# Full-Length ISEE Middle Level Math Practice Test

Taking a full-length ISEE Middle-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 ISEE Middle-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 ISEE Middle-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 ISEE Middle-LevelMath Test

Time to refine your Math skill with a practice test

Take a REAL ISEE Middle-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.
• 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!

## ISEE Middle-Level Practice TestQuantitative Reasoning

37 questions
Total time for this section: 35 Minutes
Calculators are not allowed at the test.

1- Jim purchased a table for $$15\%$$ off and saved $18. What was the original price of the table? A.$90

B. $100 C.$115

D. $120 2- $$981,364,454×0.0000001?$$ A. $$981.364454$$ B. $$98.1364454$$ C. $$9813.64454$$ D. $$9.81364454$$ 3- Which of the following shows the numbers in descending order? A. $$\frac{1}{3},\frac{1}{8},\frac{1}{2},\frac{3}{5}$$ B. $$\frac{1}{2},\frac{1}{3},\frac{3}{5},\frac{1}{8}$$ C. $$\frac{3}{5},\frac{1}{2},\frac{1}{3},\frac{1}{8}$$ D. $$\frac{1}{8},\frac{3}{85},\frac{1}{2},\frac{1}{3}$$ 4- What is the value of $$x$$ in the following equation? $$5^x=625$$ A. 2 B. 3 C. 4 D. 5 5- If $$f=4x-y$$ and $$g=-2x-2y$$, what is $$f-2g$$? A. $$4x-5y$$ B. $$6x-3y$$ C. $$8x+3y$$ D. $$5x-y$$ 6- Solve.$$\frac{-45 × 0.8}{4}$$ A. $$-9$$ B. $$-6$$ C. $$6$$ D. $$9$$ 7- A$54 shirt now selling for $43.2 is discounted by what percent? A. $$20\%$$ B. $$30\%$$ C. $$40\%$$ D. $$60\%$$ 8- What is the value of x in the following figure? A. $$147^\circ$$ B. $$155^\circ$$ C. $$165^\circ$$ D. $$172^\circ$$ 9- The area of a circle is 36 $$π$$. What is the circumference of the circle? A. 6 π B. 10 π C. 12 π D. 14 π 10- Round off the result of $$2.21 × 6.5$$ to the nearest tenth? A. 15 B. 17 C. 13.06 D. 14.4 11- The score of Emma was half as that of Ava and the score of Mia was twice that of Ava. If the score of Mia was 80, what is the score, Emma? A. 15 B. 18 C. 20 D. 30 12- The perimeter of the trapezoid below is 60. What is its area? A. 198 $$cm^2$$ B. 178 $$cm^2$$ C. 168 $$cm^2$$ D. 156 $$cm^2$$ 13- In four successive hours, a car travels 50 km, 48 km, 44 km, and 52 km. In the next four hours, it travels with an average speed of 50 km per hour. Find the total distance the car traveled in 8 hours. A. 324 km B. 386 km C. 392 km D. 400 km 14- What is the mean in the following set of numbers? 12,22,34,46,52,68,72,86 A. 46.2 B. 40.5 C. 45.4 D. 49 15- Two-third of 36 is equal to $$\frac{4}{9}$$ of what number? A. 28 B. 36 C. 48 D. 54 16- What is the value of $$x$$ in the following equation? $$-2(2x+3)=3(4-2x)$$ A. 12 B. 9 C. 6.2 D. 5.5 17- Find $$\frac{1}{3}$$ of $$\frac{3}{4}$$ of $$240$$? A. 72 B. 60 C. 54 D. 48 18- The ratio of boys and girls in a class is 6:8. If there are 70 students in the class, how many more boys should be enrolled to make the ratio 1:1? A. 18 B. 12 C. 10 D. 8 19- The price of a laptop is decreased by $$20\%$$ to $$420$$. What is its original price? A.$496

