Math · Module 1 · Question 1 of 22
What is the solution to 4x + 3 = 31?
Answer: D / 7 Subtract 3: 4x
Linear equations / Foundation Review: Example 1.01.
Loading your practice…
Reload this page or choose another practice activity. Your saved work has not been cleared.
Additional Math Test 1
Additional Math Test 1
Blank test, no answers
This browser is not saving your progress, so a reload will lose this attempt.
Additional Math Test 1
Math · Module 1 · Question 2 of 22
Which expression is equivalent to 32 · 33?
Answer: A / 35 When multiplying powers with the same base, add exponents: 32+3
Exponents / Foundation Review: Example 6.07.
Math · Module 1 · Question 3 of 22
What is 35% of 160?
Answer: B / 56 Convert to a decimal and multiply: 0.35(160)
Percentages / Foundation Review: Example 3.06.
Math · Module 1 · Question 4 of 22
Two adjacent angles form a straight angle. One measures 117°. What is the measure of the other angle?
Answer: C / 63° Angles forming a straight angle sum to 180°. Thus the other angle is 180 − 117
Lines and angles / Foundation Review: Geometry reference.
Math · Module 1 · Question 5 of 22
What is the slope of the line shown?
Answer: C / −3/2 The line passes through (0, 9) and (6, 0). Its slope is (0 − 9)/(6 − 0) = −9/6 = −3/2.
Lines and graphs / Foundation Review: Example 6.01.
Math · Module 1 · Question 6 of 22
What is the positive solution to x2 − 4x − 12 = 0?
Answer: A / 6 Factor as (x − 6)(x + 2)
Quadratic equations / Foundation Review: Example 6.04.
Math · Module 1 · Question 7 of 22
A delivery cost, in dollars, is modeled by C(d) = 18 + 2.5d, where d is distance in miles. What does 18 represent?
Answer: D / The fixed charge, in dollars, before any distance charge. C(0)
Linear models / Foundation Review: Example 2.09.
Math · Module 1 · Question 8 of 22
The table gives a data set. What is its mean?
Value | 4 | 7 | 10 |
|---|---|---|---|
Frequency | 2 | 4 | 2 |
Answer: C / 7 The weighted total is 4(2) + 7(4) + 10(2)
One-variable data / Standard Review: Example 1.10.
Math · Module 1 · Question 9 of 22
If x + y = 11 and x − y = 3, what is y?
Answer: C / 4 Subtract the second equation from the first: 2y
Linear systems / Standard Review: Example 3.01.
Math · Module 1 · Question 10 of 22
What is the value of ?
Answer: D / 6 Both radicands are positive, so the quotient is = = 6.
Radicals / Standard Review: Example 1.06.
Math · Module 1 · Question 11 of 22
A circle has radius 6. What is the length of the minor arc corresponding to a 60° central angle?
Answer: A / 2π The arc is 60/360
Circles / Standard Review: Example 6.09.
Math · Module 1 · Question 12 of 22
A workshop has $260 to spend on a $44 rental fee and kits costing $18 each. What is the greatest number of kits it can buy?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 12 Let n be the integer number of kits. 44 + 18n ≤ 260 gives 18n ≤ 216 and n ≤ 12. The next integer would exceed the budget.
Inequality applications / Standard Review: Example 1.04.
Math · Module 1 · Question 13 of 22
A positive exponential function f satisfies f(0) = 5 and f(2) = 45. Which equation defines f ?
Answer: D / f(x)
Exponential functions / Standard Review: Example 5.06.
Math · Module 1 · Question 14 of 22
The table summarizes a survey. Among people who prefer the train, what fraction are commuters?
Prefer train | Prefer another mode | |
|---|---|---|
Commuters | 24 | 36 |
Noncommuters | 16 | 24 |
Answer: A / 3/5 Train-preferring respondents total 24 + 16
Conditional probability / Standard Review: Example 2.08.
Math · Module 1 · Question 15 of 22
A line is perpendicular to a line of slope −3/4. What is the slope of the perpendicular line?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 4/3 For perpendicular nonvertical lines, the slopes have product −1. The negative reciprocal of −3/4 is 4/3.
Perpendicular lines / Standard Review: Example 6.01.
Math · Module 1 · Question 16 of 22
How many distinct real solutions does 2x2 + 4x + 5 = 0 have?
Answer: B / 0 The discriminant is 42 − 4(2)(5) = 16 − 40 = −24. Since it is negative, there are no real roots.
