Grade 9 MTAP 2015 Elimination Questions with Solutions – Part 2

This is the second part (questions 11-20) of the solutions of the Grade 9 MTAP 2015 Elimination Questions. The first part can be read here.

Although reasonable care has been given to make the solution accurate as possible, the solver is also human. Please comment below if you see any errors.

11.) If x \neq 1, solve for x in 2 \sqrt{x} + \frac{3}{\sqrt{x}} = 5.

Solution
Multiplying both sides by \sqrt{x}, we obtain

2x + 3 = 5\sqrt{x}

Squaring both sides of the equation, we get

4x^2 + 12x + 9 = 25x

4x^2 - 13x + 9 = 0.

Factoring, we have

(4x - 9)(x - 1) = 0

So, x = \frac{9}{4} or x = 1.

But from the given above, x \neq 1, so the only solution is x = \frac{9}{4}

Answer: 9/4  Continue reading “Grade 9 MTAP 2015 Elimination Questions with Solutions – Part 2”

2015 Grade 9 MTAP Math Challenge – Division Orals

Below are the 2015 Grade 9 MTAP Math Challenge Division Oral Competition questions with answers.

15-second question (2 points each)

1.) Determine all positive number x that satisfy 5x^2 = 10x.
Answer: x = 2

2.) What is the fourth power of \sqrt{2 + \sqrt{2}}?
Answer: 6 + 4 \sqrt{2}

3.) Simplify 4^{\frac{-k}{2}} + 8^ {- \frac{k-1}{3}}
Answer: \frac{3}{2}^k

4.) If a ♠ b = \sqrt{a^2+b^2}, what is the value of (3 ♠ 4) ♠ 12?
Answer: 13

5.) Suppose that x, y and z are positive integers such that xy = 6, xz = 10 and yz = 15. What is the value of xyz?
Answer: 30  Continue reading “2015 Grade 9 MTAP Math Challenge – Division Orals”