Problem of the Week 8

This is the 8th problem of the week of MTAP Reviewer.

Problem

The diagonal of a square is 6cm. Find the area of the square that is twice its size.

Solution

We can divide a square into several ways, one of which is using its diagonal.

square
Click on the image to enlarge

Now, using the diagonal of the square as side of the larger square, we can create a larger square as shown above. As seen, the diagonal of the square cuts the square into half. This half region makes a fourth of the larger square (Can you see why?).

Since the length of the side of the larger square is the diagonal of the smaller square 6, the area of the larger square is 6× 6 = 36.

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Grade 6 MTAP Reviewer Set 7

This is the seventh set of the MTAP Reviewer for Grade 6.

1.) Write <, =, > in the blank below.

0.78  ____ 0.780

2.) Which of the following numbers has the smallest value?

0.6, \displaystyle \frac{3}{4}, \frac{1}{2}

3.) One number is twice another number. Their sum is 48. What are the numbers?

4.) Write the expression 4 \times 4 \times 4 in exponent form. Continue reading

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Problem of the Week 8 – Shaded Part

This is the eighth problem in our Problem of the Week.

Problem

Two semi-circles are placed inside a square as shown below. What is the area of the shaded part?

circle square shaded part

 

Solution 1

To get the area of the shaded part, we have to get the area of the square and then subtract the area of the two semicircles.  Continue reading

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Grade 5 MTAP Reviewer Set 7

This is the 7th set of the MTAP Reviewer for Grade 5.

1.) When a number is divided by 5, its quotient is 12 and its remainder is 3.  What is the number?

2.) If January 30 is Monday, what day will be February 1?

3.) What is the value of (12 × 4) – (5 × 5)?

4.) The perimeter of an isosceles triangle is less than is less than 40 cm. Two of its sides are 17 cm and 8cm. What is the length of the third side?

5.) What is 875 ÷ 100?  Continue reading

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Grade 4 – MTAP Reviewer Set 7

This is the seventh set of MTAP Reviewer for Grade 4.

1.) Which property of multiplication is shown in 8 × 1 = 8?

a. associative
b. commutative
c. identity
d. zero

2.) The number 6 hundred and 3 tens is equal to 300 + ___?

3.) Which of the following fractions is less than 5/10?

a. 1/2
b. 3/4
c. 5/9
d. 4/10

4.) The sum of two numbers is 20. Their quotient is 3. What are the two numbers? Continue reading

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