograms is hung, where . What is the best interpretation of 15 in this context?

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

SAT Math Exercises for Problem-Solving and Data Analysis

Problem-solving and Data Analysis is the third content domain in SAT Math. In the SAT exam, there will be around 5 to 7 questions from the Problem-solving and Data Analysis content domain. There are 7 skills and knowledge testing points in the Problem-solving and Data Analysis content domain:

1. 1. Ratios, rates, proportional relationships, and units
   2. Percentages
   3. One-variable data: distributions and measures of center and spread
   4. Two-variable data: models and scatterplots
   5. Probability and conditional probability
   6. Inference from sample statistics and margin of error
   7. Evaluating statistical claims: observational studies and experiments

💡You might be interested in seeing our SAT Problem-Solving and Data Analysis post. It covers the hack points you should know and 15 SAT Problem-Solving and Data Analysis Practice Questions!

We’ve listed one SAT Math Exercise for each skill and knowledge testing below. To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

SAT Math Exercise Set 9: Problem-Solving and Data Analysis

Exercise I. Alisa purchased a box of 100 tea bags. She uses one tea bag for each cup of tea. If Alisa drinks 3 cups of tea every day, in how many days will the number of tea bags in the box drop below 20?

Exercise II. A store offers a 20% discount on a certain bag. During the Black Friday promotion, an additional 10% discount is applied on all products in the store. If the final price of the bag is x % of the initial price, what is the value of x?

Exercise III. 1, 3, 7, 7, 8, 5, 2, 11

What is the sum of the median and mean of the data set shown?

Exercise IV. 

The scatterplot shows the relationship between two variables, x and y. A line of best fit for the data is also shown. What is the difference between the y-coordinate of the data point with x = 4 and the y-value predicted by the line of best fit at x = 4?

Exercise V. The following table shows the number of students in each grade in a High School.

25% of the Grade 12 students attend French club. If a student is picked randomly, what is the probability of selecting a Grade 12 student not attending the French club?

Exercise VI. A random sample of 60 people from a town with a population of 18,756 were asked for their opinion on a recent government policy. If 34 people in the sample support the government policy, what is the expected number difference between the supporters and non-supporters in the town?

Note: You can use a calculator in this SAT Math Exercise

Exercise VII. A study is conducted in the state of Utah. A sample of people over 50 years old are asked how many times they visit a doctor each year. What is the largest population to which the result of the survey can be generalized?

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

SAT Math Exercises for Geometry and Trigonometry

Geometry and Trigonometry is the fourth and last content domain in SAT Math. The SAT exam will have around 5 to 7 questions from the Geometry and Trigonometry content domain. There are 4 skills and knowledge testing points in the Geometry and Trigonometry content domain:

1. 1. Area and Volume
   2. Lines, angles, and triangles
   3. Right triangles and trigonometry
   4. Circles

💡You might be interested in seeing our SAT Geometry and Trigonometry post. It covers the hack points you should know and SAT Geometry Practice Questions!

We’ve listed one SAT Math Exercise for each skill and knowledge testing below. To improve your math skills, we do not recommend using a calculator when solving these SAT Math Exercises.

SAT Math Exercise Set 10: Geometry and Trigonometry

Exercise I. One side of a rectangle and square are common. The area of the rectangle is two times the area of the square. If the perimeter of the rectangle is 10 units greater than the perimeter of the square, what is the length of the rectangle in units?

Exercise II.

In the figure, line m is parallel to line n, and line k intersects both lines. What is the value of x + y ?

Exercise III. One leg of an isosceles right triangle A is common with the shortest leg of another right triangle B. The length of the longest side of the triangle B is 17, and longer leg length is 15. What is the length of the longest side of triangle A?

Exercise IV. The graph of in the xy-plane is a circle. What is the area of the circle?

Note: You can use a calculator in this SAT Math Exercise

💡You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

The post SAT Math Exercises – FREE 50 Math Exercises – All Domains appeared first on San Francisco Business School.

Nearly two million students take the SAT every year. A good Digital SAT Math Prep is crucial to high scores on the SAT Math section. The majority of the students wobble on the SAT Math Prep. We have listed the 7 Digital SAT Math Prep ways leading to a higher SAT Math score.

📌 Hint: Do not skip this article, you will find FREE Digital SAT Math Prep resources throughout the article.

Ethan is one of our thousands of successful SAT students. He perfectly scored 1600 on the SAT, the highest SAT score a student can get! We were with thousands of students, like Ethan, in their Digital SAT Math Prep journey and that is why created this post to help many others!

