Study on the flySHSAT

Study on the flySHSATPractice testMath

SHSAT

SHSAT Math practice test

  • 50 questions
  • Nothing is deducted for a wrong answer
  • Free

The Math section of the SHSAT practice test — 50 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.

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

What is the value of 32−(−2)23^{2}-(-2)^{2}?

Show answer

Answer: C — 5

32=93^{2}=9 and (−2)2=4(-2)^{2}=4, so 9−4=59-4=5.

Question 2

A bakery packs cupcakes into boxes for a school fundraiser. The number of cupcakes used, cc, is proportional to bb, the number of boxes packed. If kk is the constant of proportionality, which equation represents the relationship between cc and bb?

Show answer

Answer: A — c=kbc = kb

A proportional relationship has the form (dependent variable) = (constant) × (independent variable), so c=kbc = kb.

Question 3

The probability that it will snow in a city on Friday is 0.18. What is the probability that Friday will be snow-free in the city?

Show answer

Answer: C — 0.82

P(not snow)=1−0.18=0.82P(\text{not snow})=1-0.18=0.82.

Question 4

Which point lies on the line y=2x−5y=2x-5?

Show answer

Answer: A — (4,3)(4,3)

Substituting x=4x=4 gives y=3y=3, so (4,3)(4,3) works.

Question 5

The school store sold 72%72\% of its notebooks. What is 72%72\% written as a fraction in lowest terms?

Show answer

Answer: B — 1825\dfrac{18}{25}

72%=7210072\%=\dfrac{72}{100}. Divide numerator and denominator by 4 to get 1825\dfrac{18}{25}.

Question 6

A triangle has base 18 centimeters and perpendicular height 7 centimeters. What is its area, in square centimeters?

Show answer

Answer: C — 63

12(18)(7)=63\dfrac12(18)(7)=63.

Question 7

Which expression is equivalent to 2(3x−5)+4x2(3x-5)+4x?

Show answer

Answer: D — 10x−1010x-10

First distribute to get 6x−106x-10, and then combine like terms with 4x4x to get 10x−1010x-10.

Question 8

In one week, Jordan deposits 56\dfrac{5}{6} of a paycheck into savings and later withdraws 25\dfrac{2}{5} of the same paycheck from savings. What is the net change in savings, as a fraction of the paycheck?

Show answer

Answer: C — 1330\dfrac{13}{30}

Net change is 56−25\dfrac{5}{6} - \dfrac{2}{5}. With denominator 30: 2530−1230=1330\dfrac{25}{30} - \dfrac{12}{30} = \dfrac{13}{30} of the paycheck.

Question 9

The table shows hours worked and pay earned for a part-time job. Pay is proportional to hours worked.

Hours workedPay earned2$363$545$90

What is the constant of proportionality, in dollars per hour?

Show answer

Answer: C — 18

Divide pay by hours for any row: 362=18\dfrac{36}{2}=18, 543=18\dfrac{54}{3}=18, and 905=18\dfrac{90}{5}=18. The constant of proportionality is 18 dollars per hour.

Question 10

Which inequality describes all solutions of 3x+5<203x+5<20?

Show answer

Answer: D — x<5x<5

Subtract 5, then divide by the positive coefficient 3. The inequality remains pointed the same way, giving x<5x<5.

Question 11

Score Distribution

10131822252831343740434650Score

The box plot summarizes a data set. What is the median?

Show answer

Answer: B — 25

The vertical line inside the box is at 25, so the median is 25.

Question 12

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.

POSSIBLE OUTCOMES

OutcomeAAAAABABABAAABBBABBBABBB

What is the probability that all three spins land on the same letter?

Show answer

Answer: B — 14\dfrac{1}{4}

There are 8 equally likely outcomes. All same letter: AAA and BBB — 2 outcomes — so the probability is 28=14\dfrac{2}{8}=\dfrac{1}{4}.

Question 13

What is the value of (−3)2−4×5+2(-3)^2-4\times5+2?

Show answer

Answer: B — −9-9

Exponents before multiply before add/subtract: (−3)2=9(-3)^2=9, then 4×5=204\times5=20, so 9−20+2=−99-20+2=-9. Treating −32-3^2 as −9-9 or ignoring order yields the distractors.

Question 14

The table shows grams of fertilizer used on different garden areas. The relationship is proportional.

Area (m2)Fertilizer (g)4186271045

What is the constant of proportionality in grams of fertilizer per square meter?

Show answer

Answer: B — 4.5

Divide fertilizer by area: 18÷4=4.518\div 4=4.5, and the other rows match, so k=4.5k=4.5.

