Free Full Length ISEE Middle Level Practice Test

The correct answer is \(- \ \frac{9}{5}\)
\(\frac{- \ 45 \ × \ 0.2}{5}=\frac{- \ 45 \ × \ \frac{2}{10}}{5}\Rightarrow\)
\(\frac{\frac{- \ 45 \ × \ 2 }{10}}{5} = \frac{- \ 90}{50}\Rightarrow\)
\(- \ \frac{9}{5}\)

The correct answer is \($250\)
\(10\%\) off equals \($25\).
Let \(x\) be the original price of the table.
Then: \(10\%\) of \(x=25→0.10 \ x=25→x=\frac{25}{0.10}=250\)

The correct answer is \( 14 \ π\)
Use the formula of areas of circles.
Area of circle \(= \pi \ r^2 ⇒ 49 \ 𝜋 = 𝑟^2 ⇒ 49 = 𝑟^2 ⇒ 𝑟 = 7\)
Radius of the circle is \(7\).
Now, use the circumference formula:
Circumference \(= 2\ π \ r = 2 \ π (7) = 14 \ π\)

The correct answer is \(3\)
Method 1: \( 9=3^2→9^x=(3^2)^x=3^{2 \ x}\)
\(729=3^6→3^{2 \ x}=3^6→2 \ x=6→x=3\)
Method 2: \(9 \ x=729\)
Let’s review the choices provided:
A. \(2 \ \ \ 9^x=729→9^2=81\)
B. \(3 \ \ \ 9^x=729→9^3=729\)
C. \(4 \ \ \ 9^x=729→9^4=6,561\)
D. \(5 \ \ \ 9^x=729→9^5=59,049\)

The correct answer is \(25\%\)
Use the formula for Percent of Change:\(\frac{ New \ Value \ − \ Old Value}{old \ value} \ × \ 100\%\)
\(\frac{30 \ − \ 40}{40} \ × \ 100\% = \ – \ 25\%\) (negative sign here means that the new price is less than old price)

The correct answer is \(\frac{1}{8}, \frac{3}{8}, \frac{2}{5}, \frac{1}{2}\)
\(\frac{1}{8}=0.125\)
\(\frac{1}{2}=0.5\)
\(\frac{2}{5}=0.4\)
\(\frac{3}{8}=0.375\)

The correct answer is \(10\)
If the score of Mia was \(40\), therefore the score of Ava is \(20\).
Since, the score of Emma was half as that of Ava, therefore, the score of Emma is \(10\).

The correct amswer is \(5 \ x \ - \ 10 \ y\)
\(2 \ 𝑓=2 \ × \ (2 \ x \ - \ 6 \ y)=4 \ x \ − \ 12 \ y\)
\(2 \ 𝑓 \ + \ 𝑔=4 \ x \ − \ 12 \ y \ + \ x \ + \ 2 \ y\)
\(2 \ 𝑓 \ + \ 𝑔=5 \ x \ - \ 10 \ y\)

The correct answer is \(712,232.691 \)
\(712,232,691 \ × \ 0.001 =712,232,691\ × \frac{1}{1000}=712,232.691 \)

The correct answer is \(16\)
Let \(x \) be the number.
Write the equation and solve for \(x\).
\(\frac{1}{3 } \ × \ 12=\frac{1}{4} \times x ⇒\)
\(\frac{1 \ × \ 12}{3}= \frac{1 \ x}{4}\) , use cross multiplication to solve for \(x\).
\(4 \ × \ 12=3 \ x \ × \ 1 ⇒48=3 \ x ⇒ x=16\)

The correct answer is \(51.5\)
Mean \(= \frac{7 \ + \ 15 \ + \ 26 \ + \ 32 \ + \ 48 \ + \ 63 \ + \ 100 \ + \ 121}{8}=\frac{412}{8}=51.5\)

The correct answer is \(7.40\)
\(1.18=\frac{118}{100}\) and \(6.3=\frac{63}{10}\)
\(→1.18 \ × \ 6.3=\frac{118}{100} \ × \ \frac{63}{10}=\frac{7,434}{1000}=7.434≅7.40\)

The correct answer is \(100\)
\(\frac{5}{6}\) of \(360=\frac{5}{6} \ × \ 360=300\)
\(\frac{1}{3}\) of \(300=\frac{1}{3} \ × \ 300=100\)

