Math · Module 1 · Question 1 of 22
What is the value of x if 9x − 8 = 46?
Answer: A / 6 Add 8 to get 9x
Linear equations / Foundation Review: Example 1.01.
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Additional Math Test 2
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Additional Math Test 2
Math · Module 1 · Question 2 of 22
Which expression is equivalent to (x − 7)(x + 7)?
Answer: D / x2 − 49 This is a difference of squares: the cross terms cancel, leaving x2 − 72
Equivalent expressions / Foundation Review: Example 1.05.
Math · Module 1 · Question 3 of 22
A runner travels 7.5 kilometers in 0.5 hour at a constant speed. What is the speed in kilometers per hour?
Answer: D / 15 Divide distance by time: 7.5/0.5
Rates / Foundation Review: Example 2.13.
Math · Module 1 · Question 4 of 22
A triangle has two equal angles of 48°. What is the third angle?
Answer: D / 84° The angle sum is 180°. Subtract both equal angles: 180 − 2(48)
Triangle angles / Foundation Review: Geometry reference.
Math · Module 1 · Question 5 of 22
The equation of a line is y = x − 6. What is its y-intercept?
Answer: A / −6 At x
Lines / Foundation Review: Example 1.02.
Math · Module 1 · Question 6 of 22
What is the smaller solution to x2 − 9x + 18 = 0?
Answer: C / 3 Factor as (x − 3)(x − 6)
Quadratics / Foundation Review: Example 6.04.
Math · Module 1 · Question 7 of 22
The model V(t) = 360 − 15t gives liters of water remaining after t minutes. What does 15 represent?
Answer: B / The decrease in water volume, in liters per minute. The coefficient of time is −15, so the tank loses 15 liters each minute. The constant 360 is the initial volume.
Linear models / Foundation Review: Example 2.09.
Math · Module 1 · Question 8 of 22
The ordered data are 3, 5, 5, 8, 11, 16. What is the median?
Answer: B / 6.5 With six values, average the third and fourth: (5 + 8)/2
Median / Standard Review: Data reference.
Math · Module 1 · Question 9 of 22
If 3x + y = 20 and x + y = 10, what is x?
Answer: C / 5 Subtract the second equation from the first: 2x
Linear systems / Standard Review: Example 3.01.
Math · Module 1 · Question 10 of 22
What is the value of 1252/3?
Answer: B / 25 Take the cube root to obtain 5, then square: 52
Rational exponents / Standard Review: Example 1.06.
Math · Module 1 · Question 11 of 22
A right triangle has legs 7 and 24. What is its hypotenuse?
Answer: D / 25 c2 = 72 + 242 = 49 + 576 = 625. The positive length is c
Right triangles / Standard Review: Example 6.03.
Math · Module 1 · Question 12 of 22
What is the least integer n such that 6n − 5 ≥ 52?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 10 The inequality gives 6n ≥ 57 and n ≥ 9.5. The smallest integer is 10. At 9 the left side is 49, below 52.
Integer inequalities / Standard Review: Example 3.07.
Math · Module 1 · Question 13 of 22
The population model is P(t) = 900(1.04)t. Which statement is correct?
Answer: A / The population increases by 4% for each increase of 1 in t. The multiplier 1.04 means retaining 100% and adding 4% each interval. The coefficient 900 is the starting population.
Exponential models / Standard Review: Example 1.09.
Math · Module 1 · Question 14 of 22
A jar contains 8 red, 5 blue, and 7 white beads. One bead is selected at random. What is the probability that it is not blue?
Answer: D / 3/4 There are 20 beads, of which 8 + 7
Probability / Standard Review: Example 6.14.
Math · Module 1 · Question 15 of 22
A line passes through (2, −1) and (8, 8). What is its slope?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 3/2 The output change is 9 and the input change is 6. Thus m = 9/6 = 3/2.
Slope / Standard Review: Example 6.01.
Math · Module 1 · Question 16 of 22
What is the maximum value of f(x) = −3(x + 1)2 + 12?
Answer: A / 12 The squared term multiplied by −3 is nonpositive, so the greatest output is 12, reached at x
Quadratic features / Standard Review: Example 6.06.
