Did you take the ISEE Upper Level Math Practice Test? If so, then it’s time to review your results to see where you went wrong and what areas you need to improve.

## ISEE Upper Level Math Practice Test Answers and Explanations

1- **Choice C is correct**

\(|15-(18÷|2-8|)|=|15-(18÷6)=|15-3|=12\)

2- **Choice D is correct**

Use FOIL (First, Out, In, Last) method.

\((x-4)(2x+2)=2x^2+2x-8x-8=2x^2-6x-8\)

3- **Choice B is correct**

Solve for \(x\). \(-4≤4x-5<7\)⇒ (add 5 all sides) \(5-4≤4x-5+5<7+5\) ⇒

\(1≤4x<12\) ⇒ (divide all sides by \(4\)) \(\frac{1}{4}≤x<3\), x is between \(\frac{1}{4}\) and \(3\). Choice B represent this inequality.

4- **Choice D is correct**

\(x_{1,2} =\frac{-b ± \sqrt{b^2-4ac}}{2a}, ax^2 + bx + c = 0, 3x^2 +8x + 4 = 0\)⇒then: \(a = 3, b = 8\) and \(c = 4\)

\(x = \frac{-8 + \sqrt{8^2 – 4 .3 .4}}{2 .3}= –\frac{2}{3}, x = \frac{-8 – \sqrt{8^2 – 4 .3 .4}(}{2 .3} = – 2\)

5- **Choice B is correct**

\(\frac{8}{23} = 0.347\) and \(45\% = 0.45\) therefore x should be between \(0.0.347\) and \(0.45\)

Choice B. \(\frac{8}{19} = 0.421\) is between \(0.347\) and \(0.45\)

6- **Choice A is correct**

A linear equation is a relationship between two variables, \(x\) and \(y\), and can be written in the form of \(y=\) m\(x +\) b.

A non-proportional linear relationship takes on the form \(y =\) m\(x +\) b, where b\( ≠\) 0 and its graph is a line that does not cross through the origin.

7- **Choice D is correct**

Translated 6 units down and 5 units to the left means: \((x.y) ⇒ (x-5,y-6)\)

8- **Choice B is correct**

Write the proportion and solve for missing side.

\(\frac{Smaller \space triangle \space height}{Smaller \space triangle \space base}=\frac{Bigger \space triangle \space height}{Bigger \space triangle \space base}

= ⇒ \frac{100 \space cm}{150 \space cm} =\frac{100+280 \space cm}{x} ⇒ x=570 cm\)

9- **Choice B is correct**

\(0.00000625= \frac{6.25}{1,000,000}⇒6.25 × 10^{–6}\)

10- **Choice B is correct**

The ratio of boy to girls is 7:5. Therefore, there are 7 boys out of 12 students. To find the answer, first divide the total number of students by 12, then multiply the result by 7.

\(540 ÷ 12 = 45 ⇒ 120 × 7 = 315\)

11- **Choice C is correct**

Probability = (number of desired outcomes)/ (number of total outcomes)

In this case, a desired outcome is selecting either a red or a yellow marble. Combine the number of red and yellow marbles: \(7 + 6 = 13\) and divide this by the total number of marbles: \(5 + 7 + 6 = 18.\) The probability is \(\frac{13}{18}\).

12- **Choice A is correct**

Emily = Daniel, Emily = 9 Claire, Daniel \(= 24 +\) Claire, Emily = Daniel → Emily\( = 20 +\) Claire

Emily = 9 Claire → 9 Claire \(= 24 +\) Claire→9 Claire \(–\) Claire = 24, 8 Claire = 24, Claire = 3

13- **Choice B is correct**

\(\frac{1}{4}\) of the distance is \(4 \frac{2}{5}\) miles. Then: \(\frac{1}{4}×4 \frac{2}{5}=\frac{1}{4}×\frac{22}{5}=\frac{22}{20}\)

Converting \(\frac{22}{20}\) to a mixed number gives: \(\frac{22}{20}=1 \frac{2}{10}/20=1 \frac{1}{10}\)

14- **Choice D is correct**

Use Pythagorean theorem: \(a^2+b^2=c^2→s^2+h^2=(10s)^2→(6s)^2+h^2=100s^2\)

Subtracting \(s^2\) from both sides gives: \(h^2=64s^2\),

Square roots of both sides: \(h=\sqrt{64s^2}=8s\)

15- **Choice C is correct**

\(5 – 12 ÷ (2^4 ÷ 4) = 5 – 12 ÷ (16 ÷ 4) = 5 – 12 ÷ (4) = 5-3 =2\)

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16- **Choice C is correct**

The area of the trapezoid is: Area\(=\frac{1}{2} h(b_1+b_2 )=\frac{1}{2}(x)(14+10)=36\)

\(→12x=36→x=3, y=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5\)

The perimeter of the trapezoid is: \(10+4++10+3+5=32\)

17- **Choice D is correct**

average\(=\frac{sum}{total}=\frac{40+30+38}{3}=\frac{108}{3}=36\)

18- **Choice A is correct**

Area = w \(×\) h, Area \(= 212 × 58 = 12,296\)

19- **Choice A is correct**

\((6.2+6.3+6.5) x = x+2, 19x =x+2, Then x = \frac{1}{9}\)

20- **Choice C is correct**

\(16\%\) of \(x = 15.4, x = 16/100 x = 15.4, x =\frac{16 × 15.4}{100} = 96.25\)

21- **Choice D is correct**

\(\frac{9}{30} = 0.3\)

22- **Choice B is correct**

\(\frac{240}{8} < x < \frac{320}{8}, 30 < x < 40\), Then:Only choice b is correct

23- **Choice D is correct**

\(75 ÷ \frac{1}{6} =\frac{\frac{75}{1}}{\frac{1}{6}}= 75 × 6 = 450\)

24- **Choice D is correct**

For sum of 5: (1 & 4) and (4 & 1), (2 & 3) and (3 & 2), therefore we have 4 options.