The correct answer is \( - \ 2\)
Simplify: \(3 \ (x \ + \ 5) = 2 \ (x \ − \ 1) \ + \ 15\)
\(3 \ x \ + \ 15 = 2 \ x \ − \ 2 \ + \ 15\)
\(3 \ x \ + \ 15 = 2 \ x \ + \ 13\) Subtract \(2 \ x\) from both sides:
\(x \ + \ 15 = 13\) Add \(- \ 15\) to both sides:
\(x = - \ 2\)

The correct answer is \(164^\circ\)
\(x=30 \ + \ 134=164^\circ\)

The correct answer is \(148^\circ\)
Supplementary angles sum up to \(180\) degrees.
\(x \) and \(32\) degrees are supplementary angles.
Then: \(x=180^\circ \ − \ 32^\circ=148^\circ\)

The correct answer is \(21\)
The ratio of boy to girls is \(2:5\).
Therefore, there are \(2\) boys out of \(7\) students.
To find the answer, first divide the total number of students by \(7\), then multiply the result by \(2\).
\(49 \ ÷ \ 7 = 7 ⇒ 2 \ × \ 7 = 14\)
There are \(14\) boys and \(35 \ (49 \ – \ 14) \) girls.
So, \(21\) more boys should be enrolled to make the ratio \(1:1\)

The correct answer is \(495\) km
Add the first \(5\) numbers.
\(38 \ + \ 40 \ + \ 54 \ + \ 32 \ + \ 61 = 225\)
To find the distance traveled in the next \(5\) hours, multiply the average by number of hours.
Distance \(=\) Average \(×\) Rate \(= 54 \ × \ 5 = 270\)
Add both numbers.
\(270 \ + \ 225 = 495\) km

The correct answer is \($300\)
Let \(x\) be the original price.
If the price of a laptop is decreased by \(20\%\) to \($280\), then:
\(80\%\) of \(x=280⇒ 0.80 \ x=240 ⇒ x=240 \ ÷ \ 0.80=300\)

The correct answer is \(0.05 \ x \ + \ 5,000\)
Let \(x\) be the sales profit.
Then, \(5\%\) of sales profit is \(0.05 \ x\).
Employee’s revenue:
\(0.05 \ x \ + \ 5,000\)

The correct answer is \(88\) cm\(^2\)
The perimeter of the trapezoid is \(45\).
Therefore, the missing side (height) is \(=45 \ – \ 15 \ – \ 12 \ – \ 10 = 8\)
Area of the trapezoid:
\(A = \frac{1}{2} \ h \ (b1 \ + \ b2) = \frac{1}{2} \ (8) \ (12 \ + \ 10) = 88\) cm\(^2\)

The correct answer is \(49\)
\(− \ 22 \ − \ (− \ 71)=− \ 22 \ + \ 71=71 \ − \ 22=49\)

The correct answer is \(\frac{2}{5} \ > \ 0.3\)
Let’s review the choices:
A. \(\frac{3}{2} \ > \ 2.8\) This is not a correct statement.
Because \(\frac{3}{2}=1.5\) and it’s less than \(0.8\).
B. \(10\%=\frac{1}{5}\) This is not a correct statement.
Because \(10\% = 0.1\) and \(\frac{1}{5}=0.2\)
C. \(4 \ < \ \frac{3}{6}\) This is not a correct statement.
Because \(\frac{3}{6}=0.6\) and it’s less than \(4\).
D. \(\frac{2}{5} \> \ 0.3\) This is a correct statement.

The correct answer is \(36\)
The diagonal of the square is \(6\).
Let \(x\) be the side.
Use Pythagorean Theorem:
\(a^2 \ + \ b^2 = c^2\)
\(x^2 \ + \ x^2= 6^2 ⇒ 2 \ x^2 = 6^2 ⇒ \)
\(2 \ x^2= 36 ⇒ x^2= 36 ⇒x= \sqrt{36} =6\)
The area of the square is:
\(6 \ × \ 6= 36\)

The correct answer is \(14\)
Petrol of car A in \(350\) km \(=\frac{10 \ × \ 350}{100}=35\)
Petrol of car A in \(350\) km \(=\frac{6 \ × \ 350}{100}=21\)
\(35 \ − \ 24.5=14\)

