# Category Archives: Problems with Solutions

## 2010 4th Year Math Challenge – National Level with answer key

Below are the 2010 MTAP 4th Year Math Challenge – National Level questions and answers. Solutions will be posted later. More reviewers can be found on the Past Tests and All Posts pages.

Easy

1.) Ricky has (4a + 1) ₧100 bills and Emil has (2a – 2) Php 50 bills. How much more money has Ricky than Emil?

2.) The graphs of $y = 10 - x^2$ and $y + 1 = 0$ intersect at two points. Find the distance between these points

3.) If r and s are the roots of $x^2 = x + 30$, what is ∣r – s∣?

4.) A triangle has sides with integral length. If its perimeter is 12 cm, what is the longest possible side of the triangle?

5.) If the length of a rectangle is increased by 10% and the area is increased by 120%, by how many percent is the width increased?

## 2004 Grade 2 MTAP Sectoral Finals

2004 Metrobank-MTAP-NCR Math Challenge

A. 15-second questions – 2 points each

1) There are 48 pupils in a class. If 1/6 are absent, how many are present?

2) What is the remainder when 97 is divided by 4?

3) How many prime numbers are there between 10 and 20?

4) Jasmin and Jack bought two pairs of shoes. Each pair cost P425, how much in all did they pay?

5) Eight boys have P4.50 each. How much money do they have in all?

## 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

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

## Grade 7 MTAP 2015 Questions with Solutions Part 2

This is the second part of the full solution series for the MTAP 2015 Questions with solutions. You may also want to read the solutions for problems 1 – 10 and download the questions.

11.) Danny had some stickers. He gave 1/3 of the stickers plus 1 sticker to his brother. Then, he gave 1/3 of the remaining stickers plus 4 stickers to his sister. Finally, he gave ½ of what remained plus 3 stickers to best friend. He found that he had 4 stickers left. How many stickers did Danny have at first?

Solution
If we let $x$ = number of stickers
$\frac{1}{3}x + 1$ = number of stickers given to his brothers. If we subtract the stickers given to his brother, we have  Continue reading

## Grade 7 MTAP 2015 Questions with Solutions Part 1

Below are actual MTAP Questions that has been released. I have created a detailed solution for each question. In this post, we answer 1-10. You can also read the solutions of problems 2-20.  The file can be downloaded here.

1.) Simplify: $2(3)^2 - 3(2)^3 + (1 - 4)^3$

Solution
$2(3)^2 - 3(2)^3 + (1-4)^3$
$= 2(9)- 3(8) + (-3)^3$
$= 18 - 24 + (-27)$
$= -33$

Answer: $-33$

2.)  By how much is 3 – 1/3 greater than 2 and 1/2?

Solution

$3 - \frac{1}{3} = 2 \frac{2}{3}$
$2 - \frac{1}{2} = 1 \frac{1}{2}$

Subtracting the two results, we have  Continue reading