## 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 $x = \frac{9}{4}$

Below are the 2004 Grade 4 MTAP Elimination questions with solutions/answers (numbers 26 – 50). You can read items 1 – 25 here. Although these are old questions, you can still use them as reviewer since the coverage of the quiz has not changed. I have written the solution to relatively hard problems, but I leave the easy ones to the coach and the student.

Note that even though reasonable care was given to the accuracy of the solutions, the solver is only human. Please use the comment box if you see any errors.

26.) 6 2/3 is equal to how many thirds?

27.) Change 8 7/12 to an improper fraction.

28.) Change 128/11 to a mixed number.

29.Which is greater, 11/13 or 16/19 ?

30.) Reduce 54/72 to lowest terms.

Below are the 2004 Grade 4 MTAP Elimination questions with solutions/answers. Although these are old questions, you can still use them as reviewer since the coverage of the quiz has not changed. I have written the solution to relatively hard problems, but I leave the easy ones to the coach and the student.

Note that even though I took a lot of time reviewing the solutions, I am only human. Please use the comment box if you see any errors.

2004 – ELIMINATION Metrobank-MTAP-DepEd Math Challenge (Grade 4)

Solve each item on scratch paper and write the answer on the blank.
1.) Round 23,503 to the nearest thousand.

2.) What is the remainder when 7 893 is divided by 26?

3.) Write two million, seventy-eight thousand, six hundred five in figures.

4.) Three million is equal to how many thousands?

5.) What is the biggest common divisor of 32 and 48?

## 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.

Also available: Questions 11-20

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 $(1, 1)$?
$2x + 5y = -6$
$5y = -2x - 6$
$y = \frac{-2}{5}x - \frac{6}{5}$
So, the slope of the given line is $-\frac{2}{5}$Continue reading “Grade 8 MTAP 2015 Elimination Questions with Solutions – Part 5”