SHSAT Math

Question 1

A chemistry flask holds $3\dfrac{1}{3}$ milliliters of solution. Each trial uses $\dfrac{5}{6}$ milliliter. How many complete trials can be run from one full flask?

Accepted Answer

$4$

Answer

$2$

Answer

$3$

Answer

$5$

Question 2

A pancake recipe uses $3$ cups of flour to make $8$ servings. How many cups of flour are needed to make $20$ servings using the same recipe?

Accepted Answer

$7.5$

Answer

$5$

Answer

$6$

Answer

$15$

Question 3

A spinner is spun $3$ times. Each spin lands on either A or B with equal probability, and the spins are independent. The table lists every possible outcome. What is the probability that all three spins land on the same letter?

Accepted Answer

$\dfrac{1}{4}$

Answer

$\dfrac{1}{8}$

Answer

$\dfrac{3}{8}$

Answer

$\dfrac{1}{2}$

Question 4

A taxi charges $\$2.50$ to start plus $\$2.25$ per mile. The cost $C$ in dollars for an $m$-mile ride can be written as $C = am + b$. What is the value of $a$? Enter your answer in the space.

Accepted Answer

2.25

Question 5

A rectangular prism measures 10 centimeters by 5 centimeters by 4 centimeters. What is its volume, in cubic centimeters?

Accepted Answer

$200$

Answer

$100$

Answer

$110$

Answer

$220$

Question 6

A jacket that costs $\$80$ is marked up by $15\%$. What is the new price of the jacket?

Accepted Answer

$\$92$

Answer

$\$88$

Answer

$\$90$

Answer

$\$95$

Question 7

Which is greater, $2^{10}$ or $10^{3}$, and by how much?

Accepted Answer

$2^{10}$, by $24$

Answer

$10^{3}$, by $24$

Answer

$2^{10}$, by $240$

Answer

They are equal

Question 8

Of $80$ students in a class, $28$ arrived early. Which pair gives the early-arrival fraction in lowest terms and the matching percent?

Accepted Answer

$\dfrac{7}{20}$ and $35\%$

Answer

$\dfrac{14}{40}$ and $35\%$

Answer

$\dfrac{7}{20}$ and $3.5\%$

Answer

$\dfrac{28}{80}$ and $35\%$

Question 9

A printing press runs at a constant rate. The table shows pages printed and time in minutes. What is the constant of proportionality in pages per minute?

Accepted Answer

$45$

Answer

$2$

Answer

$30$

Answer

$90$

Question 10

The number line above shows the solution set of an inequality in terms of $p$. Which inequality is graphed?

Accepted Answer

$-2 \le p < 6$

Answer

$-2 < p \le 6$

Answer

$-2 \le p \le 6$

Answer

$-2 < p < 6$

Question 11

The bar graph shows the number of hours a student practiced with the school band on four days. What is the mean number of practice hours per day for these four days?

Accepted Answer

$4$

Answer

$3$

Answer

$5$

Answer

$16$

Question 12

A fair number cube has faces numbered 1 through 6. What is the probability of rolling an even number?

Accepted Answer

$1/2$

Answer

$1/6$

Answer

$1/3$

Answer

$2/3$

Question 13

Each yard of fabric weighs $3\frac{1}{3}$ pounds. What is the total weight, in pounds, of $4\frac{1}{2}$ yards?

Accepted Answer

$15$

Answer

$7\frac{5}{6}$

Answer

$12$

Answer

$13\frac{1}{2}$

Question 14

The table shows a basketball player’s points scored and games played over three stretches of the season.

POINTS AND GAMES

Is the number of points proportional to the number of games? Choose the response with the correct justification.

Accepted Answer

No; the points-per-game rates are $7$, $7$, and $8$

Answer

No; the points differ in each row

Answer

Yes; points increase whenever games increase

Answer

Yes; each row has the same points-per-game rate of $7$

Question 15

What is the slope of the line through $(2,3)$ and $(8,15)$? Enter your answer in the space.

Accepted Answer

2

Question 16

Which expression is equivalent to $\dfrac{2^{9}	imes 2^{2}}{2^{1}}$?

Accepted Answer

$2^{10}$

Answer

$2^{9}$

Answer

$2^{12}$

Answer

$4^{10}$

Question 17

Each lap of a track is $\frac{5}{8}$ mile long. A runner completes $1\frac{1}{3}$ laps. How many miles does the runner cover?

