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SAT Math — Module 2 (easier) practice test

  • 22 questions
  • 35 minutes
  • Nothing is deducted for a wrong answer
  • Free

The Math — Module 2 (easier) section of the SAT practice test — 22 questions. Mark your answers, then press Finish at the bottom to see your score.

This is the same test the app serves as Practice Test 1. Working it here spends it: these questions will not be new when you take the test against the clock in the app.

The real SAT chooses your second module from how you did on the first, so both versions of Module 2 are here. In the app, your Module 1 result decides which one you take.

Nothing is marked while you work, just as on the real test. The answers and the worked explanations open when you finish. What you mark is kept in this browser, so closing the tab does not lose it.

Question 1

nc(n)011−22−33−241

The table shows several values of the quadratic function c. What are the coordinates of the vertex of the graph of y=c(n) in the ny-plane?

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Answer: C — (2,−3)

The table values are symmetric about n=2: c(0)=c(4)=1 and c(1)=c(3)=−2. For a quadratic, the vertex lies on the axis of symmetry, so the vertex is (2,−3).

Question 2

Which expression is equivalent to 7a+3a+2b?

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Answer: B — 10a+2b

Combine the like a-terms: 7a+3a=10a, leaving 10a+2b.

Question 3

6x=138

What is the value of x?

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Answer: A — 23

Divide both sides by 6: x=1386=23.

Question 4

c(x)=4x+k

The function c is defined by the given equation, where k is a constant. If c(3)=19, what is the value of k?

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Answer: B — 7

19=4(3)+k gives k=7.

Question 5

h+28=jk

For the given equation, which equation correctly expresses h in terms of j and k?

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Answer: D — h=jk−28

Subtracting 28 from both sides of h+28=jk gives h=jk−28.

Question 6

A store offers a discount on any purchase of $50 or more. Which inequality represents the purchase amount, p, in dollars, that qualifies a customer for the discount?

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Answer: C — p≥50

The purchase must be $50 or more: p≥50.

Question 7

In right triangle DEF, the right angle is at E, DE=9, and EF=12. What is the length of DF‾?

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Answer: B — 15

DF is the hypotenuse of right triangle DEF, so by the Pythagorean theorem DF=DE2+EF2=92+122=225=15.

Question 8

The graph of a system of two linear equations in two variables is shown.

Which statement describes the ordered pairs (x,y) that are solutions to the given system of equations?

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Answer: B — There is exactly one such ordered pair.

The two lines have different slopes, so they intersect at exactly one point. That intersection is the unique ordered pair (x,y) that satisfies both equations. Two distinct lines cannot meet at exactly two points, and they are not the same line, so the system does not have infinitely many solutions.

Question 9

A vehicle travels 180 miles at a constant speed of 22.5 miles per hour. How many hours does the trip take?

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Answer: B — 8

The time is 180/22.5=8 hours.

Question 10

A regional library system has 9 neighborhood branches and 26 school branches.

9n+26s=1,262

The given equation represents the total number of hours that all the branches are open each week, where n and s are constants. Which of the following is the best interpretation of 26s in this context?

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Answer: D — The total number of hours the 26 school branches are open each week

The value s is the average weekly operating time of one school branch. Multiplying by 26 gives the total number of hours the 26 school branches are open each week.

Question 11

What is 16% of 425?

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Answer: B — 68

Convert 16% to 0.16 and multiply: 0.16(425)=68.

Question 12

−6−4−2246−20−101020xyO

Which function could be represented by the graph shown?

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Answer: A — f(x)=x3−4x

The graph has zeros at −2, 0, and 2 and falls to the left and rises to the right, matching f(x)=x3−4x=x(x−2)(x+2). f(x)=x2−4x is a parabola with zeros at 0 and 4. f(x)=−x3+4x has the same zeros but rises to the left and falls to the right. f(x)=x3−4x+4 is shifted up by 4 and does not pass through the origin.

Question 13

Triangle JKL has side lengths JK=7, KL=10, and JL=15. Which angle of the triangle has the greatest measure?

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Answer: B — Angle K

In any triangle, the largest angle is opposite the longest side. The longest side is JL=15, and the angle opposite JL is ∠K, so ∠K is the greatest.

Question 14

In the xy-plane, a circle with center (0,0) has radius 7. The line y=c, where c>0, is tangent to the circle. What is the value of c?

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Answer: B — 7

The circle centered at (0,0) with radius 7 is tangent to the line y=c when the perpendicular distance from the center to the line equals the radius. That distance is c (given c>0), so c=7.

Question 15

Two pentagonal emblems are similar. The perimeter of the larger emblem is 74 times the perimeter of the smaller emblem. If the smaller emblem has an area of 80 square centimeters, what is the area, in square centimeters, of the larger emblem?

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Answer: C — 245

Perimeters of similar figures scale by the same factor as corresponding side lengths, so the linear factor is 74. Areas of similar figures scale by the square of the linear factor. The larger area is 80(74)2=245 square centimeters.

Question 16

Data Set P

012345678910010203040

Data Set Q

012345678910010203040

Two data sets of 21 integers each are summarized in the histograms shown. Which of the following best compares the means of data sets P and Q?

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Answer: C — The mean of Data Set P is greater than the mean of Data Set Q.

Data Set P has more values concentrated at higher intervals (20–40) while Data Set Q has more values concentrated at lower intervals (0–20), so P’s mean is greater.

Question 17

Measurements of variables u and v are plotted below.

02468101214161820012345678910vu

Which linear equation is the best model for the data shown in the scatterplot?

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Answer: B — v=1.5u+4

The cloud rises from near 4 when u=0 with a slope near 1.5 per unit u, matching v=1.5u+4.

Question 18

x2+8x−105=0

What is the positive solution to the given equation?

✓ Correct✗ Not correct
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Answer: 7

The quadratic factors as (x+15)(x−7)=0, so its solutions are −15 and 7. The positive solution is 7.

Question 19

A community had collected 85% of its fundraising goal. After an additional $34 was collected, the total amount collected was $459. What was the fundraising goal, in dollars?

✓ Correct✗ Not correct
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Answer: 500

If the fundraising goal was g, then 0.85g+34=459. Thus 0.85g=425, so g=500.

Question 20

xp(x)16316526

The table gives values of the linear function p. What is the value of p(10)?

✓ Correct✗ Not correct
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Answer: 51

Rate of change is (16−6)/(3−1)=5; p(x)=5x+1, so p(10)=51.

Question 21

The function f is defined by

f(x)=(1.21)x2.

The given equation can be rewritten as

f(x)=(1+p100)x,

where p is a constant. What is the value of p?

✓ Correct✗ Not correct
Show answer

Answer: 10

(1.21)x/2=(1.21)x=(1.1)x=(1+10100)x, so p=10.

Question 22

cd(c)−717−612−59−48−39−212−117

The table shows values of the quadratic function d. The horizontal line y=j intersects the graph of y=d(c) at exactly one point. What is the value of j?

✓ Correct✗ Not correct
Show answer

Answer: 8

A horizontal line intersects a parabola at exactly one point at its vertex; the vertex here is (−4,8), so j=8.

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