The correct answer is if the quantity in Column A is greater
\( x^2 \ + \ 15=64 \to x^2=64 \ - \ 15=49\to x^2=49 \to x=7\)
\(124 \ - \ 15 \ y\ =49 \to - \ 15 \ y=49 \ - \ 124=- \ 75\to y=\frac{- \ 75}{-\ 15}=5\)

The correct answer is if the relationship cannot be determined from the information given
Simply change the fractions to decimals.
\(\frac{3}{4}=0.75\)
\(\frac{3}{2}=1.5\)
\(\frac{4}{3}=1.3333\)...
As you can see, \(x\) lies between \(0.75\) and \(1.5\) and it can be \(0.76\) or \(1.4\).
The first one is less than \(1.5\) and the second one is greater than \(0.75\) .
The relationship cannot be determined from the information given.

The correct answer is the two quantities are equal
Choose different values for a and b and find the values of quantity A and quantity B.
\(a=2\) and \(b=3\), then:
Quantity A: \(|2\ -\ 3|=|-\ 1|=1\)
Quantity B: \(|3\ -\ 2|=|1|=1\)
The two quantities are equal. 
\(a=-3\) and \(b=2\), then:
Quantity A: \(|-3\ -\ 2|=|-\ 5|=5\)
Quantity B:\(|2\ -\ (-\ 3)|=|2\ +\ 3|=5\)
The two quantities are equal.
Any other values of a and b provide the same answer.

The correct answer is if the quantity in Column A is greater
Simplify quantity B.
Quantity B:\((\frac{x}{5})^5=\frac{x^5}{5^5}\)
Since, the two quantities have the same numerator (\(x^5\)) and the denominator in quantity B is bigger (\({5^5}\gt 5\)), then the quantity A is greater.

The correct answer is "The quantity in Column B is greater"
Column A: Use order of operation to calculate the result.
\(6 \ + \ 2 \ × \ 7 \ + \ 5=6 \ + \ 14 \ + \ 5=25\)
Column B: \(4 \ + \ 4 \ × \ 7 \ − \ 3→4 \ + \ 28
\ − \ 3=29\)

The correct answer is "The quantity in Column A is greater"
Column A: Simplify. \(\sqrt{49} \ + \ \sqrt{64} = 7 \ + \ 8 = 15\)
\(15\) is greater than \(\sqrt{81} \ (\sqrt{225} = 15)\)

The correct answer is if the quantity in Column A is greater
Column A: Simplify.
\(\sqrt{121 \ − \ 49} = \sqrt{72}\)
Column B:
\(\sqrt{121} \ −\ \sqrt{49} = 11 \ − \ 7 = 4 , \sqrt{72}\) is bigger than \(4. (\sqrt{16} = 4)\)

The correct answer is the relationship cannot be determined from the information given
Column A: Based on information provided, we cannot find the average age of Joe and Michelle
or average age of Michelle and Nicole.

The correct answer is "The quantity in Column A is greater"
Column A: The value of \(x\) when \(y=8\):
\(y=− \ 5 \ x \ − \ 12→8=− \ 5 \ x \ − \ 12→− \ 5 \ x=20→x=− \ 4\)
Column B: \(− \ 9\)
\(− \ 4\) is greater than \(− \ 9\).

The correct answer is "The quantity in Column A is greater"
Column A: The value of \(x\) when \(y=8\):
\(y=− \ 5 \ x \ − \ 12→8=− \ 5 \ x \ − \ 12→− \ 5 \ x=20→x=− \ 4\)
Column B: \(− \ 9\)
\(− \ 4\) is greater than \(− \ 9\).

The quantity in Column A is greater
Quantity A is: \(\frac{5 \ +\ 7 \ +\ x}{3}=2\to x=- \ 6\)
Quantity B is: \(\frac{- \ 6\ + \ (- \ 6 \ - \ 2) \ + \ (- \ 6 \ + \ 6)\ + \ (4 \ × \ (- \ 6))}{4}=- \ 9.5\)

The correct answer is the relationship cannot be determined from the information given
Choose different values for \(x\) and find the value of quantity A.
\(x=1\), then:
Quantity A: \(\frac{3}{x}\ + \ 2 \ x= \frac{3}{1}\ + \ 2=5\)
Quantity B is greater
\(x=0.1\), then:
Quantity A: \(\frac{3}{0.1}\ + \ 2 \ x= \frac{ 1}{0.1} \ + \ 0.2=30 \ + \ 0.2=30.2\)
Quantity A is greater
The relationship cannot be determined from the information given.

