## Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 4

This is the fourth part (questions 31-40) of the solutions of the Grade 8 MTAP 2015 Elimination Questions. You can read the solutions for questions 1-10 11-20, and 21 – 30

Although these solutions were carefully checked, the solver is only human. Kindly comment in the box below if you see any errors.

31.) Factor completely: $a^2c^2 + b^2d^2 - a^2d^2 - b^2c^2$.

Solution

Rearranging the terms, we obtain
$a^2c^2 - a^2d^2 - b^2c^2 + b^2d^2$.

Factoring by grouping, we have
$a^2(c^2 - d^2) - b^2(c^2 - d^2)$
$= (c^2 - d^2)(a^2 - b^2)$
$= (c - d)(c + d)(a - b)(a + b)$.

Answer: (a + b)(a – b)(c + d)(c – d)  Continue reading “Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 4”

## Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 3

This is the third part (questions 21-30) of the solutions of the Grade 8 MTAP 2015 Elimination Questions. You can read the solutions for questions 1-10 and 2-10.

Although much care was given in solving these problems, the solver is only human. If you found any errors in the solution, please comment in the box below.

Note: If you have old MTAP questions, you can send them to mtapreviewers@gmail.com and I will solve them for you and post it here.

21.) When $P (x)$ is divided by $x^2 + 2$, the quotient and remainder are both $x$. What is $P(-1)$?

Solution
If we divide 5 by 3, then we get a quotient of 1 and a remainder of 2. If we generalize latex $a$ the dividend, $b$ as the divisor, $q$ as the quotient and $r$ as the remainder, we can form the equation Continue reading “Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 3”

## Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 2

This is the second part (questions 11-20) of the solutions of the Grade 8 MTAP 2015 Elimination Questions. You can read the solutions for questions 1-10 here. If you found any errors in the solution, please comment in the box below.

11.) If $x = 4$ and $y = -3$, what is $x^2y + xy^2$?

Solution

$x^2y + xy^2 = (4^2) (-3) + (4) (-3)^2 = (16) (-3) + 4(9)$
$= (-48) + 36 = -12$

12.) Simplify $x(1 + y) - 2y(x - 2) + xy$Continue reading “Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 2”

## Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 1

Below is the first part of the Grade 8 MTAP 2015 Elimination Questions with Solutions and answers. If you find any errors, please comment on the box below.

1.) Find the average of the numbers -1, 3/2, and 1/2.

Solution

(- 1 + 3/2 + 1/2)/3 = 1/3

2.) How much larger is 2/3 than 1/6?

Solution
2/3 – 1/6 = 4/6 – 1/6 = 3/6 = 1/2

3.) If one ream contains 500 sheets of paper and a sheet of paper is 0.3 mm thick, how thick is one ream in meters?

Solution

500 × 0.3mm = 150 mm = 0.15m

4.) What is the second largest number among numbers $\sqrt{2}$, 3/2 , 1.4, $\sqrt{3}$ and 1.6?

Solution

$\sqrt{2}$ is around 1.41 and $\sqrt{3}$ is around 1.7.

5.) If an inch is about 2.54 cm, what is 1 cm to the nearest hundredth of an inch?

Solution

$1:2.54 = x: 1, x = 0.39$

## 2015 Grade 6 MTAP Math Challenge – Division Orals

Below are the 2015 Grade 6 MTAP Math Challenge Division Oral Competition questions with answers.

15-second question (2 points each)

1.) If N 15 + 10 – 2 × 5 = N× 3, what is N?
4.) $(2^4) (9^) = (4^2) (y)$. Express y in exponential form.