For sum of 7: (1 & 6) and (6 & 1), (2 & 5) and (5 & 2), (3 & 4) and (4 & 3) we have 6 options.

To get a sum of 6 or 9 for two dice: 6 + 4 = 10

Since, we have 6 × 6 = 36 total number of options, the probability of getting a sum of 4 and 6 is 10 out of 36 or \(\frac{10}{36}=\frac{5}{18}\).

25- **Choice D is correct**

Simplify: \(\frac{\frac{1}{4}-\frac{x+7}{8}}{\frac{x^2}{4}-\frac{1}{4}}=\frac{\frac{1}{4}(1-\frac{x+7}{2})}{\frac{x^2-1}{4}}=\frac{1-\frac{x+7}{2}}{x^2-1}⇒Simplify:1-\frac{x+7}{2}=\frac{2-x-7}{2} =\frac{-x-5}{2}

Then:\frac{1-\frac{x+7}{2}}{x^2-1}=\frac{\frac{-x -5}{2}}{x^2-1}=\frac{-x – 5}{2(x^2 – 1)}=\frac{-x – 5}{2x^2- 2}\)

26- **Choice C is correct**

The distance of A to B on the coordinate plane is: \(\sqrt{(x_1-x_2 )^2+(y_1-y_2 )^2 }= \sqrt{(9-1)^2+(8-2)^2 }=\sqrt{8^2+6^2}, =\sqrt{64+36}=\sqrt{100}=10\)

The diameter of the circle is 10 and the radius of the circle is 5. Then: the circumference of the circle is: \(2πr=2π(5)=10π\)

27- **Choice B is correct**

\(102.5 ÷ 0.55 = 186.36\)

28- **Choice C is correct**

Diameter = 14, then: Radius = 7, Area of a circle \(= πr^2 ⇒ A = 3.14(7)^2 = 153.86\)

29- **Choice D is correct**

\(\frac{15}{45} = \frac{X}{120} → x =\frac{15 ×120}{45} = 40\)

30- **Choice B is correct**

\(4x^2 – 34 = 66, 4x^2 = 100, x^2 = 25, x = ± 5\)

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31- **Choice B is correct**

\(\frac{x+7+15+23+7}{5} = 12 → x + 52 = 60 → x = 62 – 52 = 8\)

32- **Choice A is correct**

The difference of the file added, and the file deleted is: \(793,352 – 652,159 + 599,986 = 741,179, 856,036 -741,179 = 114,857\)

33- **Choice B is correct**

6 days 14 hours 42 minutes – 4 days 12 hours 35 minutes = 2 days 2 hours 7 minutes

34- **Choice D is correct**

\(x^{\frac{1}{2}}\) equals to the root of x. Then: \(15+x^{\frac{1}{2}}=24→15+\sqrt{X}=24→\sqrt{X}=9→x=81\)

\(x=81\) and \(8×x\) equals: \(8×81=648\)

35- **Choice D is correct**

\(0.35% of 60 = 21, 60 + 21= 81\)

36- **Choice C is correct**

\(2(8h – 4) = 42\)

37- **Choice D is correct**

The area of the circle is 64π \(cm^2\), then, its diameter is 8cm.

area of a circle \(=πr^2=64π→r^2=64→r=8\)

Radius of the circle is 8 and diameter is twice of it, 16.

One side of the square equals to the diameter of the circle. Then:

Area of square\(=side×side=16×16=256\)

38- **Choice C is correct**

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 \(= \frac{1}{2} (base × height) = \frac{1}{2} (4 × 4) = 8\)

39- **Choice D is correct**

When a point is reflected over y axes, the \((x)\) coordinate of that point changes to \((-x)\) while its x coordinate remains the same. \(C (5, 4) → C’ (-5, 4)\)

40- **Choice A is correct**

A set of ordered pairs represents \(y\) as a function of \(x\) if: \(x_1=x_2→y_1=y_2\)

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 \(x\).

In choice D: (6, 1) and (6, 3) are ordered pairs with same \(x\)and different \(y\), therefore \(y\)isn’t a function of \(x\).

41- **Choice D is correct**

If the length of the box is 24, then the width of the box is one fourth of it, 6, and the height of the box is 2 (one third of the width). The volume of the box is: V=lwh = (24)(6) (2) = 288

42- **Choice C is correct**

The area of the square is 64 square inches. Area of square\(=side×side=8×8=64\)

The length of the square is increased by 4 inches and its width decreased by 2 inches. Then, its area equals: Area of rectangle = width × Length\(=12×6=72\)

The area of the square will be increased by 3 square inches. \(72-64=8\)

43- **Choice B is correct**

Write a proportion and solve. \(\frac{3}{5}=\frac{x}{120}\)

Use cross multiplication: \(5x=360→x=72\)

44- **Choice A is correct**

Number of squares equal to: \(\frac{42×20}{5×5}=33.6\)

45- **Choice C is correct**

David’s weekly salary is \($250\) plus \(12\%\) of \($1,800\). Then: \(12\%\) of \(1,800=0.12×1,800=216, 250+216=466\)

46- **Choice C is correct**

\(5x^3 y^4+14x^2 y-(3x^3 y^4-3x^2 y)=2x^3 y^4+17x^2 y\)

47- **Choice C is correct**

Let P be circumference of circle A, then; \(2πr_A=20π→r_A=10\)

\(r_A=5r_B→r_B=\frac{10}{5}=2\)→ Area of circle B is; \(πr_B^2=4π\)