The correct answer is the relationship cannot be determined from the information given
Choose different values for \(x\) and find the value of quantity A.
\(x=1\), then:
Quantity A: \(\frac{3}{x}\ + \ 2 \ x= \frac{3}{1}\ + \ 2=5\)
Quantity B is greater
\(x=0.1\), then:
Quantity A: \(\frac{3}{0.1}\ + \ 2 \ x= \frac{ 1}{0.1} \ + \ 0.2=30 \ + \ 0.2=30.2\)
Quantity A is greater
The relationship cannot be determined from the information given.

The correct answer is \(55\%\)
Number of pencils are blue \(=60 \ − \ 27=33\)
Percent of blue pencils is: \(\frac{33}{60} \ × \ 100=55\%\)

The correct answer is \(-\ 2.95\)
\(10 \ x=-\ 42 \ +\ 12.5=-\ 29.5 \to x=\frac{-\ 29.5}{10}=-\ 2.95\)

The correct answer is \(7\)
\((x \ - \ 2)^3=125→x \ - \ 2=\sqrt[3]{125}→x \ - \ 2=\sqrt[3]{5^3}→x \ - \ 2=5→x=7\)

The correct answer is \(20\%\)
Use this formula: Percent of Change \(= \frac{New \ Value \ − \ Old Value}{Old \ Value} \ × \ 100\%\)
\(\frac{16000 \ − \ 20000}{20000} \ × \ 100\% = 20\%\) and \(\frac{12800 \ − \ 16000}{16000 } \ × \ 100\% = 20\%\)

The correct answer is \(8\)
\(3 \ (\frac{1}{2} \ - \ \frac{1}{6}) \ + \ 7=\)
\(3 \ (\frac{3 \ - \ 1 }{6} \ + \ 7 =\)
\(3 \ (\frac{2}{6}) \ + \ 7 =\)
\(3 \ (\frac{1}{3}) \ + \ 7 =\)
\(1 \ + \ 7 =8\)

The correct answer is \((\frac{9}{3} \ × \ 2) \ + \ (\frac{30}{2} \ × \ 2)\)
\((\frac{9}{3} \ × \ 2) \ + \ (\frac{30}{2} \ × \ 2) = (3 \ × \ 2) \ + \ ( 15 \ × \ 2) = 6 \ + \ 30 =36\)

The correct answer is \(2.6\)
\(40\%\) of \(24\) is: \(\frac{40}{100} \ × \ 24=9.6\)
Let \(x\) be the number then: \(x=9.6 \ − \ 7=2.6\)

The correct answer is \(72\)
\(\frac{3}{5} \ × \ 120=72\)

The correct answer is \(20\)
If \(\frac{2 \ x}{5}=40\), then \(\frac{2 \ x}{10}:\)
\( 2 \ x = 40 \times 5→2 \ x = 200 → x =100\)
\(\frac{2 \ x}{10}=\frac{2 \ × \ 100}{10}=\frac{200}{10}=20\)

The correct answer is \(16\) cm
The perimeter of rectangle is: \(2 \ × \ (6 \ + \ 5)=2 \ × \ 11=22\)
The perimeter of circle is: \(2 \ \pi \ r=2 \ × \ 3 \ × \ \frac{12}{2}=36\), Difference in perimeter is: \(36 \ − \ 22=16\) cm

The correct answer is \(39.6\)
\(12\% \) of \( 230 =\frac{12}{100}\times {230}={27.6}\)
Let \(x\) be the number then, \(\ x\ =\ 27.6 \ +\ 12\ =\ 39.6\)

The correct answer is \(32\)
First, find the number.
Let \(x \) be the number.
Write the equation and solve for \(x\).
\(170%\) of a number is \(68\), then: \(1.7 \ × \ x=68 ⇒68 \ ÷ \ 1.7=40\)
\(80\%\) of \(40\) is: \(0.8 \ × \ 40 =32\)