Solution counts / Standard Review: Example 6.05.
Math · Module 1 · Question 17 of 22
A cone has diameter 8 and perpendicular height 9. 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: 48 The radius is 4, so the volume is π(42)(9)
Volume / Standard Review: Example 6.11.
Math · Module 1 · Question 18 of 22
For what value of a does (a + 4)x = 2a − 1 have no solution?
Answer: B / −4 A nonzero coefficient gives one solution. At a
Parameter equations / Standard Review: Example 2.12.
Math · Module 1 · Question 19 of 22
If x ≠ 1 and = , what is x?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 5 Cross-multiply to obtain 12
Rational equations / Standard Review: Example 1.05.
Math · Module 1 · Question 20 of 22
A random-sample estimate of support is 54% with a margin of error of 6 percentage points. Which statement about the reported interval is correct?
Answer: C / It includes proportions below 50%. The reported interval is 48% to 60%. It contains values below 50%, so the interval alone does not establish majority support.
Inference and margin of error / Standard Review: Example 5.08.
Math · Module 1 · Question 21 of 22
The equations 7x + 4y = 53 and 3x + 4y = 25 hold. What is 2x?
Answer: D / 14 Subtracting gives 4x
Systems and targets / Challenge Review: Example 2.04.
Math · Module 1 · Question 22 of 22
For a positive constant p, the equation px2 − 12x + 9 = 0 has exactly one distinct real solution. What is p?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 4 Because p > 0, the equation is genuinely quadratic. A repeated root requires discriminant zero: 144 − 36p
Parameter discriminants / Challenge Review: Example 4.07.
Math · Module 2 · Question 1 of 22
What is the coefficient of x in (x + 5)(x − 2)?
Answer: D / 3 Expansion gives x2 − 2x + 5x − 10
Polynomial operations / Foundation Review: Example 1.05.
Math · Module 2 · Question 2 of 22
What is the solution to + 5 = 9?
Answer: B / 12 Subtract 5 to get x/3
Linear equations / Foundation Review: Example 1.01.
Math · Module 2 · Question 3 of 22
In a right triangle, an acute angle A has opposite side 5 and adjacent side 12. What is tan A?
Answer: D / 5/12 Tangent is opposite over adjacent, so the value is 5/12. No hypotenuse calculation is required.
Trigonometry / Foundation Review: Example 6.12.
Math · Module 2 · Question 4 of 22
The histogram uses intervals that include their left endpoint and exclude their right endpoint. How many observations are at least 10 but less than 30?
Answer: B / 11 Add the frequencies in the [10, 20) and [20, 30) intervals: 6 + 5
Data displays / Standard Review: Data reference.
Math · Module 2 · Question 5 of 22
What is the minimum value of f(x) = 4(x − 1)2 + 6?
Answer: A / 6 The squared term is nonnegative, so the minimum output is 6, attained at x
Quadratic functions / Foundation Review: Example 1.07.
Math · Module 2 · Question 6 of 22
A linear function satisfies f(2) = 13 and f(7) = 33. 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: 45 The slope is (33 − 13)/(7 − 2)
Linear functions / Standard Review: Example 2.01.
Math · Module 2 · Question 7 of 22
Which ordered pair satisfies both y ≥ 2x − 1 and x + y ≤ 8?
Answer: A / (2, 4) For (2, 4), 4 ≥ 3 and 6 ≤ 8. For (4, 3) the first inequality fails; for (3, 6) the second fails; for (0, −2) the first fails.
Systems of inequalities / Standard Review: Algebra reference.
Math · Module 2 · Question 8 of 22
A quantity retains 81% of its value every 2 years, following a positive exponential model. What percent of its value does it retain each year?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 90 Let the annual retention factor be b > 0. Then b2
Exponential intervals / Standard Review: Example 1.09.
Math · Module 2 · Question 9 of 22
Similar figures have areas 16 and 100. A corresponding side in the smaller figure is 6. What is the corresponding side in the larger figure?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 15 The length factor is
Similarity / Standard Review: Example 1.14.
Math · Module 2 · Question 10 of 22
Five values have mean 12, and fifteen other values have mean 20. What is the mean of all twenty values?
Answer: C / 18 The totals are 5(12)
Weighted means / Standard Review: Example 1.10.
Math · Module 2 · Question 11 of 22
What is the sum of the solutions to |3x − 6| = 12?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 4 The two cases give 3x − 6
Absolute-value equations / Standard Review: Advanced Math reference.
