How to Master the SAT Math Section

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To master the SAT Math section (70 minutes, 44 questions), focus on consistent, timed practice using Onlinemath4all's SAT Math Resources to build speed. Key strategies include mastering the Desmos calculator, analyzing every mistake to identify content gaps, and focusing on high-weight topics like algebra and data analysis. The following 20 questions will cover the primary areas of SAT Math and help you to improve your score.

Question 1 :

The curve y= a^x – b passes through points (c, 8) and (2c, 350). Find the value of b.

Answer :

Question 2 :

The function p is defined by

p(x) = a((x + 7)² – b)((x + 7)² – c),

where a, b and c are constants. In the xy-plane, the graph of y = p(x) passes through the points (–12, 45) and (0, 256). What is the value of p(–2) + p(–14)?

Answer :

Question 3 :

In the xy-plane above, O is the center of the circle and the measure of ∠POQ is kπ. What is the value of k?

A) 2/3

B) 3/2

C) 1/2

D) 5/2

Answer :

Question 4 :

Which expression is equivalent to 16x⁴ – 81?

A) (4x² + 9)²

B) (2x + 3)²(2x – 3)²

C) (4x² + 27)(4x² – 3)

D) (4x² + 9)(2x + 3)(2x – 3)

Answer :

Question 5 :

Two numbers, p and q, are each greater than zero, and the square of p is equal to the cube root of q. For what value of x is p^{1
– x} equal to the square root of q?

Answer :

Question 6 :

The given equation relates the positive real numbers x, y and z. Which equation correctly expresses x in terms y and z?

A) x = z² – y² + 2zy – 3

B) x = y² – z² + 2yz – 3

C) x = y² + z² + 2yz – 3

D) x = z² + y² – 2zy – 3

Answer :

Question 7 :

In circle P, the two chords intersect at point X, with the lengths as indicated in the figure. Which could NOT be the sum of lengths a and b, if a and b are integers?

A) 49

B) 30

C) 26

D) 16

Answer :

Question 8 :

The expression (x + 10)(x + b) and x² + 3bx + c, where b and c are constants, are equivalent. What is the value of c?

Answer :

Question 9 :

Functions f and g are defined by f(x – 1) = 6x and g(x) = x + 3. What is the value of f(g(2))?

Answer :

Question 10 :

Line m passes through the points (k, 7) and (3, k – 4) in the xy-plane. If the slope of line m is 3, what is the value of k?

Answer :

Question 11 :

In the figure below, O is the center of the circle and RT is tangent to the circle at X. If triangle RST is equilateral, what is the value of RT/YZ?

Answer :

Question 12 :

In triangle XYZ, the measure of angle X is x°, the measure of angle Y is y°, and the measure of angle Z is 31°. If x > y > 31, which of the following additional pieces of information is NOT sufficient to determine the values of x and y?

A) The value of 31 – x – 3y

B) The value of 31 + 3x + y

C) The value of 31 – 3x + 3y

D) The value of 31 – 3x – 3y

Answer :

Question 13 :

Let the function p defined as

where c is a constant. If p(c) = 0, what is the value of p(12)?

Answer :

Question 14 :

The quadratic function g models the depth, in meters, below the surface of the water of a seal t minutes after the sealentered the water during a dive. The function estimates that the seal reached its maximum depth of 302.4 meters 6 minutes after it entered the water and then reached the surface of the water 12 minutes after it entered the water. Based on the function, what was the estimated depth, to the nearest meter, of the seal 10 minutes after it entered the water?

Answer :

Question 15 :

h(x) = x³ + ax² + bx + c

The function h is defined above, where a, b and c are integer constants. If the zeros of the function are –5, 6 and 7, what is the value of c?

Answer :

Question 16 :

For the exponential function f, the value of f(1) is k, where k is a constant. Which of the following equivalent forms of the function f shows the value of k as the coefficient or the base?

A) f(x) = 50(1.6)^x^{+ 1}

B) f(x) = 80(1.6)^x

C) f(x) = 128(1.6)^x^{– 1}

D) f(x) = 204.8(1.6)^x^{– 2}

Answer :

Question 17 :

The regular price of a shirt at a store is $11.70. The sale price of the shirt is 80% less than the regular price, and the sale price is 30% greater than the store's cost for the shirt. What was the store’s cost, in dollars, for the shirt?

Answer :

Question 18 :

The functions f and g are defined by the given equations, where x ≥ 0. Which one of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where x ≥ 0?

I. f(x) = 33(0.4)^x^{+ 3}

II. g(x) = 33(0.16)(0.4)^x^{– 2}

A) I only

B) II only

C) I and II

D) Neither I nor II

Answer :

Question 19 :

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface.The model indicates the object has an initial height of 10 feet above the ground and reaches its maximum height of 1,034 feet above the ground 8 seconds after being launched. Based on the model, what is the height, in feet, of the object above the ground 10 seconds after being launched?

A) 234

B) 778

C) 970

D) 1,014

Answer :

Question 20 :

The area of a rectangular banner is 2,661 square inches. The banner's length x, in inches, is 24 inches longer than its width, in inches. Which equation represents this situation?

A) 0 = x² - 24x - 2,661

B) 0 = x² - 24x + 2,661

C) 0 = x² + 24x - 2,661

D) 0 = x² + 24x + 2,661

Answer :