The correct answer is \(6\)
Let \(x \) be the number.
Write the equation and solve for \(x\).
\((18 \ – \ x) \ ÷ \ x = 3\)
Multiply both sides by \(x\).
\((18 \ – \ x) = 3 \ x\), then add \(x\) both sides.
\(18 = 3 \ x\), now divide both sides by \(3\).
\(x = 6\)

The correct answer is \(78.5\)
Area \(=\pi \ r^2=\pi \ × \ (\frac{10}{2})^2=25 \ \pi=25 \ × \ 3.14=78.5\)

The correct answer is \(18\)
\(\frac{3}{4} \ × \ 24=\frac{72}{4}=18\)

The correct answer is \(140\%\)
The question is this:
\(1.84\) is what percent of \(1.25\)?
Use percent formula:
Part \(= \frac{percent}{100 } \ ×\) whole, \(1.75 = \frac{percent}{100 } \ × \ 1.25 ⇒\)
\(1.75=\frac{ percent \ × \ 1.25}{100} ⇒\)
\(175 =\) percent \(× \ 1.25 ⇒\)
percent \(= \frac{175}{1.25} =140\)

The correct answer is \(45^\circ, 45^\circ, 90^\circ\)
All angles in a triangle sum up to \(180 \) degrees.
Then: \(2 \ \alpha \ + \ 90^\circ=180^\circ→2 \ \alpha=90→𝛼=45^\circ\)

The correct answer is \(30\)
\(\frac{5}{7}\times 42=\frac{210}{7}=30\)

The correct answer is \(\frac{5}{8}\)
\(\frac{1}{2}=0.5\)
\(\frac{5}{8}=0.625\)
\(54\%=0.54\)
\(\sqrt{0.36}=0.6\)

The correct answer is \(120 \ x \ + \ 12,000 \ ≤ \ 21,000\)
Let \(x \) be the number of shoes the team can purchase.
Therefore, the team can purchase \(120 \ x\).
The team had \($21,000\) and spent \($12000\).
Now the team can spend on new shoes \($9000\) at most.
Now, write the inequality: \(120 \ x \ + \ 12,000 \ ≤ \ 21,000\)

The correct answer is Length of AB equal to length DC.
In rectangle sides that face to face each other is equal.

The correct answer is \(23\)
Find the difference of each pairs of numbers:
\(2, 3, 5, 8, 12, 17, \) ___,\( 30\)
The difference of \(2\) and \(3\) is \(1, \ 3\) and \(5\) is \(2, \ 5\) and \(8\) is \(3, \ 8\) and \(12\) is \(4, \ 12\) and \(17\) is \(5\) and next number should be \(6\).
The number is \(17 \ + \ 6 = 23\)

The correct answer is \(50\)
The capacity of a red box is \(18\%\) greater than a blue box.
Let \(x\) be the capacity of the blue box.
Then: \(x \ + \ 18\%\) of \(x=59→1.18x=59→x=\frac{59}{1.18}=50\)

The correct answer is \(28\) inches
The area of the square is \(49\) inches.
Therefore, the side of the square is square root of the area. 
\(\sqrt{49}=7\) inches
Four times the side of the square is the perimeter: \(4 \times 7 = 28\) inches

The correct answer is \(- \ 33\)
Use PEMDAS (order of operation):
\([3 \times (–\ 18) \ +\ 6] \ – \  (– \ 8) \ +\  [2 \times 7] \div 2 =\)
\([–\ 54 \ +\  6]\  –\  (–\ 8) \ +\  [14] \div 2 =\)
\([–\ 54 \ +\  6]\  –\  (–\ 8) \ +\  7 = \)
\([–\ 48] \ –\  (\ –\ 8) \ +\  7 =\)
\([–\ 48] \ + \  8 \ + \  7 = \ – \ 33\)

The correct answer is \(3.05\) hours
\(60\) minutes \(= 1\) Hours \(\to \frac{183}{60}=3.05\) Hours

The correct answer is \($10.45\)
Let \(x\) be one-kilogram orange cost, then:
\(2 \ x \ +\ (2 \ ×\ 3.2)=27.3 \to\)
\(2 \ x\ +\ 6.4=27.3\to\)
\(2 \ x\ =27.3 \ - \ 6.4 \to\)
\(2 \ x\ =20.9 \to\)
\(x=\frac{20.9}{2}=$10.45\)

