Full-Length SSAT Upper Level Math Practice Test

Taking a Full-length SSAT Upper-Level Math practice test is the best way to help you get familiar with the test format and feel more confident. Not only will this help you measure your exam readiness and solidify the concepts you’ve learned, but it is the best way to simulate test day.
To help you get the best out of this complete and realistic SSAT Upper-Level Math practice test and prepare your mind and body for the actual test, we recommend that you treat this practice test as a real test. Prepare scratch papers, a pencil, a timer, and a calculator and take the test in one sitting and follow the time limits to the minute.
Take the following full-length SSAT Upper-Level Math practice test to simulate the test day experience. After you’ve finished, score your tests using the answer keys.
Good luck!

The Absolute Best Book to Ace the SSAT Upper Level Math Test

Time to refine your Math skill with a practice test

Take a REAL ISEE Upper-Level Mathematics test to simulate the test day experience. After you’ve finished, score your test using the answer key.

Before You Start

• You’ll need a pencil, a calculator, and a timer to take the test.
• It’s okay to guess. You won’t lose any points if you’re wrong. So be sure to answer every question.
• After you’ve finished the test, review the answer key to see where you went wrong.
• Calculators are permitted for HiSET Math Test.
• Use the answer sheet provided to record your answers.
• The HiSET Mathematics test contains a formula sheet, which displays formulas relating to geometric measurement and certain algebra concepts. Formulas are provided to test- takers so that they may focus on application, rather than the memorization, of formulas.
• For each multiple-choice question, there are five possible answers. Choose which one is best.

Good Luck!

Best SSAT Upper Level Math Prep Resource for 2022

SSAT Upper Level Math Practice Test

SSAT Upper Level Practice Test
Quantitative Reasoning

1- How many tiles of \(6 cm^2\) are needed to cover a floor of dimension \(9 cm\) by \(36 cm\)?

A. 11

B. 20

C. 36

D. 42

E. 54

2- A school wants to give each of its 31 top students a football ball. If the balls are in boxes of four, how many boxes of balls do they need to purchase?

A. 4

B. 5

C. 6

D. 7

E. 8

3- If \(\frac{35}{A} + 2=7\), then \(35+A=\) ?

A. 6

B. 12

C. 25

D. 42

E. 46

4- A shaft rotates 400 times in 6 seconds. How many times does it rotate in 15 seconds?

A. 950

B. 1000

C. 1125

D. 1250

E. 1300

5- Which of the following statements is correct, according to the graph below?

A. Number of books sold in April was twice the number of books sold in July.

B. Number of books sold in July was less than half the number of books sold in May.

C. Number of books sold in June was half the number of books sold in April.

D. Number of books sold in July was equal to the number of books sold in April plus the number of books sold in June.

E. More books were sold in July than in April.

6- Jack earns $756 for his first 54 hours of work in a week and is then paid 1.5 times his regular hourly rate for any additional hours. This week, Jack needs $924 to pay his rent, bills, and other expenses. How many hours must he work to make enough money this week?

A. 40

B. 48

C. 55

D. 62

E. 68

7- What is the value of the sum of the tens and thousandths in number \(6,684.76342\)?

A. 5

B. 9

C. 11

D. 14

E. 16

8- If \(160 \%\) of a number is 80, then what is the \(70 \%\) of that number?

A. 35

B. 50

C. 60

D. 70

E. 85

9- \(18.236÷0.004\)?

A. 455.0059

B. 455.09

C. 455.59

D. 455.9

E. 4559

10- The average weight of 12 girls in a class is 55 kg and the average weight of 21 boys in the same class is 59 kg. What is the average weight of all the 33 students in that class?

A. 50

B. 51.28

C. 55.88

D. 56.9

E. 57.54

11- If \(3≤x<6\), what is the minimum value of the following expression? \(3x+5\)

A. 5

B. 8

C. 10

D. 14

E. 23

12- If \(x∎y=\sqrt{x^2+y}\), what is the value of \(6∎13\)?

A. \(\sqrt{22}\)

B. 5

C. 6

D. 6.5

E. 7

13- \(\frac{2 \frac{2}{3} + \frac{1}{6}}{3 \frac{3}{4} – \frac{11}{4}}\) is approximately equal to.