💡You might be interested in reading the Digital SAT Math Ultimate Guide post.

Digital SAT Math Section

Before diving into Digital SAT Math Prep ways, you must understand the SAT Math structure, question types, and how to approach different types of questions.

The SAT exam consists of two modules, Module I and Module II. Each module consists of 22 questions, and there will be a total of 44 questions. You will have 35 minutes for each module. There are two types of questions:

1. Four-option multiple-choice questions: Around 75% of the questions will be in this format. There is only one option correct. You should find the correct option and mark it as the answer.
2. Student-Produced Response questions: Around 25% of the questions will be in this format. You should find the answer and type the answer.

👉 Take our full-length FREE SAT Practice Test, see where you stand!

A solid Digital SAT Math Prep will help you to get a higher score on SAT Math. We prepared the following table to summarize the structure of the  SAT Math sections.

The most critical aspect of the Digital SAT is being adaptive. In SAT Math Module I, you will be asked a broad mix of easy, medium, and hard questions. Then, the difficulty of the SAT Math Module II will depend on your score in the SAT Math Module I. This means that the test “adapts” to present questions that are more appropriate to a student’s performance level. The following figure depicts the Digital SAT adaptive testing model.

💡You might be interested in reading the Digital SAT Math Ultimate Guide post. We have provided further details about the SAT Math structure, examples of easy, medium, and hard questions, answers, rationales, and frequently asked questions about the SAT Math.

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

Now, let’s go through the 7 steps for a perfect Digital SAT Math Prep.

Digital SAT Math Prep – 7 Ways to Get 800 on SAT Math

After helping thousands of SAT exam students, we are confident to say that it is not impossible to get a high SAT Math score. We’ve noticed that high-scoring students went through similar SAT Math Prep paths and we’ve exposed their paths with you in this post. Are you ready for a higher SAT Math score?

Step 1. A Solid SAT Math Study Guide

The first and most important point to SAT Math success is having a solid study plan. A solid SAT Math Study Guide covers:

• Initial SAT scores from your SAT Math Practice Tests. You should score your initial scores to monitor your progress during your Digital SAT Math Prep journey.
• Target SAT Score for your dream college. Each college has a different SAT score percentile and acceptance rate. If you are aiming for a popular college and a popular department, you should score higher respectively. You can look for Colleges’ SAT Score Percentiles and Acceptance rates in our post.
• Plan Off-Weeks and Finalize Your Study Guide. On average, successful students spend around 150 hours for the SAT exam prep. You should plan your weeks and days to make sure you are ready for the exam day.

💡We’ve prepared a 7-Step Digital SAT Math Study Guide helping students to prepare their unique SAT Math Study Guide.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

Step 2. Determine Your Weak Areas

College Board assesses the students’ attainment of critical college and career readiness knowledge and skills in math in math sections of the Digital SAT.

SAT Mathematics covers four content domains.

1. Algebra. In this domain, SAT measures the ability to analyze, fluently solve, and create linear equations and inequalities and analyze and fluently solve equations and systems of equations using multiple techniques. You might be interested in seeing our SAT Algebra post. It covers the hack points you should know and 31 SAT Algebra Practice Questions!
2. Advanced Math. This domain measures skills and knowledge central for progression to more advanced math courses, including demonstrating an understanding of absolute value, quadratic, exponential, polynomial, rational, radical, and other nonlinear equations. You might be interested in seeing our SAT Advanced Math post. It covers the hack points you should know and 27 SAT Advanced Math Practice Questions!
3. Problem-solving and Data Analysis. In this domain, SAT measures the ability to apply quantitative reasoning about ratios, rates, and proportional relationships; understand and apply unit rates; and analyze and interpret one- and two-variable data. You might be interested in seeing our SAT Problem-Solving and Data Analysis post. It covers the hack points you should know and 15 SAT Problem-Solving and Data Analysis Practice Questions!
4. Geometry and Trigonometry. This fourth domain measures the ability to solve problems focusing on area and volume; angles, triangles, trigonometry; and circles. You might be interested in seeing our SAT Geometry and Trigonometry post. It covers the hack points you should know and SAT Geometry Practice Questions!

💡You can use our SAT Math Exercises which has 50 exercises on all SAT Math domains. You can identify your weak areas with the help of SAT Math Exercises.

