SHSAT Math Practice Test – Full Length Exam

Last Updated on July 10, 2026

SHSAT Math Practice Test – Full-Length Exam 2026. The Math section is the second section on the test. It contains 57 questions and accounts for half of your total points on the SHSAT. The suggested total time for the section is 90 minutes, or 1 hour and 30 minutes.

Based on the latest information available from the New York City Department of Education, the math section will include:

SHSAT Math Practice Test - Full Length Exam

While you have likely seen most, if not all, of these concepts in school, you need to approach SHSAT math differently from how you would approach other math. You don’t necessarily have to do the math differently from how you would in class; it’s just that you have to do it very methodically. You’ll be timed during the test, so you’ll want to use your time wisely.

SHSAT Math Practice Test – Full-Length Exam

Part 2—Mathematics
57 QUESTIONS—SUGGESTED
TIMING: 90 MINUTES

1) A certain test consists of multiple-choice questions and essay questions in the ratio of 5:2. If the test contains 6 essay questions, what is the total number of questions on the test?

2) In a scale drawing of a rectangular patio, the length is 14 inches and the width is 10 inches. In the drawing, 4 inches represents 5 yards. What is the length of the actual patio, in yards?

3) Carin opened a money market account with a deposit of $3,000. This account earns 2% simple interest annually. How many years will it take for her $3,000 deposit to earn $420 in interest, assuming she does not withdraw any of the money?

4) If 3x + 8 = 44, what is the value of x ?

5) 4 - 6 ÷ | 2  + (-33) × 2 \frac13

What is the value of the expression shown above?

6) The sum of 6 consecutive odd numbers is 36. What is the difference between the highest and the lowest of these numbers?

7) The population of a particular bacteria doubles in size every 19 hours. If the population is 100 at 2:15 p.m. on a given day, at what time of day will the bacteria have doubled twice?

8) In March, the electricity used in New York was 5,000,000 watts. In April, the number of watts used was 4,000,000. By what percentage did the electricity usage decrease from March to April?

9) Jin completed 8 pages in his math workbook and 12 pages in his science workbook. This is 25% of the total number of pages in both workbooks together. If there are 32 pages in his math workbook, how many pages are there in his science workbook?

10) Angle A and angle B are supplementary. If the measure of angle B is one-third the measure of angle A, what is the measure of angle B?

11) Joe answered 37 out of 50 questions correctly on his history exam. What percentage of the questions did he get wrong?

12) David is now 4 years more than twice the age of Henry. If Henry will be 18 in 3 years, how old was David 2 years ago?

13) What is the least common multiple of 8, 32, and 48 ?

14) If n is an even integer that is greater than −3.75, what is the least possible value of n ?

15) Suppose point Z is halfway between points W and X on a standard number line, and point X is halfway between points Z and Y. Where is W if Z is located at \frac{1} {3} and Y is located at \frac{11} {3} ?

16) Jennifer has $200 in her checking account. She makes $6.48 per hour babysitting her cousins. If she wants to buy a guitar that costs $310.04 (including tax), how many hours must she work?

17) What is the average of all the even numbers in the set {2, 3, 4, . . . , 12, 13, 14} ?

18) \frac{n} {100} = \frac{x} {y}

In the equation above, if n = 30 and y = 300, what is the value of x ?

19) A bus travels 1,070 miles from Jacksonville, FL, to Syracuse, NY. The bus covers the first 310 miles in 5 hours. If the bus continues to travel at this rate, how many more hours will it take to reach Syracuse? Round your answer to the nearest whole hour.

20) Daniel is packing crates of tires for storage in a warehouse. Each crate can hold 9 tires. If Daniel has 469 tires to store and fills all but the last crate, how many full crates of tires will Daniel have to put in the warehouse?

21) There are 250 giggles in one laugh and 3 laughs in a burst. How many giggles are in 2 bursts?

22)

According to the table above, salami made up what percentage of the total number of pounds of meat sold at the deli counter?

23) If x + y = 12 and x = 15, then what is -\frac xy

24)

What is the circumference of the circle inscribed in the square above?

25)

What is the mean price paid by the 100 customers in the table above?

26) Isabel has 10 boards that are x meters long. She has 5 boards that are 2x meters long. She also has 4 boards that measure 3 meters, 6 meters, 9 meters, and 13 meters, respectively. If she were to lay all her boards in a straight line with no gaps between them, the boards would measure 271 meters. What is the value of x ?

27) Between which two consecutive integers is the fraction \frac{43} {8}

28) \frac{72} {7} = \frac{12} {x}

What value of x makes the equation above true?