Accepted Answer

$\frac{5}{6}$

Answer

$\frac{5}{8}$

Answer

$\frac{2}{3}$

Answer

$1\frac{1}{3}$

Question 18

A trapezoid has parallel bases of $8$ meters and $14$ meters and a height of $5$ meters. What is its area, in square meters?

Accepted Answer

$55$

Answer

$44$

Answer

$70$

Answer

$110$

Question 19

A backpack originally costs $48$ dollars. During a sale, the price is reduced by $25\%$, and then a coupon worth $6$ dollars is applied. What is the final price before tax?

Accepted Answer

$30$

Answer

$32$

Answer

$36$

Answer

$42$

Question 20

The table shows the gallons used and miles driven at three fuel stops for each of two cars. Which statement is true?

Accepted Answer

Only Car Q shows a proportional relationship, because its miles-per-gallon rate is constant.

Answer

Both cars show a proportional relationship between gallons and miles because miles increase whenever gallons increase.

Answer

Neither car shows a proportional relationship, because each car has three different gallon amounts.

Answer

Only Car P shows a proportional relationship, because two of its stops share the same miles-per-gallon rate.

Question 21

A rectangular playing card measures $8$ inches by $5$ inches. A rectangular stamp-sized prize zone printed on the card measures $3$ inches by $2$ inches. A speck of ink lands at a random point on the card. What is the probability that the speck lands in the prize zone? Enter your answer as a percent. Enter your answer in the space.

Accepted Answer

15

Question 22

Two sides of a triangle measure $7$ and $10$. Which value could be the third side?

Accepted Answer

$16$

Answer

$1$

Answer

$2$

Answer

$17$

Question 23

A step counter shows $|s-8000|=1200$, where $s$ is today's step count and $s>8000$. How many steps were taken today?

Accepted Answer

$9200$

Answer

$6800$

Answer

$8000$

Answer

$10400$

Question 24

A rectangular garden measures $3$ centimeters by $5$ centimeters on a drawing where $1$ centimeter represents $4$ meters. What is the actual area of the garden, in square meters?

Accepted Answer

$240	ext{ m}^2$

Answer

$60	ext{ m}^2$

Answer

$120	ext{ m}^2$

Answer

$180	ext{ m}^2$

Question 25

A museum visitor follows two gallery corridors from $(0,0)$ to $(3,4)$; another route uses a direct walkway between the same points. How much longer, in units, is the grid route than the direct walkway?

Accepted Answer

$2$ units

Answer

$5$ units

Answer

$7$ units

Answer

$12$ units

Question 26

A bake-sale recipe mixes flour, sugar, and butter in the ratio $5:3:2$. Flour is what percent of the total mixture? Enter your answer in the space.

Accepted Answer

50

Question 27

If $5(x-2)=3x+14$, what is the value of $x$?

Accepted Answer

$12$

Answer

$6$

Answer

$8$

Answer

$10$

Question 28

Solve $2x+4y=12$ for $y$ in terms of $x$.

Accepted Answer

$y=3-\frac{x}{2}$

Answer

$y=3+\frac{x}{2}$

Answer

$y=6-2x$

Answer

$y=12-4x$

Question 29

A ticket booth computes a block total with the expression $5^{2} - (-2)^{3} 	imes 3$. What is the value of the expression?

Accepted Answer

$49$

Answer

$-1$

Answer

$1$

Answer

$31$

Question 30

A dealer has $4$ distinctly labeled prize cards and deals them one at a time into a single row. How many different arrangements of the $4$ cards are possible? Enter your answer in the space.

Accepted Answer

24

Question 31

In the figure above, lines $l$ and $m$ are parallel. What is the value of $x$?

Accepted Answer

$115$

Answer

$65$

Answer

$105$

Answer

$125$

Question 32

The table shows pages printed by a press after $t$ minutes of run time. Which conclusion about the relationship between time and pages is correct?

Accepted Answer

The relationship is not proportional, because $\dfrac{140}{6}$ is not equal to $\dfrac{50}{2}$.

Answer

The relationship is proportional, because time doubles from $2$ to $4$ and pages also double.

Answer

The relationship is proportional, because every ratio of pages to time equals $25$.

Answer

The relationship is not proportional, because $6$ is not a multiple of $2$.

Question 33

A digital archive has $48$ scanned maps. It has $25\%$ more scanned photographs than scanned maps. If one-third of the scanned photographs still need captions, how many scanned photographs already have captions?

Accepted Answer

$40$

Answer

$20$

Answer

$36$

Answer

$60$

Question 34

A carpenter has one board that is $24$ inches long and another that is $36$ inches long. Both boards will be cut into congruent pieces of the **greatest** possible whole-inch length, with no wood left over. What is that piece length, in inches?