Math · Module 1 · Question 17 of 22
A cylinder has radius 5 and height 7. Its volume is kπ. What is k?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 175 The volume is πr2 h = π(25)(7) = 175π. Therefore k
Volume / Standard Review: Example 6.11.
Math · Module 1 · Question 18 of 22
For which value of a does a(x − 3) = 4x − 12 hold for every real x?
Answer: C / 4 Matching the x coefficients gives a
Identities / Standard Review: Example 1.03.
Math · Module 1 · Question 19 of 22
What is the solution to = x?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 4 Require x ≥ 0. Squaring gives x2 − x − 12 = (x − 4)(x + 3) = 0. Reject −3 and check
Radical equations / Standard Review: Example 1.08.
Math · Module 1 · Question 20 of 22
A random sample of 400 shoppers contains 118 who prefer paper bags. What is the best estimate of the number preferring paper bags among 12,000 comparable shoppers?
Answer: A / 3540 The sample fraction is 118/400
Population inference / Standard Review: Example 2.15.
Math · Module 1 · Question 21 of 22
For f(x) = mx + b, f(4) = 17 and f(9) = 32. What is f(0)?
Answer: A / 5 The slope is (32 − 17)/(9 − 4)
Linear functions / Standard Review: Example 5.02.
Math · Module 1 · Question 22 of 22
For what value of c is the line y = 8x + c tangent to y = x2 + 2x + 10?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 1 Equating outputs gives x2 − 6x + 10 − c
Tangency / Challenge Review: Example 2.14.
Math · Module 2 · Question 1 of 22
For x ≠ 0, which expression is equivalent to ?
Answer: B / x4 For the same nonzero base, subtract exponents: x7−3
Exponent laws / Foundation Review: Example 6.07.
Math · Module 2 · Question 2 of 22
What is the solution to 5 − 2x = 17?
Answer: B / −6 Subtract 5 to get −2x
Linear equations / Foundation Review: Example 3.02.
Math · Module 2 · Question 3 of 22
A 45°–45°–90° triangle has one leg of length 11. What is its hypotenuse?
Answer: C / 11 The equal legs have length 11. The special-triangle relationship gives hypotenuse 11.
Special right triangles / Foundation Review: Example 3.03.
Math · Module 2 · Question 4 of 22
The box plot summarizes a data set. What is its interquartile range?
Answer: C / 6 The left and right box edges are Q1
Data displays / Standard Review: Data reference.
Math · Module 2 · Question 5 of 22
Which expression reveals the zeros of x2 + 2x − 15?
Answer: B / (x + 5)(x − 3) The numbers 5 and −3 multiply to −15 and add to 2. The factored form is (x + 5)(x − 3), revealing zeros −5 and 3.
Factoring / Standard Review: Example 1.05.
Math · Module 2 · Question 6 of 22
A linear function satisfies f(0) = −7 and f(6) = 11. What is f (10)?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 23 The slope is (11 − (−7))/6
Linear functions / Standard Review: Example 2.01.
Math · Module 2 · Question 7 of 22
Which point satisfies 2x + 3y ≤ 12 and y > 1?
Answer: C / (0, 4) At (0, 4), the first left side is 12 and the second condition is 4 > 1. Each other choice either makes the first total too large or has y
Inequalities / Standard Review: Algebra reference.
Math · Module 2 · Question 8 of 22
A positive exponential function has f(0) = 6 and f(3) = 162. What is f(4)?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 486 The 3-unit factor is 162/6
Exponential functions / Standard Review: Example 2.05.
Math · Module 2 · Question 9 of 22
Similar triangles have areas 27 and 75. The smaller triangle has perimeter 18. What is the larger triangle's perimeter?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 30 The area factor is 75/27
Similarity / Standard Review: Example 1.14.
Math · Module 2 · Question 10 of 22
A model for data is = 3x + 5. At x = 4, the observed value is 20. If residual is observed minus predicted, what is the residual?
Answer: C / 3 The predicted value is 3(4) + 5
Models and residuals / Standard Review: Example 2.09.
Math · Module 2 · Question 11 of 22
If |x + 2| = 7, what is the smaller solution?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: −9 The cases are x + 2
Absolute-value equations / Standard Review: Advanced Math reference.
Math · Module 2 · Question 12 of 22
For what value of k does the system 2x − 5y = 8, 6x + ky = 25 have no solution?