B. $482 C.$485

D. $525 20- A company pays its employee $$6,500$$ plus $$3\%$$ of all sales profit. It is all sold profit, which of the following represents the employee’s revenue? A. $$0.03x$$ B. $$0.97x-6,500$$ C. $$0.03x+6,500$$ D. $$0.97x+6,500$$ 21- Car A uses 7-liter petrol per 100 kilometers; car B use 9-liter petrol per 100 kilometers. If both cars drive 300 kilometers, how much more petrol does car B use? A. 12 B. 10 C. 6 D. 4 22- What is the value of $$x$$ in the following figure? A. 150 B. 140 C. 125 D. 105 23- What is the area of a square whose diagonal is 10? A. 16 B. 32 C. 40 D. 50 24- What is value of $$-42-(-73)$$? A. $$31$$ B. $$-105$$ C. $$-39$$ D. $$91$$ 25- Which of the following is a correct statement? A. $$\frac{4}{5}>0.81$$ B. $$12\%=\frac{1}{5}$$ C. $$4<\frac{6}{2}$$ D. $$\frac{8}{9}>0.8$$ Quantitative Comparisons Direction: Questions 26 to 37 are Quantitative Comparisons Questions. Using the information provided in each question, compare the quantity in column A to the quantity in Column B. Choose on your answer sheet grid A if the quantity in Column A is greater B if the quantity in Column B is greater C if the two quantities are equal D if the relationship cannot be determined from the information given 26- ### Column A ### Column B $$5+5×7-4$$ $$4+6×6-6$$ 27- $$y=3x+18$$ ### Column A ### Column B The value of $$x$$ when $$y=9$$ $$-4$$ 28- ### Column A ### Column B $$\sqrt{25}+\sqrt{25}$$ $$\sqrt{100}$$ 29- The average age of Joe, Michelle, and Nicole is 30. ### Column A ### Column B The average age of Joe and Michelle The average age of Michelle and Joe 30- ### Column A ### Column B $$\sqrt{144-121}$$ $$\sqrt{144}-\sqrt{121}$$ 31- A right cylinder with radius 5 inches has volume $$80π$$ cubic inches. ### Column A ### Column B The height of the cylinder 3 inches 32- $$x$$ is an integer greater than zero. ### Column A ### Column B $$\frac{2}{x}+x$$ 5 33- $$\frac{2}{5}<x<\frac{5}{9}$$ ### Column A ### Column B $$x$$ $$\frac{5}{8}$$ 34- ### Column A ### Column B $$\frac{x^3}{3}$$ $$(\frac{x}{3})^3$$ 35- The average of 5, 6, and $$x$$ is 6. ### Column A ### Column B $$x$$ average of $$x,x+3,x+1,-x$$ 36- $$a$$ and $$b$$ are real numbers. $$a>b$$ ### Column A ### Column B $$|a-b|$$ $$|b-a|$$ 37- $$4x^3-80=17$$ $$63-4y=-13$$ ### Column A ### Column B $$x$$ $$y$$ 38- In a bundle of 75 pencils,33 are red and the rest are blue. About what percent of the bundle is composed of blue pencils? ☐A. $$62\%$$ ☐B. $$56\%$$ ☐C. $$54\%$$ ☐D. $$52\%$$ 39- If a box contains red and blue balls in ratio of 4 :6, how many red balls are there if 120 blue balls are in the box? ☐A. 80 ☐B. 60 ☐C. 30 ☐D. 10 40- $$2(\frac{3}{5}-\frac{6}{10})+2$$? ☐A. 4 ☐B. 4.5 ☐C. 2 ☐D. $$\frac{3}{2}$$ 41-What number is $$15$$ more than $$12\%$$ of $$160$$? ☐A. $$40.2$$ ☐B. $$34$$ ☐C. $$32.2$$ ☐D. $$28.2$$ 42- When twice a number is subtracted from 21 and the difference is divided by that number, the result is 5. What is the value of the number? ☐A. 10 ☐B. 8 ☐C. 3 ☐D. 6 43- What number is $$3$$ less than $$25\%$$ of $$48$$? ☐A. $$9$$ ☐B. $$11$$ ☐C. $$12$$ ☐D. $$23$$ 44- What is the difference in perimeter between a 6 cm by 5 cm rectangle and a circle with diameter of 12 cm? (π=3) ☐A. 14 cm ☐B. 12 cm ☐C. 10 cm ☐D. 9 cm 45- The price of a car was$25,000 in 2014, $21,000 in 2015 and$17,640 in 2016. What is the rate of depreciation of the price of car per year?