The correct answer is \(8\) hours
The distance between Jason and Joe is \(12\) miles.
Jason running at \(4.5\) miles per hour and Joe is running at the speed of \(6\) miles per hour.
Therefore, every hour the distance is \(1.5\) miles less. 
\(12 \div 1.5 = 8\)

The correct answer is \(23\)
There are twice as many girls as boys.
Let \(x\) be the number of girls in the class. Then: 
\( x\ +\ 2\ x\ =\ 69\  \to \)
\(3\ x\ =\ 69\  \to \ x\ =\ 23\)

The correct answer is \(30\%\)
\($15\) is what percent of \($50\)?
\(15 \div 50 = 0.3 = 30\%\)

The correct answer is \(99\)
The ratio of lions to tigers is \(2 \) to\( 5\) at the zoo.
Therefore, total number of lions and tigers must be divisible by \(7. \ 2 \ +\ 5=7\)
From the numbers provided, only \(99\) is not divisible by \(8\).

The correct answer is \(58\)
\(58\) is not prime number, it is divisible by \(2\).

The correct answer is \(- \ 3\)
\((((- \ 15) \ +\ 24)\ ×\ 2)\ +\ (- \ 21)=((9) \times 2)\ - \ 21=18 \ - \ 21=- \ 3\)

The correct answer is \(18\%\)
The percent of girls playing tennis is:
\(50\% \times 36\% = 0.50 \times 0.36= 0.18 = 18\%\)

The correct answer is \(600\)
Number of rotates in \(15\) second \( =\frac{(200\ \times\  15)}{5}=600\)

The correct answer is \($600\)
Let \(x\) be the original price. If the price of the sofa is decreased by \(30\% \) to \( $420 \), then:
\( 70\%\) of \(x=420 \Rightarrow 0.70 \ x=420 \Rightarrow x=420\div 0.70=600\)

The correct answer is \(3\)
The width of a rectangle is \(2 \ x\) and its length is \(5 \  x\).
Therefore, the perimeter of the rectangle is \(14\ x\). 
Perimeter of a rectangle \(=2\) (width \( + \) length)\(=2\ (2 \ x\ + \ 5 \ x)=2 \ (7 \ x)=14 \ x\)
The perimeter of the rectangle is \(42\). 
Then: \(14 \ x=42 \to x=3\)

The correct answer is \(40\)
The area of trapezoid is: \((\frac{8 \ +\ 12}{2}) \times 4=40\)

The correct answer is \($5.51\)
\(18\ -\ 12.49=$5.51\)

The correct answer is \(1.1\)
\(\frac{7\times12}{80}=\frac{84}{80}=1.05\cong 1.1\)

The correct answer is \(1.1\)
\(\frac{7\times12}{80}=\frac{84}{80}=1.05\cong 1.1\)

The correct answer is \(0\)
\(10\ +\ 4\ (x\ +\ 5\ -\ 5\ x)=10\ +\ 4\ (-\ 4\ x\ +\ 5)=30\to 10\ -\ 16\ x\ +\ 20=30\to -\ 16\ x\ +\ 30=30\to -\ 16\ x=0\to x=0\)

The correct answer is \(8\) feet 
Use formula of rectangle prism volume.
\(V =\) (length) (width) (height) \(\Rightarrow 2000 = (25) \ (10)\) (height) \(\Rightarrow\) height \(= 2000 \div 250 = 8\)

The correct answer is \(300\%\)
Write the equation and solve for B:
\(0.60\)A \(=0.20\)B , divide both sides by \(0.20\), then you will have \(\frac{0.60}{0.20}\) A \(=\) B, therefore: 
B \(=3\) A , and B is \(3\) times of A or it’s \(300\% \) of A .

The correct answer is \(6,062\)
\(12.124\div 0.002=\frac{\frac{12124}{1000}}{\frac{2}{1000}}=\frac{12,124}{2}=6,062\)

The correct answer is \(\frac{ 1}{4}\)
The probability of choosing a Hearts is \(\frac{13}{52} =\frac{ 1}{4}\)

The correct answer is \(4\)
\(1269=6^4\to 6^x=6^4\to x=4\)