Question 15

A phone plan costs $3 per gigabyte of data plus a fixed monthly fee. When 12 gigabytes are used, the bill is $56. What is the monthly fee, in dollars?

Enter your answer in the space.

✓ Correct✗ Not correct
Show answer

Answer: 20

The bill satisfies C=3g+fC = 3g + f. Substitute g=12g = 12 and C=56C = 56: 56=36+f56 = 36 + f, so f=20f = 20.

Question 16

On a map of a hiking trail, the scale shows that 2 inches represents 5 miles of actual trail. A trail segment measures 7 inches on the map. What is the actual length of that trail segment, in miles?

Show answer

Answer: C — 17.5

The scale gives 2.5 miles per inch (5 ÷ 2). Multiplying by 7 inches gives 2.5×7=17.52.5 \times 7 = 17.5 miles.

Question 17

Which fraction is equal to a terminating decimal?

Show answer

Answer: A — 18\dfrac{1}{8}

A fraction in lowest terms terminates only if its denominator’s prime factors are limited to 2 and/or 5. Here 18=123=0.125\dfrac{1}{8}=\dfrac{1}{2^{3}}=0.125 terminates; the others repeat.

Question 18

An escrowed payment of 640 dollars earns 2.5%2.5\% simple interest per year for 4 years. How much interest does the payment earn?

Show answer

Answer: C — 64 dollars

Use I=PrtI=Prt: 640(0.025)(4)=64640(0.025)(4)=64 dollars.

Question 19

116

What is the area, in square units, of the parallelogram shown?

Show answer

Answer: C — 66

A parallelogram’s area is base times height, so the area is 11×6=6611\times 6=66 square units.

Question 20

A school printing press runs at a constant rate. The table shows the number of pages printed after several amounts of time.

PRINTING PRESS

MinutesPages printed2304606908120

At this rate, how many pages does the press print in 1 hour?

Show answer

Answer: B — 900

From the table, the press prints 30 pages in 2 minutes, or 15 pages per minute. In 60 minutes it prints 15×60=90015 \times 60 = 900 pages.

Question 21

SCHOOL LOCKERS

Numeric codeWord codeEast hall128West hall155

A locker is chosen at random from the 40 lockers in the table. What is the probability that it is in the East hall and uses a word code?

Show answer

Answer: A — 15\dfrac{1}{5}

The East-and-word cell has 8 lockers out of 40, so 840=15\dfrac{8}{40}=\dfrac{1}{5}.

Question 22

Which expression is equivalent to (4.5×103)×(2×10−5)(4.5 \times 10^3)\times(2 \times 10^{-5})?

Show answer

Answer: B — 9×10−29 \times 10^{-2}

Multiply coefficients: 4.5×2=94.5\times 2=9. Add exponents: 3+(−5)=−23+(-5)=-2. Result: 9×10−29\times 10^{-2}.

Question 23

How many 38\dfrac38-cup servings are in 2142\dfrac14 cups?

Show answer

Answer: B — 6

9/4÷3/8=(9/4)(8/3)=69/4\div3/8=(9/4)(8/3)=6.

Question 24

2021

A right triangle has legs measuring 20 units and 21 units, as shown. What is the length, in units, of the hypotenuse? Enter your answer in the space.

✓ Correct✗ Not correct
Show answer

Answer: 29

By the Pythagorean theorem, the hypotenuse is 202+212=400+441=841=29\sqrt{20^2+21^2}=\sqrt{400+441}=\sqrt{841}=29.

Question 25

Grams of coffee beans used is proportional to liters of brew made. Making 2.5 liters of brew uses 45 grams of beans. How many grams of beans are needed for 7 liters of brew?

Show answer

Answer: C — 126

The constant of proportionality is k=452.5=18k = \dfrac{45}{2.5} = 18 grams per liter. For 7 liters, 18×7=12618 \times 7 = 126 grams.

Question 26

Gym A charges $36 per month with no visit fee. Gym B charges $12 per month plus $3 per visit. After how many visits in a month is the total cost the same at both gyms?

Show answer

Answer: C — 8

Set 36=12+3v36 = 12 + 3v. Then 24=3v24 = 3v, so v=8v = 8 visits.

Question 27

The formula T=6h+9T=6h+9 relates the variables TT and hh. Which expression gives hh in terms of TT?

Show answer

Answer: C — T−96\dfrac{T-9}{6}

Subtracting 9 gives T−9=6hT-9=6h, and dividing by 6 gives h=T−96h=\dfrac{T-9}{6}.

Question 28

In a class, 56\dfrac{5}{6} of the students attended, and 35\dfrac{3}{5} of those who attended submitted homework. What fraction of the whole class both attended and submitted homework?