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

SAT Math Content Domains, Skills, and Knowledge Testing Points

Under each content domain, there are several skills and knowledge testing domains with a total of 19 skill and knowledge testing points. The following table summarizes the Digital SAT Math contain domains, each skill and knowledge testing point under each content domain and approximately how many questions appear from each content domain.

Content Domains	Algebra	Advanced Math	Problem-solving and Data Analysis	Geometry and Trigonometry
Skill and Knowledge Testing Points	Linear equations in one variable	Equivalent expressions	Ratios, rates, proportional relationships, and units	Area and volume
	Linear equations in two variables	Nonlinear equations in one variable and systems of equations in two variables	Percentages	Lines, angles, and triangles
	Linear functions	Nonlinear functions	One-variable data: distributions and measures of center and spread	Right triangles and trigonometry
	Systems of two linear equations in two variables		Two-variable data: models and scatterplots	Circles
	Linear inequalities in one or two variables		Probability and conditional probability
			Inference from sample statistics and margin of error
			Evaluating statistical claims: observational studies and experiments
Number of Questions	13 to 15 questions.	13-15 Questions	5-7 Questions	5-7 Questions

Once you grasp the details of how to approach each skill and knowledge testing point question, you will double your chances of reaching an 800 score on the SAT Math test.

Make a Full-Length SAT Math Practice Test

To determine your weak areas, make a full-length SAT Math Prep Practice Test. Note down your scores in each content domain, skill, and knowledge testing point. The lowest score percentages are your weakest areas. For instance, consider the results for an SAT Math Practice test as follows.

	Algebra	Advanced Math	Problem-Solving and Data Analysis	Geometry and Trigonometry	Total
Number of Questions	15	15	7	7	44
Number of Correct Answers	13	12	5	2	32
% of Correct Answers	86.67%	80.00%	71.43%	28.57%

The weakest area of this student is Geometry and Trigonometry. Therefore, he or she should focus on studying Geometry and Trigonometry. Improving scores on this content domain will make the biggest difference to this student’s SAT scores.

💡You might be interested in seeing our Digital SAT Math Practice Test. It covers the hardest questions you may see on the SAT Math exam for each skill and knowledge testing point!

Step 3. Go Through Your Weak Areas

If your scores are typically high in the SAT Math Practice Test in the Algebra content domain, and lower in the SAT Geometry and Trigonometry content domain, studying and making more practice tests in the Algebra content domain will not improve your SAT Math scores. Getting better in your weak areas will make a difference in your SAT score.

Journeys of Two SAT Exam Prep Students

Consider two friends, Jen and Noah who are good at Algebra. They each score around 12 out of ~14 Algebra questions on a full-length SAT Math Practice test of 44 questions. Both of their Advanced Math content domain are weak and they score around 6 out of ~14 questions. During their Digital SAT Math Prep journey, they choose different paths.

Like the majority of the SAT exam prep students do, Jen focuses on the content domains she knows better, and feels better as she scores higher on these content domains. So, she studies and practices more Algebra.

On the other hand, Noah goes through his weak areas, studies more Advanced Math topics, and practices more on this topic.

On their actual SAT exam, Jen improved her Algebra scores and answered all Algebra questions correctly. So, she improved her scores by 2 more questions correctly. Noah improved his SAT Advanced Math scores while his level for Algebra remained the same. He improved his Advanced Math scores by 5 more questions correctly.

In total number of correct questions for Algebra and Advanced Math, Both Jen and Noah started with 18. Jen improved to 20 and Noah improved to 23. Most probably, Noah’s SAT Math Score will be higher than Jen’s.

List your weak content domains and skill and knowledge testing points. Do as much practice as possible to improve your results in your weak areas. Improvement in your weaker areas will bring you the highest score improvements. You can use our Digital SAT Score Calculator to calculate your scores in SAT practice tests and quizzes.

Step 4. Attend a Digital SAT Math Prep Course

There are several SAT Math Prep books, SAT Math classes, SAT tutors, and Online SAT Math Prep courses. Each student’s study habits and tactics are different. While some students prefer studying morning or during the weekend, some students prefer the evening. Many students find it hard to sit for predefined SAT Math class hours. Because, if they are not in the mood, tired, or have other priorities, they cannot postpone a class. This demotivates the majority of the SAT students.

After teaching thousands of SAT students for the exam, we can tell that most of them liked the self-paced delivery so they could study when they wanted to, not when they were forced to sit for a class. This is very important. Students must study when they feel the best time to do so. Otherwise, they will lose their concentration easily during their study.

