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”

2004 Grade 4 MTAP Elimination Questions with Answers Part 2

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?
Answer: 10

27.) Change 8 7/12 to an improper fraction.
Answer: 103/12

28.) Change 128/11 to a mixed number.
Answer: latex 7 \frac{7}{11}$

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

30.) Reduce 54/72 to lowest terms.
Answer: 3/4  Continue reading “2004 Grade 4 MTAP Elimination Questions with Answers Part 2”

2004 Grade 4 MTAP Elimination Questions with Answers Part 1

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.
Answer: 24 000

2.) What is the remainder when 7 893 is divided by 26?
Answer: 15

3.) Write two million, seventy-eight thousand, six hundred five in figures.
Answer: 2 078 605

4.) Three million is equal to how many thousands?
Answer: 3 000

5.) What is the biggest common divisor of 32 and 48?
Answer: 16  Continue reading “2004 Grade 4 MTAP Elimination Questions with Answers Part 1”

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

Answer: 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}.

Answer: 5/12  Continue reading “Grade 9 MTAP 2015 Elimination Questions with Solutions – Part 1”

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

Answer: – 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 5”