Show answer

Answer: A — 12\dfrac{1}{2}

56×35=12\dfrac{5}{6}\times\dfrac{3}{5}=\dfrac{1}{2} of the class submitted homework.

Question 29

-8-6-4-20246810ABC

On the number line above, what is the distance, in units, between the midpoint of AB‾\overline{AB} and point CC?

Show answer

Answer: C — 10

Midpoint of ABAB: −6+22=−2\dfrac{-6+2}{2} = -2. Distance from −2-2 to 8 is 10.

Question 30

A team builds jersey codes in three stages: choose 1 of 4 color patches, then 1 of 7 logos, then a number from 1 through 12. How many different jersey codes are possible?

Show answer

Answer: C — 336

Multiply the stage counts: 4×7×12=3364\times7\times12=336.

Question 31

Parallel lines mm and nn are cut by a transversal. A 67∘67^\circ angle and angle xx are same-side interior angles. What is xx?

Enter your answer in the space.

✓ Correct✗ Not correct
Show answer

Answer: 113

Same-side interior angles are supplementary, so x=180−67=113x=180-67=113.

Question 32

A printing press produces color pages and black-and-white pages in the ratio 2:72{:}7. In one run, 63 black-and-white pages are printed. What is the total number of pages printed in that run?

Show answer

Answer: B — 81

Black-and-white pages are 7 parts, so each part is 63÷7=963\div7=9 pages. Color pages are 2×9=182\times9=18, and the total is 18+63=8118+63=81.

Question 33

The table shows field-day event choices.

RelaySprintTotalGirls12820Boys151025Total271845

Of the girls, what percent participated in the Relay?

Show answer

Answer: C — 60%60\%

Among the 20 girls, 12 chose Relay, so 1220=60%\dfrac{12}{20}=60\%.

Question 34

At a track meet, Runner A finishes a loop every 40 seconds and Runner B every 60 seconds. If they start together, after how many seconds do they next finish a loop at the same time?

Show answer

Answer: C — 120

That time is LCM(40,60)\mathrm{LCM}(40,60). 40=23×540=2^{3}\times5 and 60=22×3×560=2^{2}\times3\times5, so the LCM is 23×3×5=1202^{3}\times3\times5=120.

Question 35

r = 15 m

Note: Figure not drawn to scale.

In the figure above, two concentric circles have radii 15 meters and 9 meters. The shaded ring is the region between the circles. What is the area of the shaded ring, in square meters?

Show answer

Answer: C — 144π144\pi

The shaded area is the difference of the two circle areas: π(15)2−π(9)2=225π−81π=144π\pi(15)^2 - \pi(9)^2 = 225\pi - 81\pi = 144\pi.

Question 36

If 3(a+4)=2a+313(a+4)=2a+31, what is the value of a−7a-7?

Show answer

Answer: C — 12

First distribute on the left: 3(a+4)=3a+123(a+4)=3a+12. Then 3a+12=2a+313a+12=2a+31, so a=19a=19. The requested value is a−7=19−7=12a-7=19-7=12.

Question 37

A grocery lists three bulk-rice prices: 2 pounds for $3.00, 5 pounds for $7.50, and 8 pounds for $13.60. Which statement correctly decides whether cost is proportional to weight for these prices?

Show answer

Answer: A — Cost is not proportional to weight, because 13.608\dfrac{13.60}{8} is not equal to 3.002\dfrac{3.00}{2}.

Proportionality requires a constant unit price. The first two bags are $1.50 per pound, but the 8-pound bag is $1.70 per pound, so the relationship is not proportional.

Question 38

Which of the following is closest to 70\sqrt{70}?

Show answer

Answer: B — 8.4

82=648^2=64 and 92=819^2=81, so 70\sqrt{70} is a little more than 8. Squaring nearby choices gives 8.12=65.618.1^2=65.61 and 8.42=70.568.4^2=70.56. Because 70.56 is nearer to 70 than 65.61 is, 8.4 is closest to 70\sqrt{70}.

Question 39

The table shows the grade levels of students who volunteered for a school committee. One volunteer is chosen at random.

GradeNumber ofvolunteers6th47th68th5

What is the probability that the volunteer chosen is a 6th or 7th grader?

Show answer

Answer: C — 23\dfrac{2}{3}

There are 4+6+5=154+6+5=15 volunteers and 5 eighth graders, so P(not 8th)=1−515=1015=23P(\text{not 8th})=1-\dfrac{5}{15}=\dfrac{10}{15}=\dfrac{2}{3}.