How to Choose an Online SAT Math Prep Course

Attending an online SAT Math Prep course is the most convenient and budget-friendly option for SAT exam prep students. On average, self-paced online SAT Math prep courses start from ~$100 and go up. When choosing an online SAT Math prep course, you can consider the following points:

• Student Reviews: Check if there are any student testimonials for the SAT Math prep course. Typically, successful programs have positive student reviews.
• Curriculum: Many SAT math prep classes and courses claim they cover all content domains and skill and knowledge testing points, however, they don’t. Go through their curriculum and make sure it covers all SAT Math topics.
• Broad Mix of Questions: SAT tests the students’ Math knowledge and skills on 4 content domains and 19 skills and knowledge testing points. While testing these, the SAT categorizes each question into three difficulty levels: easy, medium, and hard. Make sure the program you are planning to attend covers all types of questions. We see many SAT Math Prep Course providers only show easy questions and that leaves students alone with the hard questions in their actual SAT exam.
• Step-by-Step Walkthrough: There are different tactics and strategies to solve each question on SAT Math. The SAT Math Prep Course must walk through the students on each question step-by-step so students will be well-prepared for the exam day.
• Free Demo: Only the bold SAT exam prep course providers offer a Free SAT Math Prep Course sample version of their course. Because they are confident with their content and they are happy to give a free demo of their comprehensive content. You can check the free demo of the course provider and make sure their style fits you.
• Money-back Guarantee: Some providers do not offer a money-back guarantee. Make sure the provider offers a refund if you are not satisfied with their content.

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

What is the Best SAT Math Prep Course For Me?

This is a hard question to answer. While the majority of our students love our self-paced delivery method, some students prefer studying through a book, online classes, or tutor-guided SAT math prep. The Best SAT Math Prep Course for you all depends on your preferences and budget.

SAT Math Prep Books cost around $50 on average. However, they are not interactive. Many do not provide step-by-step rationale for each question and even if they provide, in case you will have questions, there is no place to ask your questions. You can see our Digital SAT Math Prep Book.

SAT Math prep classes cost around $1,200 on average and typically for around 16 hours. However, you have to force yourself to go for an in-person class and typically these courses are grueling as you need to attend after school or during the weekend. Many students find it ineffective.

Online SAT Math Prep classes cost around $700 on average. While you can attend these classes from your home, you will be forced to sit for a class for a determined time. In many cases, if you miss a class, you will not have an option to make up.

While tutor-guided SAT Math prep is exclusive and in many cases, one-on-one, the average cost for SAT tutoring is $70 per hour. However, depending on the region, it may be as much as $150 per hour or even higher. This leaves out as an option for the majority of the students as it will cost a significant amount of money.

Self-paced Online SAT Math Prep Courses cost around $100. You can study whenever you would like to study and you can revisit any lecture as many times as you wish. Therefore, self-paced online SAT Math Prep courses provide great flexibility to students. Besides, they are at a fraction of other course options.

Our Recommendation for the Best SAT Math Prep Course

Considering all these, here is our method for the best SAT Math Prep:

1. Find a Self-Paced Online SAT Math Prep Course. This will be budget-friendly, easy to attend, and flexible. Complete the course.
2. Practice with a good SAT Math Prep Book. Practicing as many questions as possible is key to the SAT exam success.
3. In case you still feel weak in particular topics, find a tutor for those particular topics only. This will limit the amount of money you will spend on SAT Math tutors.

📚 San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

Step 5. Note Down and Revisit Your Wrong Answers

Going through your wrong answers will improve your skills in your weak areas the most. Because, you will remember the mistakes you make, and in case you see a similar question next time, you will decrease your chances of making the same mistake again.

When you are practicing SAT Math Prep questions, mark your wrong answers. Once you finish the book, quiz, or SAT practice test go back and review your wrong answers one more time. Take notes on why you make those mistakes and go through the notes frequently.

Step 6. Take Notes During Your SAT Math Prep

There are several SAT Math Prep cheat sheets, formulas, or guides. However, none of them will be as good as you will prepare for yourself.

When studying for the SAT Math, take notes for important points. Go through your notes every week or at least a month. Going through your notes will keep your memory fresh around those topics.

Some students take notes in their notebooks, and some write on sticky notes and paste them on the walls in their rooms. Choose your own way, and you will know the best one for you.

🗎 Download the 15-page Digital SAT Math Formula Sheet.

