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 $$=πr^2=64π→r^2=64→r=8$$
The radius of the circle is 8 and the diameter is twice it, 16.
One side of the square equals 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; $$πr_B^2=4π$$

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