29) ucia speed walks 3 kilometers in \frac23 of an hour. At that rate, how many meters does she speed walk per minute?

30) Which of the following numbers does not have factors that include the smallest factor (other than 1) of 119 ?

31) In a pond of 1,600 fish, 25% of the fish are trout. The remaining fish are bass. How many fewer trout are there than bass?

32)

If AD = 20 centimeters, DC = 15 centimeters, BC = 7 centimeters, and AB = 24 centimeters, what is the area of quadrilateral ABCD?

33) The side length of square A is shorter than the side length of square B by 5 inches. The perimeter of square A is 100 inches. What is the difference, in square inches, between the area of square A and the area of square B?

34) On Monday, 100 people played golf at a certain golf course. The pro shop sold 14 dozen golf balls that day. At this rate, approximately how many dozens of golf balls can the pro shop expect to sell on Tuesday if 150 people are scheduled to play?

35) Larissa spends 3 times as many hours reading as Tom does, and Nela spends half as many hours as Tom does. If all 3 people read for a total of 18 hours, for how many hours did Tom read?

36) A survey asked students what types of exercise they regularly do. Based on the results, the following statements are all true.

  • 40 students jog
  • 36 students lift weights
  • 12 students both jog and lift weights
  • 16 students neither jog nor lift weights

How many students were surveyed?

37) ( frac{3} {4} - frac{2} {7}) ÷ frac{1} {4} =

38) Bob, Ted, and Carol are all splitting a reward they received for returning someone’s wallet. If Bob and Ted each take one-quarter of the reward, and Carol gets $40, how much was the reward in total?

39) For what value of x does 6(8 − x) = 3(x − 2) ?

40) A can contains 40 chips: 10 each of red and blue, 12 white, and the remaining black. If Susan were to remove 3 black and 2 red chips, what is the probability that the next one she removes is black?

41) 11 + 4x) − (2 − x) =

42)

If 5,000 children were surveyed, how many have bedtimes that are 10:30 p.m. or earlier, according to the circle graph above?

 

43) On Friday, Marvin sold 4 suits that had a mean sale price of $125. On Saturday, he sold 6 suits that had a mean sale price of $140. What was the mean sale price, to the nearest dollar, for all 10 of the suits he sold on Friday and Saturday?

44)

P is the center of the circle shown above. AB is a diameter. The perimeter of rectangle ABCD is 72 cm. PQ is a radius, and Q is on CD. What is the circumference of the circle?

45) The sum of the numbers m, n, and p is 24. The ratio of m to n is 2:5, and the ratio of n to p is 5:3. What is the value of n ?

46)

In the figure above, the measure of ∠BGC is 10° less than the measure of ∠CGD, and the measure of ∠DGE is 25° more than the measure of ∠EGF. What is the measure of ∠DGE?

47) Burt has b action figures, and Cho has c action figures. If Burt gives 4 action figures to Cho, Burt will have twice as many action figures as Cho. Which equation shows the relationship between b and c ?

48) The probability of picking a red marble from a bag of 30 red and blue marbles is \frac{1}{5} . How many blue marbles must be removed from the bag to increase the probability to \frac{1}{4} ?

49) How many numbers in the set of consecutive integers from 1 to 99, inclusive, have 3 as a factor but do not have 6 as a factor?

50) At summer camp, campers are randomly assigned to one of 25 cabins and one of 4 cafeterias. Josef likes 8 of the cabins and 2 of the cafeterias. What is the probability that he is assigned to both a cabin and a cafeteria that he likes?

51)

In the figure above, point A is both a vertex of square ABCD and the center of a circle that contains arc BD. If the area of square ABCD is 100 square meters, what is the area of the shaded region?

52) Nick and Alex worked on a paper together. If Nick wrote \frac{2}{7} of the paper and Alex wrote 20 pages, then what was the total length of the paper?

53) Margo bowled a mean of 110 points per game in her first 4 games. In her 5th game, she bowled 160 points. What is her mean score for the first 5 games?

54) A mixed box of frozen yogurt bars contains exactly 8 strawberry bars. The probability of choosing a strawberry bar from the box is \frac25 . How many of the yogurt bars in the box are not strawberry?

55) If x = 2 and 2x(2y − x) = 16, what is the value of y ?

56) A painter uses a certain shade of green paint made from \frac13 ounces of blue paint and 1 \frac{2}{3} ounces of yellow paint. What is the ratio of blue paint to yellow paint in this shade of green?

57) N belongs to the set of rational numbers {0.4, 0.5, 1.1, 2.0, 3.5}. If \frac{4.9N}{1.4} is an integer, what is N?

Your score is

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