Step 7. Go and Crack the SAT Exam

You spent hours on your SAT exam and practiced thousands of SAT Math Prep questions. You are ready for the big day!

Try not to study hard on your exam week. You can go through your notes, practice a few questions, or maybe go over your wrong answers. Make sure you will have a good sleep before the exam day and relax. If you practice enough, the questions will be similar to the ones you practiced several times before.

We recommend using your own laptop which you use regularly for the SAT Exam. While the College Board allows school-owned devices or they can provide a device for the exam day, using a new device may cost you additional time as you will need time to get used to a new keyboard, screen, etc. Therefore, we recommend using your own laptop for the exam. Make sure you bring your device fully charged on the exam as there may not be enough power outlets in your testing room.

The post Digital SAT Math Prep – 7 Steps to Get 800 on SAT Math appeared first on San Francisco Business School.

Every year, nearly two million students take SAT tests in the US and worldwide. After teaching thousands of students, we’ve seen that there are certain steps for a successful SAT Math score. We’ve outlined 7 steps in this SAT Math Study Guide that will bring you a higher SAT Math score.

📌 Hint: Do not skip this article, you will find FREE Digital SAT Math Prep resources throughout the article.

What is the SAT Math Study Guide?

SAT score is one of the most important factors that will get you into your dream college. SAT consists of two parts: Reading and Writing and Math. When it comes to math, several students struggle to score a higher score although it is not hard as long as you have a solid SAT Math Study Guide. Several SAT Math prep students ask “Is there a proven SAT Math Study Guide?”, “What is a good SAT Math Study Plan?”, “What are the steps of an SAT Math Study Guide”.

After teaching thousands of SAT exam prep students, we’ve seen that there is no fixed SAT Math Study Guide that fits all. Some blogs, websites, or tutors have bold claims that “if you follow this SAT Math Study Guide, you will increase your math scores.” You should be careful of these kinds of bold claims as a study guide that fits many may not be a good one for you.

💡You might be interested in reading the Digital SAT Math Ultimate Guide post!

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

We will teach you to create your own, unique and tailored for you SAT Math Study Guide in this post.

7-Step SAT Math Study Guide

Our SAT Math Study Guide includes 7 major steps. We will go over each step one by one.

Step #1 – Determine the Target Date for Sitting SAT Exam

The first step of the SAT Math Study Guide is determining the target SAT test date you will take the SAT exam. This is crucial because you have to plan your preparation time accordingly. The average preparation duration of our SAT exam prep students is ~150 hours. Note that this is an average value, we have students who studied much more than 150 hours as well as less than 150 hours.

However, you can take this ~150 hours of preparation time as a ballpark range. The next step is planning how many hours you can study each week until the exam date. Let’s say it is the 1st of September, and you are planning to sit for the SAT exam on December 7th. There are 13 weeks until the exam. Therefore, you have to study around 12 hours each week for a good SAT score.

There might be unexpected things during your preparation such as sickness, activities in school, etc. Therefore, it is better to plan around 2 weeks for these in your SAT Math Study Guide.

👉 Take our full-length FREE SAT Practice Test, see where you stand!

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

Step #2 – Set a Target Score

Before you start your SAT exam preparation, take a SAT practice test to see your results. The administrator of the SAT, The College Board, offers several full-length SAT Practice Tests. These tests are calibrated correctly and the distribution and difficulty of the questions are consistent as you will experience in your actual SAT exam.

Then, take a look at the colleges’ SAT score percentiles you are planning to apply for. We’ve given some of the colleges’s SAT score percentiles below. You can look for other Colleges’ SAT Score Percentiles and Acceptance rates in our post.

For instance, if you are planning to apply to Boston College, you should be scoring around 1330 and 1500. Note that, that is the average of all college applications. If you are planning to apply for a popular department of a college, you need to score more than these averages. For instance,  Economics, Finance, and Computer Science are popular departments at Boston College. Therefore, the score percentiles of the accepted students in these departments are expected to be above the 1330 – 1500 range.

Depending on your initial result, if there is a huge gap from the target score, you should be studying harder. You can use our Digital SAT Score Calculator to calculate your scores in practice tests and quizzes.

7-Step SAT Study Guide – YouTube Video

You can view our 7-Step SAT Study Guide on YouTube.

Step #3 Take Notes During Your SAT Math Study

There will be lots of concepts, SAT Math formulas, tips, and tricks throughout your SAT exam preparation. Note that, some concepts and formulas are frequently occurring on the SAT exam. Therefore, it is crucial to take notes during your SAT Math study.

