## About the Math Section:

Inside the SAT Math section Description from the College Board including quick facts, sample questions, and video.

- SAT questions = 80 min. timed test of 58 multiple choice questions.
- No calculator: 25 min, 20 questions: 15 multiple choice, 5 grid-in questions.
- Calculator: 44 min., 38 questions: 30 multiple choice, 8 grid-in questions.

- Heart of Algebra section, focuses on linear equations and inequalities.
- Problem Solving and Data Analysis, focuses on quantitative reasoning, the interpretation and synthesis of data, and solving problems in rich and varied contexts.
- Passport to Advanced Math section, focuses on advanced mathematics, such as understanding the structure of expressions, reasoning with more complex equations, and interpreting and building functions.

## Sites for Practice:

- Khan Academy SAT math practice & tutorials.
- Desmos Covers tables, regressions, statistics, and includes an online graphing calculator. Plot any equation, from lines and parabolas up through derivatives and Fourier series. Data tables allow for curve-fitting and modeling; sliders demonstrate function transformations.
- Geogebra Helps with procedures and definitions.

## Skills Tested:

**Number and operations**: Operations, ratio and proportion, complex numbers, counting, elementary number theory, matrices, sequences, series, vectors**Algebra and functions**: Expressions, equations, inequalities, representation and modeling, properties of functions (linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric, periodic, piecewise, recursive, parametric)**Geometry and measurement**:- Coordinate: Lines, parabolas, circles, ellipses, hyperbolas, symmetry, transformations, polar coordinates
- Three-dimensional: Solids, surface area and volume (cylinders, cones, pyramids, spheres, prisms), coordinates in three dimensions
- Trigonometry: Right triangles, identities, radian measure, law of cosines, law of sines, equations, double angle formulas

**Data analysis, statistics and probability**: Mean, median, mode, range, interquartile range, standard deviation, graphs and plots, least-squares regression (linear, quadratic, exponential), probability

## Test-Taking Tips:

- Write in your test booklet.
- Re-read the question – if it asks for 5x, don’t give the value for x.
- Look for patterns. Always pay special attention to simple patterns or repetitions in a problem, because exploiting them is usually the key to the solution.
- Find key words. Pay attention to words like integer, even, odd, and consecutive when they show up. And make sure you don’t confuse area with perimeter.
- If you’re stuck, try working backwards from the choices, or plug in numbers for the unknowns.
- Keep it simple. If you’re doing lots of calculations, you might be overlooking a key fact that simplifies the problem. Always look for the easy way.
- Don’t overuse a calculator. If you’re doing a lot of calculator work for a problem, you’re probably making it too hard.
- Know basic formulas so you can easily recognize when to use them. Many formulas are given to you in the “reference information” at the beginning of each Math Test section.
- Use flash cards to review key formulas from algebra, geometry, trigonometry, and statistics.
- Check your work. There are many ways to make careless mistakes, so give yourself time to go back and check over your work.

## Sample Question: Heart of Algebra

**Heart of Algebra (with calculator):**

When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface?

A) p = 0.44d + 0.77

B) p = 0.44d + 14.74

C) p = 2.2d – 1.1

D) p = 2.2d – 9.9

**Answer and Explanation**:

Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives [fraction numerator 20.9 −18.7 over denominator 14 − 9 end fraction] equals [fraction numerator 2.2 over denominator 5 end fraction] comma or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation 18.7 = 0.44 ( 9 ) + b gives b = 14.74. Therefore, the model that can be used to relate the pressure and the depth is p = 0.44 d + 14.74.

## Sample Question: **Problem-Solving and Data Analysis**

A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day?

A) 3

B) 10

C) 56

D) 144

A) 3

B) 10

C) 56

D) 144

**Answer and Explanation:**## Sample Question: Passport to Advanced Math

The function f is defined by f (x) = 2x³ + 3x² + cx + 8, where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the three points (−4, 0), (1/2, 0 ), and

( p, 0). What is the value of c?

A) –18

B) –2

C) 2

D) 10

Choice A is correct. The given zeros can be used to set up an equation to solve for c. Substituting –4 for x and 0 for y yields –4c = 72, or c = –18.

Alternatively, since –4, 1/2, and p are zeros of the polynomial function

f (x) = 2x³ + 3x² + cx + 8, it follows that f (x) = (2x − 1)(x + 4)(x − p).

Were this polynomial multiplied out, the constant term would be

(−1)(4)(− p) = 4 p. (We can see this without performing the full expansion.)

Since it is given that this value is 8, it goes that 4p = 8 or rather, p = 2. Substituting 2 for p in the polynomial function yields

f (x) = (2x − 1)(x + 4)(x − 2),

and after multiplying the factors one finds that the coefficient of the x term, or the value of c, is –18.

( p, 0). What is the value of c?

A) –18

B) –2

C) 2

D) 10

**Answer and Explanation:**Choice A is correct. The given zeros can be used to set up an equation to solve for c. Substituting –4 for x and 0 for y yields –4c = 72, or c = –18.

Alternatively, since –4, 1/2, and p are zeros of the polynomial function

f (x) = 2x³ + 3x² + cx + 8, it follows that f (x) = (2x − 1)(x + 4)(x − p).

Were this polynomial multiplied out, the constant term would be

(−1)(4)(− p) = 4 p. (We can see this without performing the full expansion.)

Since it is given that this value is 8, it goes that 4p = 8 or rather, p = 2. Substituting 2 for p in the polynomial function yields

f (x) = (2x − 1)(x + 4)(x − 2),

and after multiplying the factors one finds that the coefficient of the x term, or the value of c, is –18.