# SAT Math

Introduction to SAT Math

The Math section of the SAT is designed to assess your ability to reason and think about high school level mathematical problems. Your SAT Math score is based on your performance on 3 timed math sections:

• one 25-minute section with 20 multiple choice questions
• one 25-minute section with 8 multiple choice, and 10 grid-in questions
• one 20-minute section with 16 multiple choice questions

Multiple choice questions require you to select the correct answers from among five answer choices, and the ‘grid in’ questions require you to calculate the correct answer and enter it into the answer sheet.

Breakdown of the Math Topics Covered on the SAT with Sample Questions

Each SAT Math section includes questions drawn from four main topic areas, which are discussed below:

• Number and Operations
• Algebra and Functions
• Geometry and Measurement
• Data Analysis, Statistics, and Probability

1. Number and Operations Concepts

Mathematical concepts you need to know for these types of questions include:

• Basic properties of numbers and their terminology (e.g. negative numbers, prime numbers, factors, integers, sets, sequences)
• Squares, square roots, and exponents
• Order of Operations
• Fractions and decimals
• Percents
• Ratios and Proportions
• Averages
• Arithmetic Word Problems

Number and Operations Sample Questions

Here are some examples of sample questions from this topic area that you might see in SAT Math sections:

1. If the average of 45,70, 80, and a number x is 55, what is the value of x?

A) 15
B) 20
C) 25
D) 95
E) 220

2. If 25% of x is 80, what is 10% of x?

A) 10
B) 12
C) 30
D) 32
E) 35

3. The ratio of 1.4 to 2 is equal to which of the following ratios?

A) 7:10
B) 10:7
C) 14:2
D) 14:0.2
E) 3:5

2. Algebra and Functions Concepts

To answer SAT Math questions on Algebra and Functions you need to be familiar with the following topics and skills:

• Simplifying algebraic expressions
• Operations on Algebraic expressions (including factoring of quadratic equations)
• Equations and inequalities involving roots, exponents, and absolute values
• Solving systems of equations and inequalities
• Direct and inverse variation
• Algebraic word problems
• Functions (their domain, range, translations of graphs, functions using special symbols)
• Equations of lines (slope, intercept)

Algebra and Functions Sample Questions

Algebra and function questions that are representative of what you might see on SAT Math sections are below:

1. If x and y are inversely proportional and x = 10 when y = 5, what is y when x is 30?

A) 1/15
B) 5/3
C) 10/3
D) 4
E) 7

2. If 22x = 83x-1, what is the value of x?

A) 0
B) 3/7
C) 3/8
D) 7/3
E) it cannot be determined from the information given

3. If x•y = 2x - 3y, and 1•2 = 2•z, what is the value of z?

A) -8/3
B) 0
C) 2 2/3
D) 3 2/3
E) 8

3. Geometry and Measurement Concepts

SAT Math questions in this topic area will require you to know about:
• The properties of parallel and perpendicular lines
• Coordinate Geometry (slopes, distance between points, midpoints of lines)
• Triangles (area, angles, properties of equilateral, isosceles, right and special triangles, the congruency and similarity of triangles, Pythagorean theorem)
• Quadrilaterals and other polygons (including area, interior and exterior angles, perimeters)
• Circles (area, circumference)
• Solid geometry (volume and surface area of solids)
• Transformations (translations, rotations, reflections)

Geometry and Measurement Sample Questions

Below are sample questions on Geometry and Measurement that you might see in SAT Math sections:

1. A triangle has two angles that are equal. If the length of two of the sides of the triangle are 40 and 20, what is the least possible value for the perimeter of the triangle?

A) 60
B) 70
C) 80
D) 100
E) 120

2. Three line segments meet at a point to form three angles. One angle is equal to 2x?, the second angle is equal to 3x?, the fourth is equal to 4x?. What is the value of x?

A) 35
B) 40
C) 50
D) 55
E) 65

3. In the xy-coordinate place, the distance between A(7,14) and B(x,2) is 13. What is one possible value of x?

A) 0
B) 3
C) 4
D) 10
E) 12

4. Data Analysis, Statistics, and Probability Concepts

The topics you need to know to master questions on this section are:

• Data interpretation (reading tables and line, bar, and other graphs)
• Descriptive statistics (mean, median, mode, weighted average)
• Probability (of one event or two or more independent or dependent events)
• Geometric Probability (probably that a random point chosen will fall within a particular geometric figure)

Data Analysis, Statistics, and Probability Sample Questions

Below are example SAT Math questions on this topic area:

1. In the following figure, the circle has a radius of 9 and the small square has sides of length 4. If a point is chosen at random from the large circle, what is the probability that the point chosen will fall in the small circle?

A) .225
B) 4/9pi
C) 1/2pi
D) pi
E) 81/36pi

2. According to the graph above, between what two consecutive months was there the greatest change in auto sales

A) Jan-Feb
B) Feb-March
C) March-April
D) April-May
E) May-June

3. The complete cycle of a fly’s life is 80 days. It spends 10 days as an egg, 40 days in larval form, and lives as a mature adult for 30 days. At a randomly chosen time, what is the probability that a given fly will NOT be in its adult form?

A) .375
B) .4
C) 0.5
D) 0.625
E) 0.675

Study Strategies for SAT Math

1. Get familiar with the SAT Math section instructions

Make sure you know how to correctly enter answers into the answer sheet for the grid-in questions. Don’t waste time on test day figuring out how to enter fractions and decimals into the grid, know this stuff in advance. Also be aware of the formulas that are available at the beginning of the test (e.g. the formula for the volume of a cylinder or circumference of a circle), although you are never required to memorize these formulas, your work will go much quicker during the test if you do not have to refer to this information, so take the time to memorize it now. It will always be there if you need to refer to it on the test, but try not to rely on it.

2. Practice taking timed math sections

One of the things that makes the SAT Math section challenging is the time limit. The College Board offers an SAT preparation book with real practice tests designed by the test-maker and these are the best bet for getting an idea of the pace you need to be going at to get to every question. Remember that more difficult questions are not worth more points, so if a question seems difficult on first reading, skip it, move on to easier questions, and come back to try and make an educated guess if you have time left over.

When taking practice tests, make sure to go through your answers carefully and note what questions you got wrong and why. Keep track of what types of questions you are missing consistently (e.g. algebra, geometry, etc.) and then do a focused review of material in that area, using the practice drills found in SAT prep books.

4. Try questions from many different sources

Although the practice tests from the College Board are going to be the most representative of what real SAT questions will look like, if you try the math exercises from many different SAT prep books you will build up your general skill level and be more prepared for new question types you haven’t seen before.