## Grade 9 MTAP 2015 Elimination Questions with Solutions – Part 1

This is the first part (questions 1-10) of the solutions of the Grade 9 MTAP 2015 Elimination Questions. Although much care has been given to make the solution as accurate as possible, the solver is also human. Please comment below if you see any errors.

1.) Simplify $\sqrt{\frac{3}{2}} - \sqrt{\frac{2}{3}}$

Solution

$\sqrt {\dfrac{3}{2}} - \sqrt {\dfrac{2}{3}} = \dfrac {\sqrt {3}}{\sqrt {2}} - \dfrac {\sqrt {2}}{\sqrt {3}} = \dfrac {(\sqrt {3})^2-(\sqrt {2})^2}{\sqrt {2}\sqrt {3}} = \dfrac {1}{\sqrt {6}}$.

Rationalizing the denominator,

$\dfrac {1}{\sqrt {6}} \times \dfrac {\sqrt {6}}{\sqrt {6}} = \dfrac {\sqrt {6}}{6}$.

Answer: $\sqrt{6}/6$

2.) Evaluate $\dfrac{2^0 + 2{^-1}}{2^{-2} + 2^{-3}}$

Solution

$\dfrac {2^0 + 2^{-1}}{2^{-2} + 2^{-3}} = \dfrac {1 + \frac {1}{2}}{\frac {1}{4} + \frac {1}{8}} = \dfrac {\frac {3}{2}}{\frac {3}{8}} = \dfrac {3}{2} \times \dfrac {8}{3} = 4$

3.) Simplify $\sqrt{ \dfrac{1}{9} + \dfrac{1}{16}}$.

Solution

$\sqrt{\dfrac{1}{9} + \dfrac {1}{16}} = \sqrt {\dfrac{16 + 9}{(9)(16)}} = \sqrt{\dfrac{25}{(9)(16)}} =\dfrac{5}{(3)(4)} = \dfrac{5}{12}$.

## Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 5

This is the fifth part (questions 41-50) of the solutions of the Grade 8 MTAP 2015 Elimination Questions. You can read the solutions for questions 1-10 11-20, 21 – 30, and 31 – 40

41.) If $f (2x) = 2 - 3x$, what is $f(10)$?

Solution
$2x = 10$, $x = 5$.
$f(10) = 3 - 3(5) = -13$

42.) What is the equation of the line that is parallel to $2x + 5y + 6 = 0$ and passes through $(1, 1)$?

Solution

Parallel lines have the same slope, so we get the slope of the given line. That is,

$2x + 5y = -6$
$5y = -2x - 6$
$y = \frac{-2}{5}x - \frac{6}{5}$

So, the slope of the given line is $-\frac{2}{5}$Continue reading

## 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 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 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