A. 1.33

B. 2.6

C. 2.83

D. 3.33

E. 6.67

14- There are two equal tanks of water. If \(\frac{1}{8}\) of a tank contains 350 liters of water, what is the capacity of the two tanks of water together?

A. 1500

B. 2600

C. 3800

D. 4950

E. 5600

15- David’s current age is 58 years, and Ava’s current age is 10 years old. In how many years David’s age will be 3 times Ava’s age?

A. 4

B. 6

C. 8

D. 10

E. 14

16- Four-kilogram apple and four-kilogram orange cost $26.4. If a one-kilogram apple costs $4.6 how much does one-kilogram orange cost?

A. $1.5

B. $2

C. $2.5

D. $3.5

E. $4

17- What is the value of \(x\) in the following figure?

A. 150

B. 145

C. 125

D. 115

E. 105

18- What is the answer of\( 9.5÷0.25\)?

A. 38

B. 40

C. 48

D. 52

E. 60

19- Michelle and Alec can finish a job together in 140 minutes. If Michelle can do the job by herself in 7 hours, how many minutes does it take Alec to finish the job?

A. 180

B. 190

C. 195

D. 210

E. 220

20- A football team won exactly \(60\%\) of the games it played during the last session. Which of the following could be the total number of games the team played last season?

A. 11

B. 16

C. 19

D. 23

E. 35

21- What is the slope of a line that is perpendicular to the line \(8x-4y=24\)?

A. \(-2\)

B. \(-\frac{1}{2}\)

C. 4

D. 12

E. 14

22- A cruise line ship left Port A and traveled 7 miles due west and then 24 miles due north. At this point, what is the shortest distance from the cruise to port A?

A. 10 miles

B. 15 miles

C. 20 miles

D. 25 miles

E. 30 miles

23- The Jackson Library is ordering some bookshelves. If \(x\) is the number of bookshelves the library wants to order, which each costs $200 and there is a one-time delivery charge of $600, which of the following represents the total cost, in the dollar, per bookshelf?

A. \(200x+600\)

B. \(2100+600x\)

C. \(\frac{200x+600}{100}\)

D. \(\frac{200x+600}{x}\)

E. \(200x-600\)

24- The sum of four different negative integers is \(-40\). If the smallest of these integers is \(-9\), what is the largest possible value of one of the other five integers?

A. \(-14\)

B. \(-16\)

C. \(-18\)

D. \(-19\)

E. \(-21\)

25- The width of a box is one-third of its length. The height of the box is one-third of its width. If the length of the box is 36 cm, what is the volume of the box?

A. 95 cm\(^3\)

B. 192 cm\(^3\)

C. 238 cm\(^3\)

D. 1008 cm\(^3\)

E. 1980 cm\(^3\)

26- When number 87,436 is divided by 287, the result is closest to?

A. 3

B. 30

C. 305

D. 350

E. 400

27- If the perimeter of the following figure be 30, what is the value of \(x\)?

A. 2

B. 3

C. 6

D. 9

E. 12

28- There are 14 marbles in bag A and 22 marbles in bag B. If the sum of the marbles in both bags will be shared equally between two children, how many marbles bag A has less than the marbles that each child will receive?

A. 2

B. 3

C. 4

D. 5

E. 6

29- If Jason’s mark is k more than Alex’s, and Jason’s mark is 20, which of the following can be Alex’s mark?

A. \(20+k\)

B. \(k-20\)

C. \(\frac{k}{20}\)

D. 20k

E. \(20-k\)

30- Which of the following expression is not equal to 8?

A. \(16×\frac{1}{2}\)

B. \(40×\frac{1}{5}\)

C. \(4×\frac{8}{4}\)

D. \(6×\frac{8}{6}\)

E. \(8×\frac{1}{8}\)

31- The price of a sofa is decreased by \(50\%\) to $405. What was its original price?

A. $480

B. $520

C. $560

D. $600

E. $810

32- \(860-6 \frac{8}{13}=\)?

A. \(842 \frac{7}{13}\)

B. \(842 \frac{8}{13}\)

C. \(850 \frac{1}{15}\)

D. \(851 \frac{8}{15}\)

E. \(853 \frac{5}{13}\)

33- A driver rests one hour and 5 minutes for every 8 hours driving. How many minutes will he rest if he drives 32 hours?

