Study on the flySAT

Study on the flySATPractice testMath — Module 2 (easier)

SAT

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

The function hh is defined by h(x)=2(x−1)2+3h(x)=2(x-1)^2+3. What is the xx-coordinate of the vertex of the graph of y=h(x)y=h(x)?

Show answer

Answer: B — 1

The function h(x)=2(x−1)2+3h(x)=2(x-1)^2+3 is in vertex form a(x−h)2+ka(x-h)^2+k, so the vertex is (1,3)(1,3) and the xx-coordinate is 1.

Question 2

A bike rental shop charges a one-time fee plus an hourly rate. The total cost, in dollars, of renting a bike for tt hours is modeled by C(t)=4t+8C(t)=4t+8. Which of the following is the best interpretation of the yy-intercept of the graph of y=C(t)y=C(t)?

Show answer

Answer: B — The shop charges a one-time fee of $8.

The y-intercept of y=C(t)y=C(t) is C(0)=8C(0)=8. In this model, the cost when t=0t=0 is the one-time fee, in dollars.

Question 3

Which expression is equivalent to 3(x+4)+2x3(x+4)+2x?

Show answer

Answer: C — 5x+125x+12

Distribute: 3x+12+2x=5x+123x+12+2x=5x+12.

Question 4

A family paid a total of $95 to attend a fair. The total cost included a $15 parking fee plus pp tickets at $8 each. How many tickets did the family buy?

Show answer

Answer: B — 10

Subtracting the $15 parking fee from $95 leaves $80. Each ticket costs $8, so the family bought 80÷8=1080\div8=10 tickets.

Question 5

x2+x−12=0x^2+x-12=0

What is the positive solution to the given equation?

✓ Correct✗ Not correct
Show answer

Answer: 3

Factor as (x+4)(x−3)=0(x+4)(x-3)=0, so x=−4x=-4 or x=3x=3; the positive solution is 3.

Question 6

A bicycle rental company charges a one-time fee of $9 plus $6 for each hour a bicycle is rented. Which equation represents this situation, where cc is the total cost, in dollars, of renting a bicycle for hh hours?

Show answer

Answer: A — c=6h+9c=6h+9

The company charges a one-time fee of $9 plus $6 for each of hh hours. The total cost cc of renting a bicycle for hh hours is therefore c=6h+9c=6h+9.

Question 7

Three adjacent angles form a straight line, and their measures are x∘x^\circ, 47∘47^\circ, and 81∘81^\circ. What is the value of xx?

✓ Correct✗ Not correct
Show answer

Answer: 52

Angles along a straight line sum to 180, so x+47+81=180x+47+81=180, giving x=52x=52.

Question 8

x=7x=7
2x+y=202x+y=20

What is the value of yy in the solution to the given system of equations?

Show answer

Answer: A — 6

Substitution gives 14+y=2014+y=20, so y=6y=6.

Question 9

On a map, 2 centimeters represents 15 kilometers. How many kilometers are represented by 8 centimeters?

Show answer

Answer: B — 60

Eight centimeters is four times 2 centimeters, so the distance is 4(15)=604(15)=60 kilometers.

Question 10

In a right triangle, one acute angle measures 30∘30^\circ and the side opposite that angle has length 6. What is the length of the hypotenuse?

Show answer

Answer: D — 12

In a 30∘30^\circ-60∘60^\circ-90∘90^\circ triangle, the side opposite the 30∘30^\circ angle is half the hypotenuse. That opposite side has length 6, so the hypotenuse has length 12.

Question 11

−6−5−4−3−2−1123456−6−5−4−3−2−1123456

The shaded region shown in the graph represents all the solutions to an inequality. Which point (x,y)(x, y) lies in the solution set?

Show answer

Answer: A — (0,−4)(0,-4)

The boundary line has slope −0.5-0.5 and passes through (0,0)(0,0), so y=−0.5xy=-0.5x; the shaded region, including the solid boundary, represents y≤−0.5xy\le-0.5x. Only (0,−4)(0,-4) satisfies −4≤0-4\le 0.

Question 12

The function ff is defined by f(x)=x2−4f(x)=x^2-4. A second function is defined by h(x)=f(x−2)+1h(x)=f(x-2)+1. What is the value of h(3)h(3)?

Show answer

Answer: B — −2-2

Since 3−2=13-2=1, h(3)=f(1)+1=(12−4)+1=−2h(3)=f(1)+1=(1^2-4)+1=-2.

