# Category Archives: Solved Problems

## 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

## Solved Problem 1: Largest 3 Digit Number

What is the largest number 3-digit number that can be formed between 300 and than 800 using the digits 2, 5, 8 and 6 if the digits cannot be repeated?

Solution

In this problem, we need to find a 3 digit number that is more than 300 and less than 800.

Selecting the Hundreds Digit

There are only two possible number that can be placed in the hundred’s digit. Since the number that we are looking for is more than 300, we cannot place 2 in the hundred’s digit. Also, we cannot place 8 in the hundred’s digit since it will be more than 800. Therefore, we can only choose between 5 and 6. Since we want the largest number, we have to choose 6. So our number is 6AB where A and B are the tens and the ones digit respectively.  Continue reading

## Shaded Area – Right Triangle Inscribed in a Circle

A right triangle is inscribed in a circle such that its longest side is the diameter of the circle. If the shorter sides of the triangle measure 6cm and 8cm, find the area of the shaded region. Use $\pi = 3.14$

Solution

A triangle inscribed in a circle with its longest side as the diameter of the circle is always a right triangle (by Thales’ Theorem). So, we can find the area $A_T$ of the triangle.

Finding the area of the triangle,

$A_T = \frac{6 \times 8}{2} = 24$Continue reading

## Shaded Region – Circle Inscribed in a Square

A circle with radius 3 cm is inscribed in a square.

Find the area of the shaded region. Let pi = 3.14 and round your answer to the nearest tenths.

Solution

We know that

area of shaded region = area of square – area of circle  Continue reading

## Shaded Area – Square Inscribed in a Circle

The diagonal of the square inscribed in the circle below is 8cm. Find the shaded area. (Use pi = 3.14)

Solution

From the diagram above, we can get the shaded area by subtracting the area of the square from the area of the circle.

We let the diagonal of the square be the base of two the triangles. Next, we draw the height of one of the triangles. Continue reading