Answer: A / −15 The x coefficient in the second equation is 3 times the first. Parallel lines therefore require k = 3(−5) = −15. The right side would be 24 for the same line, but is 25, so the lines are distinct.
Solution counts / Standard Review: Example 1.03.
Math · Module 2 · Question 13 of 22
For x ≠ −3, the equation = 8 holds. What is x?
Answer: B / 11 Factor and cancel to obtain x − 3
Rational equations / Standard Review: Example 1.05.
Math · Module 2 · Question 14 of 22
What is the radius of the circle x2 + y2 − 2x + 12y = 12?
Answer: B / 7 Complete squares: (x − 1)2 + (y + 6)2 = 12 + 1 + 36 = 49. The radius is
Circle equations / Standard Review: Example 1.15.
Math · Module 2 · Question 15 of 22
A store sells small boxes for $6 and large boxes for $11. A customer buys 17 boxes for $142. How many large boxes are purchased?
Answer: C / 8 If l is large boxes, then 6(17 − l) + 11l
Systems in context / Standard Review: Example 2.04.
Math · Module 2 · Question 16 of 22
The roots of 5x2 − 20x + 6 = 0 are r and s. What is 1/r + 1/s?
Answer: D / 10/3 The root sum is 4 and the product is 6/5, which is nonzero. Thus the reciprocal sum is 4/(6/5)
Root relationships / Challenge Review: Example 6.15.
Math · Module 2 · Question 17 of 22
Two random samples from the same population are used to estimate a proportion using the same confidence level and sampling method. One has 100 observations; the other has 900. Which is generally expected?
Answer: D / The larger sample has a smaller margin of error. Other features held comparable, a larger random sample generally reduces sampling uncertainty. It does not remove bias automatically or guarantee that the two estimates are identical.
Sample size and precision / Standard Review: Example 5.08.
Math · Module 2 · Question 18 of 22
A sector of a circle has radius 8 and central angle 135°. Its area is kπ. What is k?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 24 The sector is 135/360
Sector area / Standard Review: Example 6.10.
Math · Module 2 · Question 19 of 22
For a positive integer k, the equation x2 − (k + 1)x + 4k = 0 has two distinct real solutions. What is the least possible value of k?
Answer: D / 14 The discriminant must be positive: (k + 1)2 − 16k = (k − 7)2 − 48 > 0. For integers 1 ≤ k ≤ 13, (k − 7)2 ≤ 36, so none work. At k
Discriminants / Challenge Review: Example 6.05.
Math · Module 2 · Question 20 of 22
For all real x, a(4x − 1) + b = 12x + 8. What is b?
Answer: A / 11 Compare coefficients: 4a
Identities / Challenge Review: Example 1.03.
Math · Module 2 · Question 21 of 22
The graphs y = x2 − 6x + 11 and y = 2x − 5 intersect. What is the y-coordinate of their intersection?
Answer: A / 3 Equating gives x2 − 8x + 16 = (x − 4)2 = 0. The unique input is 4. Substitute into the line: y = 2(4) − 5 = 3. The question asks for the output, not the repeated root.
Nonlinear systems / Challenge Review: Example 3.05.
Math · Module 2 · Question 22 of 22
A line passes through (2, 7) and (8, 25). Its equation is ax − 2y = c. What is a + c?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 4 The slope is (25 − 7)/(8 − 2)
Equivalent line forms / Challenge Review: Example 1.02.
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Reference sheet
AVAILABLE DURING BOTH MODULES
Formula reference
The relationships below match the standard SAT-provided Math reference. This is a newly typeset reference, not a reproduction of the official sheet. [4]
Area and circumference
Circle A
Rectangle A
Triangle A
Right triangles
Pythagorean theorem a2 + b2
45°–45°–90° Side lengths s, s, s, in increasing order.
30°–60°–90° Side lengths x, x, 2x, opposite 30°, 60°, 90°, respectively.
Volume
Rectangular prism V
Circular cylinder V
Sphere V
Right circular cone V
Rectangular pyramid V
Angle facts
A full circle has 360° or 2π radians. The interior angles of a triangle sum to 180°.
Symbols: r is radius; l is length; w is width; b is base length; h is perpendicular height; A is area; C is circumference; V is volume. Source: official reference linked in the directions, [4].