Top 10 ISEE Middle-Level Math Practice Questions

B. 145

C. 125

D. 105

3- What is the area of a square whose diagonal is 8?

A. 16

B. 32

C. 36

D. 64

4- Which of the following shows the numbers in descending order?

A. \(\frac{1}{6},\frac{2}{5},\frac{1}{3},\frac{3}{4}\)

B. \(\frac{1}{6},\frac{2}{5},\frac{3}{4},\frac{1}{3}\)

C. \(\frac{1}{6},\frac{1}{3},\frac{2}{5},\frac{3}{4}\)

D. \(\frac{1}{6},\frac{3}{4},\frac{1}{3},\frac{2}{5}\)

5- \(452,357,841×0.0001\)?

A. 452,357.841

B. 45,235.7841

C. 4,523.57841

D. 452.357841

6- A $40 shirt now selling for $28 is discounted by what percent?

A. \(20 \%\)

B. \(30 \%\)

C. \(40 \%\)

D. \(60 \%\)

7- If \(f=2x-3y\) and \(g=x+4y\), what is \(2f+g\)?

A. \(3x−y\)

B. \(3x−2y\)

C. \(5x−2y\)

D. \(5x−y\)

8- The area of a circle is \(64π\). What is the diameter of the circle?

A. 4

B. 8

C. 12

D. 16

9- If there were 300 students at a school and nearly \(32\%\) prefer to learn Germany, approximately how many students want to learn Germany?

A. 300

B. 204

C. 96

D. 6

10- What is the mean in the following set of numbers?
\(9,12,29,36,45,63,99,123\)

A. 46.2

B. 40.5

C. 59.4

D. 52

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2- B
\(x=20+125=145\)

3- B
The diagonal of the square is 8. Let \(x\) be the side.
Use Pythagorean Theorem: \(a^2 + b^2 = c^2\)
\(x^2 + x^2 = 82 ⇒ 2x^2 = 82 ⇒ 2x^2 = 64 ⇒x^2 = 32 ⇒x= \sqrt {32}\)
The area of the square is:
\(\sqrt {32} × \sqrt{32} = 32\)

4- C
\(\frac{1}{6}≅0.16, \frac{1}{3}≅0.33, \frac{2}{5}=0.4, \frac{3}{4}=0.75\)

5- B
\(52357841×\frac{1}{10000}=45235.7841\)

6- B
Use the formula for Percent of Change
\(\frac{New \ Value \ – \ Old \ Value}{Old \ Value}× 100 \%\)
\(\frac{28-40}{40}× 100 \% = –30 \% \)
(negative sign here means that the new price is less than old price)

7- C
\(2f=2×(2x-3y)=4x-6y\)
\(2f+g=4x-6y+x+4y=5x-2y\)

8- D
The formula for the area of the circle is: \(A=πr^2\)
The area is \(64π\). Therefore:
\(A=πr^2 ⇒ 64π = πr^2\)
Divide both sides by \(π\):
\(64 = r^2⇒ r=8\)
Diameter of a circle is \(2 x\) radius. Then:
Diameter \(= 2 × 8 = 16\)

9- C
Number of students prefer to learn Germany \(= \frac{32}{100}×300=96\)

10- D
Mean \(=\frac{9+12+29+36+45+63+99+123}{8}=\frac{416}{8}=52\)

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