☐A. $$16\%$$

☐B. $$22\%$$

☐C. $$24\%$$

☐D. $$30\%$$

46- What is the value of $$x$$ in the following equation? $$(2x-3)^3=125$$

☐A. $$1$$

☐B. $$-4$$

☐C. $$2$$

☐D. $$4$$

47- $$85$$ is equal to?

☐A. $$4+(5×8)+(3×15)$$

☐B. $$(\frac{10}{4}×24)+(\frac{5}{2}×10)$$

☐C. $$((\frac{3}{2}+3)×\frac{18}{3})+25$$

☐D. $$(2×15)+(50×2)-10$$

48- If$$\frac{x}{2}=24,$$then$$\frac{5x}{8}$$ = ?

☐A. 8

☐B. 10

☐C. 20

☐D. 30

49- Which of the following is the greatest number?

☐A. $$\frac{3}{4}$$

☐B. $$\frac{7}{9}$$

☐C. $$0.86$$

☐D. $$85\%$$

50- Calculate the approximate area of the following circle.

☐A. $$1,257 cm^2$$

☐B. $$380 cm^2$$

☐C. $$285 cm^2$$

☐D. $$198 cm^2$$

51- If $$160\%$$ of a number is $$128$$, then what is the $$60\%$$ of that number?

☐A. $$48$$

☐B. $$52$$

☐C. $$70$$

☐D. $$85$$

52- When a gas tank can hold $$45$$gallons, how many gallons does it contain when it is $$\frac{3}{5}$$ full?

☐A. 21

☐B. 22

☐C. 24

☐D. 27

53-Which of the following angles can represent the three angles of an isosceles right triangle?

☐A. $$45^\circ, 90^\circ, 45^\circ$$

☐B. $$50^\circ, 50^\circ, 80^\circ$$

☐C. $$60^\circ, 60^\circ, 60^\circ$$

☐D. $$55^\circ, 35^\circ, 90^\circ$$

54- In following rectangle which statement is true?

☐A. Length of AB is smaller than BC.

☐B. The sum of all the angles equals $$360^\circ$$.

☐C. Length of AB equal to length DC.

☐D. AB is perpendicular to DC.

55- What is the missing term in the given numbers? 5,8,13,21,34,___,89

☐A. 65

☐B. 55

☐C. 51

☐D. 49

56- If a gas tank can hold 96 gallons, how many gallons does it contain when it is $$\frac{4}{6}$$ full?

☐A. 50

☐B. 58

☐C. 62.5

☐D. 64

57- The capacity of a red box is $$25\%$$ greater than a blue box. If the capacity of the red box is 40 books, how many books can be put in the blue box?

☐A. 9

☐B. 12

☐C. 24

☐D. 32

58- From last year, the price of gasoline has increased from $1.2 per gallon to$1.65 per gallon. The new price is what percent of the original price?

☐A. $$72 \%$$

☐B. $$128.5 \%$$

☐C. $$137.5 \%$$

☐D. $$152.5 \%$$

59- 315 minutes = …?

☐A. 5.25 Hours

☐B. 5.16 Hours

☐C. 6 Hours

☐D. 5.3 Hours

60- A football team had $32,000 to spend on supplies. The team spent$20,000 on new balls. New sport shoes cost $140 each. Which of the following inequalities represent how many new shoes the team can purchase? ☐A. $$140x+20,000≤32,000$$ ☐B. $$140x+20,000≥32,000$$ ☐C. $$9140x-20,000≤32,000$$ ☐D. $$140x+32,000≤20,000$$ 61- Which of the following is not a prime number? ☐A. 107 ☐B. 67 ☐C. 17 ☐D. 78 62- The width of a rectangle is $$5x$$ and its length is $$7x$$. The perimeter of the rectangle is 108. What is the value of $$x$$? ☐A. 4.5 ☐B. 5.5 ☐C. 6.5 ☐D. 10 63- Jason left a$18.00 tip on a lunch that cost $60.00, approximately what percentage was the tip? ☐A. $$12.5\%$$ ☐B. $$18\%$$ ☐C. $$25\%$$ ☐D. $$30\%$$ 64- five-kilograms apple and two-kilograms orange cost$34 If one-kilogram apple costs $5.2 how much does one-kilogram orange cost? ☐A.$3.8

