# 2017 Grade 8 Math Challenge Elimination Round (Questions 1-25)

This is the 2017 MTAP Grade 7 Math Challenge questions 1 to 25.Questions 26-30 including the pdf will be posted very soon.

Questions in the previous years can be accessed on the Past Tests page and all questions can be found in the All Posts page.

1.) What is the sum of the reciprocals of all the positive divisors of 8?

2.) Factor completely: $27x^5y^5 + 12x^3y^7$.

3.) Expand and simplify: $(x+y)^2 - (x - y)^2 +(x+y)(x - y)$.

4.) If $6x^2 + kx - 8 = 2(3x+1)(x - 4)$,what is the value of $k$?

5.) Factor completely:

$\dfrac{x^2y^2}{16} - \dfrac{4}{25}$ .

6.) What is the area of a square whose perimeter is $8x - 36$

7.) Factor completely: $2x^2 + 10x - 48$.

8.) What is the product of three consecutive odd integers if the middle integer is $x$?

9.) Factor completely: $12x^3y^3 + 8x^2y^4 + 32xy^5$.

10.) Write the fraction in lowest terms and without negative exponents:

$\dfrac{3x^{-2}y^{-4}}{(2x)^{-3}y}$.

11.) Simplify using scientific notation:

$\dfrac{(0.006)(500000)}{1600(0.000003)}$

12.) Expand: $(2 - 0.5y)^3$

13.) Simplify:

$\dfrac{1 + \dfrac{1}{1 + \frac{1}{x}}}{1 + \frac{1}{x + 1}}$

14.) The length, width and height of a box are in the ratio of 5 : 4 : 7. If the perimeter of the base is 54 cm, find the volume of the box.

15.) Solve for $x: 3(7^{3 - 2x}) = \sqrt{63}$.

16.) The difference between the squares of two consecutive positive multiples of 5 is 1225. What is the sum of the two multiples of 5?

17.) The ratio of an angle to its complement is 5 : 13. Find the measure of its complement.

18.) Solve for $x: (0.25)^{2x - 1} = (0.125)^{2 - x}$.

19.) If $f(x) = x(4 - x)$, for which values of $x$ is $f(x)$ equal to $x$?

20.) The midpoint of the segment joining the points $A(-5, 8)$ and $B(x, y)$ is $P (3, -1)$. What are the coordinates of $B$?

21.) Factor completely: $16x^4 - y^8$.

22.) How many digits does $(1000)^{2017}$ have when expanded?

23.) Give an equation in slope-intercept form of the line passing through the origin and perpendicular to $x + 2y = 5$.

24.) Perform the indicated operation and simplify:

$\dfrac{2x^2 - 1}{2x - 1} \cdot \dfrac{4}{6x - 9} \div \dfrac{8}{x}$

25.) If you want to determine the favorite subject of your class, which measure of central tendency should you use?