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 $4$
$1269=6^4\to 6^x=6^4\to x=4$