Especially, take notes where you found valuable information or a shortcut to a solution. These notes will be very useful, especially in the second half of your SAT exam preparation. As you progress in your SAT exam preparation, you may forget some of the topics you studied earlier. With the help of the notes you will be taking, you can memorize important points easily.

📚 San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

Step #4 Make Practice as Much as Possible

The biggest tip we can give you for a higher SAT score is to do as much practice as you can. Actually, this is not a tip only for the SAT exam, for any kind of exam, practicing with as many practice questions as possible is the key to success.

👉 Take our full-length FREE SAT Practice Test, see where you stand!

Most of the SAT exam prep students look for Free SAT Math Practice tests on the web. However, most of these exams might be outdated, giving wrong answers or rationales. Moreover, the difficulty and the skills and knowledge point distribution of the questions may not resemble the actual SAT exam. Free SAT exam prep materials not only lack the comprehensive SAT exam prep content but also guide you inappropriately during your SAT exam study. Therefore, be careful if you will use free SAT exam prep materials during your SAT exam study.

💡You can see our Free SAT Math Exercises which has 50 exercises on all SAT Math domains. 

Digital SAT Prep Online Course Program

San Francisco Business School offers a comprehensive Digital SAT Prep Online Course taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain, skills, and knowledge testing point through 1,000+ realistic Digital SAT Exam questions. You will see all the different types of questions that may appear in Digital SAT.

Step #5 Go Through Your Wrong Answers

The fifth step of the SAT Math Study Guide is going through the wrong answers that you selected during your SAT exam prep. Your wrong answers show your weaknesses. If you are making lots of mistakes for a particular content domain or skill and knowledge point, go through that particular area to improve your knowledge. The more practice you make on your weak areas, the better you will start to score.

Many students make the mistake of over-practicing questions from the areas they know better. For instance, if a student is good at SAT Algebra, but not in Geometry, he should be going through SAT Geometry over and over to improve his results. That improvement will make a significant increase in his score rather than practicing more Algebra questions.

Free Digital SAT Prep Course

SFBS offers a Free Digital SAT Prep Online Course. The course goes through particular skills and knowledge testing points and improves your problem-solving skills and test-taking strategies.

Step #6 Go Through Your Notes Frequently

The best way to keep your mind ready for the SAT exam is by going over your notes frequently. SAT exam preparation is a long journey, and the contents you completed earlier might be harder to remember when you come to further content domains. Therefore, the best way to memorize what you will learn throughout the SAT exam study is to go over your notes frequently. For instance, you can spend 15-20 minutes each week going over your notes from previous sections.

🗎 Download the 15-page Digital SAT Math Formula Sheet.

Step #7 Go and Crack the SAT Exam!

You have gone through all SAT exam topics, completed all quizzes, and scored around your target scores on quizzes and SAT practice exams.

You are ready for the Big Day! If you have still time for the SAT exam, spend your last days going over your notes. Get a good sleep before the day of the SAT exam, and stay calm during the SAT exam.

Frequently Asked Questions About SAT Math Study Guide

After helping thousands of SAT exam students, we’ve listed below the most frequently asked questions about the SAT Math Study Guide.

Is there any solid SAT Math Study Guide that will work for me?

No, there is not a solid, recipe-like SAT Math study guide that will work for all SAT exam students. However, there are important points that you must consider during your SAT exam study. We have outlined these steps in this post for you to create your own SAT exam study plan.

What is the 30-Day SAT Math Study Guide?

Most SAT exam students want to improve their SAT scores as quickly as possible. That is why you will see several SAT exam prep training providers, blogs, or platforms market “30-day SAT Math Study Guide”, “60-day SAT Math Study Guide” or “90-day SAT Math Study Guide”. However, SAT exam success requires rigorous SAT exam preparation.

Remember that average SAT exam preparation takes around 150 hours of study. To get ready for the SAT exam, you must spare around 5 hours each day if you have a 30-day SAT Exam Study Plan. We do not say this is impossible however it requires big dedication, a strong background, and sufficient time to study for the SAT exam.

If you consider the duration, time, and steps we outlined above, you can scale your SAT exam study into 30 days, 60 days, or 90 days. Respectively, you will have a “30-day study plan”, “60-day study plan” or “90-day study plan”.

The post SAT Math Study Guide – 7 Steps to SAT Math Success appeared first on San Francisco Business School.