A. 3 hours and 36 minutes

B. 4 hours and 12 minutes

C. 4 hours and 45 minutes

D. 5 hours and 36 minutes

E. 6 hours

34- To paint a wall with the area of 48m\(^2\), how many liters of paint do we need if each liter of paint is enough to paint a wall with the dimension of 96 cm\(×\)100 cm?

A. 50

B. 100

C. 150

D. 200

E. 250

35- What is the missing term in the given sequence? 3, 5, 9, 17, 33, _, 129

A. 56

B. 65

C. 73

D. 85

E. 90

Questions 11 to 12 are based on the following graph

A library has 960 books that include Mathematics, Physics, Chemistry, English, and History.
Use the following graph to answer questions 11 to 12.

36- What is the product of the number of Mathematics and number of English books?

A. 17,640

B. 26,460

C. 41,472

D. 56,124

E. 59,324

37- What are the values of angle \(α\) and \(β\) respectively?

A. \(90^\circ , 54^\circ\)

B. \(120^\circ , 36^\circ\)

C. \(120^\circ , 45^\circ\)

D. \(108^\circ , 54^\circ\)

E. \(108^\circ , 45^\circ\)

38- Find the perimeter of the following shape.

A. 21

B. 22

C. 23

D. 24

E. 25

39- If \(a×b\) is divisible by 4, which of the following expression must also be divisible by 4?

A. \(a+b\)

B. \(3a-b\)

C. \(a-3b\)

D. \(\frac{a}{3.5b}\)

E. \(4×a×b\)

40- The capacity of a red box is \(50\%\) bigger than the capacity of a blue box. If the red box can hold 45 equal-sized books, how many of the same books can the blue box hold?

A. 9

B. 15

C. 21

D. 25

E. 30

41- If the area of the following rectangular ABCD is 200, and E is the midpoint of AB, what is the area of the shaded part?

A. 25

B. 50

C. 100

D. 120

E. 125

42- There are 48.3 liters of gas in a car fuel tank. In the first week and second week of April, the car uses 7.96 and 18.21 liters of gas respectively. If the car was parked in the third week of April and 16.47 liters of gas will be added to the fuel tank, how many liters of gas are in the fuel tank of the car?

A. 21.41

B. 25.9

C. 27

D. 38.6

E.71.61

43- If \(6x+y=36\) and \(x-z=9\), what is the value of \(x\)?

A. 0

B. 5

C. 10

D. 20

☐E. it cannot be determined from the information given

44- If \(5y+6<51\), then \(y\) could be equal to?

A. 9

B. 11

C. 11.5

D. 12

E. 14

45- What is the average circumference of figure A and area of figure B? (\(π=3\))

A. 54

B. 62

C. 75

D. 80

E. 83

46- In the following figure, point \(Q\) lies on line \(n\), what is the value of y if \(x = 25\)?

A. 15

B. 25

C. 40

D. 45

E. 55

47- Which of the following could be the value of \(x\) if \(\frac{2}{7}+x>3\)?

A. \(\frac{1}{2}\)

B. \(\frac{3}{5}\)

C. \(\frac{4}{5}\)

D. \(\frac{4}{3}\)

E. \(\frac{10}{3}\)

48- A number is chosen at random from 8 to 17. Find the probability of not selecting a composite number. (A composite number is a number that is divisible by itself, 1 and at least one other whole number)

A. \(\frac{1}{25}\)

B. \(\frac{3}{10}\)

C. \(\frac{9}{25}\)

D. 3

E. 4.25

49- \(432÷4=\)?

A. \(\frac{400}{4}×\frac{30}{4}×\frac{2}{4}\)

B. \(400+\frac{30}{4}+\frac{2}{4}\)

C. \(\frac{400}{4}+\frac{30}{4}+\frac{2}{4}\)

D. \(\frac{400}{4}÷\frac{30}{4}÷\frac{2}{4}\)

E. \(\frac{4}{4}+\frac{3}{4}+\frac{2}{4}\)

50- If a gas tank can hold 36 gallons, how many gallons does it contain when it is \(\frac{4}{6}\) full?

A. 10

B. 12.5

C. 15

D. 18

E. 24

The Best Books to Ace the SSAT Upper Level Math Test

Answers and Explanations