Question 40

Five numbers have a mean of 16. Four of the numbers are 10, 14, 18, and 20. If the unknown number is increased by 5, what is the new mean of the five numbers? Enter your answer in the space.

✓ Correct✗ Not correct
Show answer

Answer: 17

A mean of 16 for 5 numbers gives an original total of 80. The unknown number is 80 − (10 + 14 + 18 + 20) = 18. Increasing that number by 5 increases the total to 85, so the new mean is 85 / 5 = 17.

Question 41

A student has scores of 82, 76, and 90 on three tests. What is the minimum score she needs on a fourth test so that her average for all four tests is at least 85?

Show answer

Answer: C — 92

The condition is 82+76+90+x4≥85\dfrac{82+76+90+x}{4}\ge 85, so 248+x≥340248+x\ge 340 and x≥92x\ge 92. The minimum score is 92.

Question 42

Machine A packs 7 boxes every 4 minutes. Machine B packs 11 boxes every 5 minutes. If both machines run at these constant rates for 1 hour, how many boxes do they pack in all?

Show answer

Answer: C — 237

Machine A packs 74×60=105\dfrac{7}{4}\times 60=105 boxes per hour. Machine B packs 115×60=132\dfrac{11}{5}\times 60=132 boxes per hour. Together they pack 105+132=237105+132=237 boxes.

Question 43

A warehouse audit uses the expression (−2)4−32×(−1)+(−5)(-2)^4-3^2\times(-1)+(-5). What is the value of the expression?

Show answer

Answer: C — 20

(−2)4=16(-2)^4=16 and 32×(−1)=−93^2\times(-1)=-9, so 16−(−9)+(−5)=16+9−5=2016-(-9)+(-5)=16+9-5=20.

Question 44

Which expression is equivalent to (2n+5)(n−3)+4n(2n+5)(n-3)+4n?

Show answer

Answer: B — 2n2+3n−152n^2+3n-15

Expand: (2n+5)(n−3)=2n2−6n+5n−15=2n2−n−15(2n+5)(n-3)=2n^2-6n+5n-15=2n^2-n-15. Adding 4n4n gives 2n2+3n−152n^2+3n-15.

Question 45

A price decreases from 120 dollars to 90 dollars. What is the percent decrease? Enter your answer in the space.

✓ Correct✗ Not correct
Show answer

Answer: 25

The decrease is 30, and 30/120=0.2530/120=0.25, so the percent decrease is 25%25\%.

Question 46

18 in.6 in.12 in.4 in.4 in.

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?

Show answer

Answer: B — 56

The original rectangle has perimeter 2(18+10)=562(18+10)=56. Cutting out a corner removes lengths 6 and 4 from the outside boundary but adds interior lengths 6 and 4, so the perimeter remains 56.

Question 47

Job A pays $480 per week plus a 4%4\% commission on weekly sales ss (in dollars). Job B pays $300 per week plus a 7%7\% commission on the same sales amount ss. For what value of ss do the two jobs pay the same amount for the week?

Show answer

Answer: C — 6000

Set 480+0.04s=300+0.07s480+0.04s=300+0.07s. Subtract 0.04s0.04s: 480=300+0.03s480=300+0.03s. Subtract 300: 180=0.03s180=0.03s. Divide: s=6000s=6000.

Question 48

Available Items

Clothing typeAvailable colorsT-shirtred, blue, greenHoodiered, blackJacketblue, black, white

A student chooses one clothing type and one available color from the table, with each listed type-color pair equally likely. What is the probability that the chosen item is not red and is not a jacket?

Show answer

Answer: B — 3/83/8

There are 3+2+3=83+2+3=8 possible type-color pairs. The pairs that are not red and not jackets are T-shirt blue, T-shirt green, and hoodie black, so the probability is 3/83/8.

Question 49

One car travels 280 miles on 8 gallons of fuel. Which value equals that car’s fuel use in gallons per 100 miles?

Show answer

Answer: C — 207\dfrac{20}{7}

Gallons per 100 miles is 8280×100=800280=207\dfrac{8}{280}\times 100 = \dfrac{800}{280} = \dfrac{20}{7}. The reciprocal 2808\dfrac{280}{8} is miles per gallon.

Question 50

Four musical note-duration ratios are written as fractions. Which one has a repeating decimal form?

Show answer

Answer: D — 512\dfrac{5}{12}

512\dfrac{5}{12} has denominator primes 2×32\times3 after simplifying, so the factor of 3 forces a repeating decimal. The others have only 2 and/or 5 in the denominator.

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 SHSAT practice test · Everything on the SHSAT

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.

SHSAT™ and Specialized High Schools Admissions Test™ are trademarks of the New York City Department of Education.

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