SAT Math Full mixed practice — Free with Answer Explanations

Question 1

If $3 x - 7 = 14$ , what is the value of $x$ ?

A.

3

B.

7

C.

9

D.

21

Question 2

A line in the $x y$ -plane has slope $- \frac{2}{3}$ and passes through the point $(6, 1)$ . What is the $y$ -intercept of this line?

A.

5

B.

- 3

C.

3

D.

- 5

Question 3

In right triangle $A B C$ , angle $C$ is the right angle, $A C = 8$ , and $B C = 6$ . What is $cos (A)$ ?

A.

\frac{6}{10}

B.

\frac{8}{10}

C.

\frac{6}{8}

D.

\frac{8}{6}

Question 4

A line passes through the points $(0, - 3)$ and $(4, 5)$ . What is the slope of the line?

A.

2

B.

\frac{1}{2}

C.

- 2

D.

\frac{5}{4}

Question 5

A jacket originally priced at $\$ 80 $i so n s a l e f or$ 25%$ off. What is the sale price?

A.

\

55$B.

\

60$C.

\

20$D.

\

100$

Question 6

A point $P$ is at coordinates $(3, - 4)$ . What is the distance from $P$ to the origin?

A.

5

B.

7

C.

1

D.

7

Question 7

A recipe requires 3 cups of flour for every 2 cups of sugar. If a baker uses 12 cups of flour, how many cups of sugar are needed?

A.

6

B.

8

C.

9

D.

18

Question 8

If $∣2 x - 6∣ = 10$ , what are the solutions for $x$ ?

A.

x = 8

onlyB.

x = - 2

onlyC.

x = 2

and

x = 8

D.

x = - 2

and

x = 8

Question 9

If $3 x + 7 = 4$ , what is the value of $x$ ?

A.

x = 3

B.

x = \frac{23}{3}

C.

x = - 1

D.

x = 9

Question 10

A store sells notebooks for $\$ 3 $e a c han d p e n s f or$ $1.50$ each. Mia bought 8 items and spent exactly $\$ 18$. How many notebooks did she buy?

A.

3

B.

4

C.

5

D.

6

Question 11

What is the area of a triangle with base $10$ and height $6$ ?

A.

60

B.

30

C.

16

D.

15

Question 12

A population of bacteria doubles every 3 hours. Starting from 500, which expression gives the population after $t$ hours?

A.

500 \cdot 2^{t /3}

B.

500 \cdot 2^{3 t}

C.

500 \cdot 3^{t /2}

D.

500 + 2 t

Question 13

A taxi charges a flat fee of $\$ 3.00 $pl u s$ $1.75$ per mile. Jared's fare totaled $\$ 15.25$. How many miles was the ride?

A.

6

B.

7

C.

8

D.

9

Question 14

A rectangle has length $l$ and width $w$ . If the length is doubled and the width is halved, how does the area change?

A.The area stays the same.B.The area doubles.C.The area is halved.D.The area is multiplied by 4.

Question 15

A sphere has a radius of $6$ . What is its volume? (Leave in terms of $π$ .)

A.

288 π

B.

144 π

C.

72 π

D.

216 π

Question 16

In the unit circle, angle $θ$ is in standard position and $cos θ = - \frac{2}{2}$ with $sin θ > 0$ . In which quadrant does angle $θ$ lie?

A.Quadrant IB.Quadrant IIC.Quadrant IIID.Quadrant IV

Question 17

In a survey of 400 people, $35%$ said they exercise daily. The margin of error is $\pm 4%$ . Which of the following is a reasonable estimate for the percentage of the entire population that exercises daily?

A.

30%

B.

37%

C.

40%

D.

50%

Question 18

What is the value of $y$ in the system of equations below?

$2 x + y = 10$
$x - y = 2$

A.

2

B.

4

C.

6

D.

8

Question 19

In a right triangle, one acute angle measures $30°$ . The hypotenuse has length $10$ . What is the length of the side opposite the $30°$ angle?

A.

5

B.

53

C.

10

D.

102

Question 20

The data set below shows test scores for 7 students:

$72, 85, 90, 90, 91, 95, 100$

What is the median score?

A.

90

B.

91

C.

90.5

D.

89

Question 21

Which value of $x$ satisfies the inequality $2 x + 5 < 13$ ?

A.

5

B.

4

C.

3

D.

8

Question 22

A car travels 240 miles in 4 hours. At this rate, how many miles will it travel in 6 hours?

A.

300

B.

360

C.

320

D.

400

Question 23

A scatterplot shows a strong positive linear association between hours studied ( $x$ ) and exam score ( $y$ ). The line of best fit is $y = 4 x + 52$ . Predict the exam score for a student who studies 8 hours.

A.

80

B.

84

C.

60

D.

96

Question 24

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If one marble is selected at random, what is the probability it is NOT red?

A.

\frac{1}{3}

B.

\frac{2}{3}

C.

\frac{5}{12}

D.

\frac{3}{12}

Question 25

The box plot below summarizes a data set. The minimum is 10, Q1 is 25, median is 40, Q3 is 55, and the maximum is 70. What is the interquartile range (IQR)?

A.

60

B.

30

C.

15

D.

40

Question 26

For which value of $k$ does the system below have infinitely many solutions?

$2 x - k y = 4$
$4 x - 6 y = 8$

A.

k = 2

B.

k = 3

C.

k = 4

D.

k = 6

Question 27

The graph of $y = a (x - 2)^{2} + 5$ is a parabola. If it opens downward, which of the following could be the value of $a$ ?

A.

a = 3

B.

a = 0

C.

a = - 2

D.

a = 1

Question 28

The expression $\frac{x ^{2} - 4}{x - 2}$ simplifies to which of the following, for $x \neq = 2$ ?

A.

x - 2

B.

x + 2

C.

x^{2} - 2

D.

x + 4

Question 29

In the figure, line $ℓ$ is parallel to line $m$ . A transversal crosses both lines, creating alternate interior angles. One alternate interior angle measures $(3 x + 10) °$ and the other measures $(5 x - 20) °$ . What is the value of $x$ ?

A.

x = 15

B.

x = 5

C.

x = 10

D.

x = 25

Question 30

Which of the following is a factor of $x^{2} - 9$ ?

A.

(x + 3)^{2}

B.

(x - 9)

C.

(x - 3)

D.

(x^{2} + 3)