Question 13

A circle has a radius of 18 inches. What is the length, in inches, of an arc that corresponds to a central angle of 60∘60^\circ?

Show answer

Answer: B — 6π6\pi

Arc length is 60360⋅2π(18)=16⋅36π=6π\dfrac{60}{360}\cdot2\pi(18)=\dfrac{1}{6}\cdot36\pi=6\pi.

Question 14

A laboratory recorded the temperature, in degrees Celsius, and reaction rate for each of several trials. The scatterplot and a line of best fit are shown.

2468101248121620242832Temperature (degrees Celsius)Reaction rate

Which ordered pair lies on the line of best fit and therefore represents a prediction consistent with the model?

Show answer

Answer: A — (4,13)(4,13)

The line has equation y=2x+5y=2x+5. Substituting x=4x=4 gives y=2(4)+5=13y=2(4)+5=13, so (4,13)(4,13) lies on the line.

Question 15

A right circular cylinder has a radius of 3 meters and a height of 11 meters. The lateral surface area LL of a right circular cylinder is given by L=2πrhL = 2\pi r h, where rr is the radius and hh is the height. What is the lateral surface area, in square meters, of the cylinder?

Show answer

Answer: B — 66π66\pi

The lateral surface area is 2πrh=2π(3)(11)=66π2\pi rh=2\pi(3)(11)=66\pi.

Question 16

What is 7.5%7.5\% of 480?

✓ Correct✗ Not correct
Show answer

Answer: 36

0.075×480=360.075 \times 480 = 36.

Question 17

The bar graph summarizes the masses, in grams, of a group of metal disks.

01234567891011126065707580Mass (grams)Frequency

How many of the disks have a mass greater than 65 grams?

Show answer

Answer: C — 22

The frequencies of the masses 70, 75, and 80 grams are 7, 9, and 6, respectively. These are the masses greater than 65 grams, so 7+9+6=227+9+6=22 disks have a mass greater than 65 grams.

Question 18

The function kk is linear, and k(3)=14k(3)=14 and k(7)=30k(7)=30. What is the value of k(0)k(0)?

Show answer

Answer: B — 2

The slope is 30−147−3=4\dfrac{30-14}{7-3}=4. Since k(3)=14k(3)=14, moving back 3 input units decreases the output by 12, giving k(0)=2k(0)=2.

Question 19

r(5x−2)+8x=38x−12r(5x-2)+8x=38x-12

In the given equation, rr is a constant. The equation has infinitely many solutions. What is the value of rr?

Show answer

Answer: B — 6

Expanding the left side gives (5r+8)x−2r(5r+8)x-2r. Matching both sides requires 5r+8=385r+8=38 and −2r=−12-2r=-12, and both conditions give r=6r=6.

Question 20

x2+6x+13=0x^2 + 6x + 13 = 0

How many distinct real solutions does the given equation have?

✓ Correct✗ Not correct
Show answer

Answer: 0

The discriminant is 36−52=−16<036 - 52 = -16 < 0, so the quadratic has no real solutions. The number of distinct real solutions is 0.

Question 21

Which expression is equivalent to 45a3b2−30a2b445a^3b^2-30a^2b^4?

Show answer

Answer: A — 15a2b2(3a−2b2)15a^2b^2(3a-2b^2)

Factoring the greatest common factor 15a2b215a^2b^2 gives 15a2b2(3a−2b2)15a^2b^2(3a-2b^2).

Question 22

The function ff is defined by f(x)=x2−3x+2f(x) = x^2 - 3x + 2. What is the average rate of change of ff from x=1x = 1 to x=5x = 5?

Show answer

Answer: C — 3

Average rate of change is f(5)−f(1)5−1=12−04=3\dfrac{f(5)-f(1)}{5-1}=\dfrac{12-0}{4}=3.

In the app the clock runs, you can pause and pick up where you left off, every question is explained afterwards, and your score is estimated on the test’s own scale. Extended time (1.5× or 2×) is there if you have an accommodation.

Take the full practice test in the app

The rest of the test

The full SAT practice test · Everything on the SAT

Study on the fly is an independent study tool and is not affiliated with, sponsored by, or endorsed by any testing organization, school, or government body.

SAT® is a registered trademark of the College Board, which is not affiliated with, and does not endorse, this product.

All practice questions and passages are original works created for Study on the fly and are not reproduced from any official test.