# 2014 Grade 8 Math Challenge Elimination Questions with answers – Part 1

This is the 2014 MTAP Grade 8 Math Challenge questions 1 to 25 with answer key. More reviewers can be found on the Past Tests and All Posts pages.

1.) Simplify: 1 – 2 +3 – 4 + … + 49 – 50 + 49 – 48 + 47 – 46 + … + 1

2.) Simplify: $\left( \dfrac{1}{2} - 1 \right) - \left( \dfrac{1}{3} - 1 \right)$

3.) In the proportion $x : 12 = 18 : x^2$, what is x?

4.) Between what two consecutive integers does $\sqrt {-100}$ lie?

5.) What is the area of a rectangle whose sides are twice as long as the sides of a smaller rectangle whose area is $17 cm^2?$

6.) What is the medium of the following numbers: $-3.1, -3\dfrac {1}{3}, 3.1, 3\dfrac{1}{2}, -\pi, 3.25?$

7.) Let U = {1, 2, 3, …, 12} be the universal set, and A = {10, 11, 12}, B = {1, 3, 5, 7, 9, 11}, and C = {4, 5, … ,11}. What is $A \cap B \cap C?$

8.) With the same sets given in Item 7, what is $A^c \cap B^c?$

9.) With the same sets given in Item 7, how many elements does $(A \cup B^c) \cap C^c$ have?

10.) With the same sets given in Item 7, how many elements does $(A \times B) \times C$ have?

11.) If $x = 2$ and $y = -3$, find the value of $xy^2 + x^2y.$

12.) Simplify: $(x + 1)(2x - 3) - x (4 - x)$

13.) Perform the indicated operations: $(2x + 1)(2x^4 - x^3 - 8x^2 + 8x - 8) \div (2x^2 - 3x - 2)$

14.) Simplify: $(x + 2)(2x - 1) + 2x(2 - x) - 2(4x + 1)$

15.) Twelve less than three times a number is 3x, what is the number?

16.) Simplify: $2014^2 - 2013^2$

17.) The legs of a right triangle are (3x – 2) cm and 2x cm long. If x = 3, how long is its hypotenuse?

18.) The product of two numbers is $6x + 9y.$ If one number is twice the other, what is their product?

19.) Christ walked x km at a constant rate of y m/hr. How many minutes did he walk?

20.) If the length of a rectangle is $2x + 4$ cm and its area is $(2x^2 - 8) cm^2,$ how much longer is its length that its width?

21.) Solve for x in the equation $(2x - 1) + 2(2x - 1) + 3(2x - 1) + 4(2x - 1) + 5(2x - 1) = 75.$

22.) What is the largest integral value of x If “=” in Item 21 is replaced by “<”?

23.) Solve for x in the equation |3 – 2x| = 3.

24.) Solve for x in the inequality |3 – 2x| > 2.

25.) In 2005, Cora was three times as old as her son Jayson. Four years back then, she was four times as old as Jayson. In what year was Jayson born?

Answer key:

1.) 0
2.) $\frac{1}{6}$
3.) 6
4.) -5 and -4
5.) $68 cm^2$
6.) 0
7.) {11}
8.) {2, 4, 6, 8}
9.) 2
10.) 144
11.) 6
12.) $3x^2 - 5x - 3$
13.) $2x^2 - 3x^2 - 2x + 4 3$
14.) -x – 4
15.) x + 4
16.) 4027
17.) $\sqrt{85} cm$
18.) $8x^2 + 24xy + 18y^2$
19.) $\frac{60000x}{y}$
20.) (x + 6)cm
21.) 3
22.) 2
23.) 0 and 3
24.) $x < \frac{1}{2}$ or $x > \frac{5}{2}$
25.) 1993

View Part 2 here: 2014 Grade 8 Math Challenge Elimination Questions with answers – Part 2

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