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?

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2004 Grade 2 MTAP Sectoral Finals

2004 Metrobank-MTAP-NCR Math Challenge
Sectoral Finals – Grade 2

A. 15-second questions – 2 points each

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

Answer: 40

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

Answer: 1

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

Answer: 4

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

Answer: P850.00

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

Answer: P36.00

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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
Answer: 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
Answer: 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
Answer: 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.
Answer: 1.6

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

Answer: 0.39  Continue reading

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