Accepted Answer

$12$

Answer

$6$

Answer

$8$

Answer

$18$

Question 35

The figure shows a rectangle $18$ inches long and $10$ inches wide with a rectangular notch cut out of one corner, as marked. What is the perimeter, in inches, of the remaining figure?

Accepted Answer

$56$

Answer

$48$

Answer

$64$

Answer

$80$

Question 36

A household's streaming bill was $\$18$ after $3$ hours of viewing in a month and $\$30$ after $9$ hours of viewing. The bill increases at a constant rate per hour. What is that rate, in dollars per hour? Enter your answer in the space.

Accepted Answer

2

Question 37

The ratio of notebooks to binders on a shelf is $5:3$. If there are $64$ notebooks and binders in all, how many notebooks are on the shelf?

Accepted Answer

$40$

Answer

$24$

Answer

$32$

Answer

$48$

Question 38

A climate model divides a weekly heat index of $4.85 	imes 10^{2}$ by a scaling factor of $9.7 	imes 10^{-1}$. Which is the best estimate of the quotient?

Accepted Answer

$500$

Answer

$0.5$

Answer

$50$

Answer

$5{,}000$

Question 39

A volunteer for a student committee is chosen according to the tree diagram. What is the probability the volunteer is experienced and available?

Accepted Answer

$\dfrac{3}{10}$

Answer

$\dfrac{3}{20}$

Answer

$\dfrac{2}{5}$

Answer

$\dfrac{1}{2}$

Question 40

A storage shelf has $4$ small boxes with $12$ markers in each box and $5$ large boxes with $18$ markers in each box. What is the average number of markers per box?

Accepted Answer

$15\dfrac13$

Answer

$13\dfrac13$

Answer

$14$

Answer

$15$

Question 41

What is the **least** integer $x$ that satisfies $3x+5<2(4x-3)$?

Accepted Answer

$3$

Answer

$0$

Answer

$1$

Answer

$2$

Question 42

A trail map marks distance along a hike. A hiker covers the stretch from marker 0 to marker 2.5 in 50 minutes at a steady pace.

What is this hiking pace in feet per hour? (1 mile $= 5280$ feet)

Accepted Answer

$15840$

Answer

$7920$

Answer

$10560$

Answer

$26400$

Question 43

A club spends $\dfrac{3}{8}$ of its budget on supplies. The rest of the budget is $54$ dollars more than the amount spent on supplies. What is the club's total budget?

Accepted Answer

$216$

Answer

$144$

Answer

$162$

Answer

$288$

Question 44

After 3 more students join a class, each student pays $p - 2$ dollars and the class collects $180. Which expression gives the number of students originally in the class?

Accepted Answer

$180/(p - 2) - 3$

Answer

$180/p - 3$

Answer

$180/(p - 2) + 3$

Answer

$177/(p - 2)$

Question 45

A tank contains $80$ liters of water. A pump removes $12$ liters every $5$ minutes. How many minutes will it take the pump to remove $45\%$ of the water in the tank?

Accepted Answer

$15$

Answer

$9$

Answer

$12$

Answer

$18$

Question 46

What is the area, in square units, of the isosceles trapezoid shown? Enter your answer in the space.

Accepted Answer

128

Question 47

A rectangle has a length that is $4$ more than its width. If the length is increased by $3$ and the width is decreased by $2$, the area does not change. What is the **original** area, in square units, of the rectangle?

Accepted Answer

$252$

Answer

$196$

Answer

$224$

Answer

$288$

Question 48

The probability of rain on any given day is $\dfrac{1}{5}$, and rain on different days may be treated as independent. What is the probability that it rains on **at least one** of the next $3$ days?

Accepted Answer

$\dfrac{61}{125}$

Answer

$\dfrac{12}{125}$

Answer

$\dfrac{64}{125}$

Answer

$\dfrac{3}{5}$

Question 49

In a germination trial, $204$ of $240$ seeds sprouted. At that same rate, how many seeds are expected to sprout from a $1.5$-kilogram bag if there are $1600$ seeds in $0.4$ kilograms of seed?

Accepted Answer

$5100$

Answer

$4080$

Answer

$5440$

Answer

$6000$

Question 50

The product of two positive integers is $96$, and their least common multiple is $24$. What is their greatest common factor? Enter your answer in the space.

Accepted Answer

4

SHSAT 2026 Math practice test

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