Math · Module 2 · Question 12 of 22
For what value of k do 5x − 2y = 7 and 15x − 6y = k describe the same line?
Answer: C / 21 The second left side is 3 times the first. To preserve the same equation, its right side must be 3(7)
Linear solution counts / Standard Review: Example 1.03.
Math · Module 2 · Question 13 of 22
What is the solution to = x?
Answer: A / 5 The right side requires x ≥ 0. Squaring gives x2 − x − 20 = (x − 5)(x + 4) = 0. Reject −4, leaving 5; the original equation checks as
Radical equations / Standard Review: Example 1.08.
Math · Module 2 · Question 14 of 22
The circle (x − 3)2 + (y + 4)2 = 25 intersects the x-axis. What are the x-coordinates of those intersections?
Answer: B / 0 and 6 On the x-axis, y
Coordinate circles / Standard Review: Example 2.10.
Math · Module 2 · Question 15 of 22
For f(x) = 5x − 4, the equation f (2a) = 26 holds. What is a?
Answer: C / 3 Substitute the full input 2a: 5(2a) − 4
Function notation / Standard Review: Example 5.02.
Math · Module 2 · Question 16 of 22
The graphs y = x2 − 1 and y = 4x + 4 intersect at inputs r and s. What is rs?
Answer: B / −5 Equating outputs gives x2 − 4x − 5
Nonlinear systems / Standard Review: Example 6.15.
Math · Module 2 · Question 17 of 22
Volunteers in a study are randomly assigned to two exercise schedules. Which feature most directly supports a causal comparison between the schedules?
Answer: A / Random assignment of the schedules. Random assignment helps separate a treatment effect from preexisting group differences. Recruiting volunteers does not itself justify generalizing to all people.
Experimental design / Standard Review: Example 4.15.
Math · Module 2 · Question 18 of 22
The figure is a rectangle of width 12 and height 5 topped by a triangle with the same base and perpendicular height 4. What is the total area?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: 84 The rectangle area is 12(5)
Composite area / Standard Review: Example 6.02.
Math · Module 2 · Question 19 of 22
For which value of c does = c have no real solution?
Answer: A / 4 For x ≠ 2, the left side simplifies to x + 2. The candidate is x
Rational restrictions / Challenge Review: Example 4.04.
Math · Module 2 · Question 20 of 22
A theater sells adult tickets for $14 and student tickets for $9. It sells 80 tickets for $970. How many adult tickets were sold?
Answer: B / 50 Let a be adult tickets. Then 14a + 9(80 − a)
Contextual systems / Challenge Review: Example 2.04.
Math · Module 2 · Question 21 of 22
For which value of k does x2 − 6x + k = 0 have two distinct positive real roots?
Answer: D / 8 Two distinct real roots require 36 − 4k > 0, so k < 9. With sum 6 positive, both roots are positive exactly when their product k > 0. Thus 0 < k < 9, and only 8 works.
Root signs and counts / Challenge Review: Example 6.05.
Math · Module 2 · Question 22 of 22
For all real x, a(2x + 3) + b = 10x − 7. What is a + b?
Enter an integer, decimal, or fraction. Up to 5 characters, or 6 including a leading minus. No units or mixed numbers.
Answer: −17 Matching coefficients gives 2a
Identities / Challenge Review: Example 1.03.
Check your work
- Answered
- Flagged
Directions
Set up your workspace. Have a permitted calculator and scratch paper ready. Use the Reference control for formulas. Keep study guides and solutions closed and silence notifications.
Work within the current module. Answer, skip, flag, and revisit questions until you submit the module or its timer expires. Submitted modules are locked. Read the next module's directions, then press Start Module when ready.
Enter answers precisely. Multiple-choice questions have one correct choice. For numeric responses, enter an integer, decimal, or fraction such as 7/4, not a mixed number. Omit units, currency signs, percent signs, and commas. Use at most five characters for a positive answer, or six including a leading minus sign for a negative answer. Decimal points and fraction bars count as characters. Every numeric answer in this test has an exact fraction or decimal that fits.
Read the mathematical conditions. Use real numbers and the real domain of each expression unless stated otherwise. Geometry sketches are schematic unless a scale is specified; rely on stated lengths and relationships. Coordinate graphs and data displays use their labeled scales.
Review after finishing. Answers and explanations become available after the full test. Your result is the number correct, not an SAT scaled score.
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].