ISEE Upper-Level Math FREE Sample Practice Questions

A. \(8 \space \)cm\(^2\)

B. \(16 \space \)cm\(^2\)

C. \(48 \space \)cm\(^2\)

D. \(64 \space \)cm\(^2\)

8- If \(10 + x^{\frac{1}{2}} = 14\), then what is the value of \(15 × x\)?

A. 15

B. 60

C. 120

D. 240

9- Triangle ABC is graphed on a coordinate grid with vertices at A \((-3, -2)\), B \((-1, 4)\) and C\( (7, 9)\). Triangle ABC is reflected over \(x\) axes to create triangle A’B’C’.
Which order pair represents the coordinate of C’?

A. \((7, 9)\)

B. \((-7, -9)\)

C. \((-7, 9)\)

D. \((7, -9)\)

10- Which set of ordered pairs represents\( y\) as a function of \(x\)?

A. \({(3, -2), (3, 7), (9, -8), (4, -7)}\)

B. \({(4, 2), (3, -9), (5, 8), (4, 7)}\)

C. \({(9, 12), (5, 7), (6, 11), (5, 18)}\)

D.\( {(6, 1), (3, 1), (0, 5), (4, 5)}\)

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Answers:

1- A
\(\frac{x+9+14+12+5}{5}=10 → x + 40 = 50 → x = 50 – 40 = 10\)

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2- D
The difference of the file added, and the file deleted is:
\( 652,159 – 599,986 = 52,173\)
\(937,036 + 52,173 = 989,209\)

3- B
5 days 19 hours 35 minutes \(– 3\) days 12 hours 22 minutes \(=\) 2 days 7 hours 13 minutes

4- A
Formula of triangle area =\( \frac{1}{2} (base × height)\)
Since the angles are \(45-45-90\), then this is an isosceles triangle, meaning that the base and height of the triangle are equal.
Triangle area = \(\frac{1}{2}\)
(base × height) = \(\frac{1}{2} (2 × 2) = 2\)

5- C
\(50\%\) of \(84 = 42\)
\(84 + 42= 126\)

6- C
\(2(6h – 3) = 30\)

7- D
The area of the circle is \(16π\) cm\(^2\), then, its diameter is 8cm.
\(area \space of \space a \space circle \space = πr^2=16π→r^2=16→r=4\)
Radius of the circle is 4 and diameter is twice of it, 8.
One side of the square equals the diameter of the circle. Then:
\( Area \space of \space square \space = side×side=8×8=64\)

8- D
\(x^\frac{1}{2}\) equals to the root of \(x\). Then:
\(10+x^\frac{1}{2}=14→10+\sqrt x=14→\sqrt x=4→x=16\)
\(x = 16\) and \(15 × x\) equals: \(15 × 16 = 240\)

9- D
When a point is reflected over \(x\) axes, the \((y)\) coordinate of that point changes to \((-y)\) while its \(x\) coordinate remains the same.
\(C (7, 9) → C’ (7, -9)\)

10- D
A set of ordered pairs represents \(y\) as a function of \(x\) if:
\( x_1=x_2→y_1=y_2 \)
In choice A: \((3, -2)\) and \((3, 7)\) are ordered pairs with same \(x \)and different \(y\), therefore \(y\) isn’t a function of \(x\).
In choice B:\( (4, 2)\) and\( (4, 7) \)are ordered pairs with same \(x \)and different \(y\), therefore\( y\) isn’t a function of \(x\).
In choice C: \((5, 7)\) and\( (5, 18)\) are ordered pairs with same\( x\) and different\( y\), therefore \(y\) isn’t a function of \(x\).

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