☐B. $4 ☐C.$5.5

☐D. $6 65- $$(((-18)+44)×(-4))+80?$$ ☐A. 21 ☐B. 22 ☐C. 23 ☐D. 24 66- What is the perimeter of a square that has an area of 81 square inches? ☐A. 52 inches ☐B. 38 inches ☐C. 36 inches ☐D. 32 inches 67- Jason is 12 miles ahead of Joe running at 6.4 miles per hour and Joe is running at the speed of 8 miles per hour. How long does it take Joe to catch Jason? ☐A. 6.5 hours ☐B. 6 hours ☐C. 7.5 hours ☐D. 8 hours 68- At a Zoo, the ratio of lions to tigers is 6 to 4. Which of the following could NOT be the total number of lions and tigers in the zoo? ☐A. 64 ☐B. 80 ☐C. 100 ☐D. 120 69- If $$30 \%$$ of a class are girls, and $$50 \%$$ of girls play tennis, what percent of the class play tennis? ☐A. $$10 \%$$ ☐B. $$15\%$$ ☐C. $$20 \%$$ ☐D. $$40 \%$$ 70- In a class, there are triple as many girls as boys. If the total number of students in the class is 56, how many girls are in the class? ☐A. 14 ☐B. 18 ☐C. 20 ☐D. 22 71- $$[(-3)×(-12)+4]-(-2)+[3×6]÷6 = ?$$ ☐A. 36 ☐B. 37 ☐C. 41 ☐D. 45 72- Solve the following equation? $$4^x=1,024$$ ☐A. 3 ☐B. 4 ☐C. 5 ☐D. 6 73- A shaft rotates 360 times in 12 seconds. How many times does it rotate in 15 seconds? ☐A. 450 ☐B. 300 ☐C. 200 ☐D. 100 74- Solving the equation: $$6x+8=2x-12$$? ☐A. $$-3$$ ☐B. $$5$$ ☐C. $$-5$$ ☐D. $$3$$ 75- A swimming pool holds 1,260 cubic feet of water. The swimming pool is 18 feet long and 14 feet wide. How deep is the swimming pool? ☐A. 2 feet ☐B. 5 feet ☐C. 7 feet ☐D. 8 feet 76- The price of a sofa is decreased by $$20\%$$ to $$380$$. What was its original price? ☐A.$465

☐B. $475 ☐C.$565

☐D. $600 77- What is the area of the trapezoid? ☐A. 88 ☐B. 98 ☐C. 106 ☐D. 112 78- If $$20 \%$$ of A is $$40 \%$$ of B, then B is what percent of A? ☐A. $$120\%$$ ☐B. $$100\%$$ ☐C. $$80\%$$ ☐D. $$50\%$$ 79-What is the value of $$x$$ in the following equation? $$2x-(12-x)=x+20$$ ☐A. 18 ☐B. 16 ☐C. 12 ☐D. 10 80- Ella bought a pair of gloves for$11.56. She gave the clerk $15.00. How much change should she get back? ☐A.$3.15

☐B. $3.44 ☐C.$3.65

☐D. \$3.85

81- $$12.56÷0.08?$$

☐A. 138

☐B. 146

☐C. 148

☐D. 157

82- A card is drawn at random from a standard 52–card deck, what is the probability that the card is of Hearts or 10? (The deck includes 13 of each suit clubs, diamonds, hearts, and spades and four of every numbers from 1 to 10)

☐A. $$\frac{1}{3}$$

☐B. $$\frac{4}{13}$$

☐C. $$\frac{1}{4}$$

☐D. $$\frac{1}{52}$$

83- $$\frac{1}{3}+\frac{\frac{8}{10}}{\frac{6}{12}}=?$$

☐A. $$-1 \frac{12}{15}$$

☐B. $$1 \frac{1}{3}$$

☐C. $$1\frac{14}{15}$$

☐D. $$2$$

84- $$\frac{8×14}{90}$$ is closest estimate to?

☐A. 1.2

☐B. 1.1

☐C. 1.3

☐D. 1.4

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