6th GRADE MATH TEST ONLINE

Problem 1 :

Find the area of the following shape :

Solution :

By drawing a vertical line, we can divide the given shape in to shapes.

Area of rectangle in the left + area of rectangle in the right

= 8 x 4 + (8 x 3)

= 32 + 24

= 56 cm²

Problem 2 :

Max has more than 4 apples but fewer than 7 apples. Alex has more than 5 apples and fewer than eight apples. How many apples do Max and Alex have altogether?

Circle all the possible values

4     5    6     7    8    9    10    11     12   13   14    15

Solution :

Given information :

4 < number of apples Max has < 7

5 < number of apples Alex has < 8

Let M be the number of apples and A be number of apples Alex has.

• M = 5, A = 6, then M + A = 11
• M = 6, A = 6, then M + A = 12
• M = 5, A = 7, then M + A = 12
• M = 6, A = 7, then M + A = 13

Then the total number of apples altogether is 11, 12 and 13.

Problem 3 :

Suki saves £12 in January, £18 in February and £5 in March. What is her mean (average) monthly saving?

Solution :

Mean = Total savings / 3

= (12 + 18 + 5) / 3

= 35/3

= 11.6

So, the mean is £11.6.

Problem 4 :

What is 1/2 of 4/5 of 35 ?

Solution :

1/2 of 4/5 of 35

Problem 5 :

Put the following numbers in order from smallest to largest :

Solution :

Here two quantities are in the form of fraction and the other quantity is in the form of percentage.

Converting everything into decimal, we can do the comparison simply.

3/5 = 0.6

5/8 = 0.625

62% = 62/100 = 0.62

Arranging from least to greatest,

0.508, 0.58, 0.6, 0.620, 0.625, 

0.508, 0.58, 3/5, 62%, 5/8

Problem 6 :

You are told that 82 × 107 = 8774 Use this to work out the value of the following:

a. 8200 × 107

b. 8774 ÷ 107

c. 8774 ÷ 41

Solution :

82 × 107 = 8774

a)  8200 x 107 = 82 x 100 x 107

= (82 x 107) x 100

= 8774 x 100

= 877400

b. 8774 ÷ 107 = 82

c. 8774 ÷ 41 

Given : 82 x 107 = 8774

2 x 41 x 107 = 8774

8774 ÷ 41 = 2 x 107

= 214

Problem 7 :

A bus can seat 82 people. 8770 people travel to a football match by bus. How many buses are needed?

Solution :

Number of seats in the bus = 82

Number of people has to travel to a foot ball match = 8770

Number of buses needed = 8770/82

= 106.9

So, 107 buses are needed.

Problem 8 :

B + A + T = 17

C + A + T = 25

C + O + A + T = 29

What is the value of B + O + A + T?

Solution :

B + A + T = 17  ----(1)

C + A + T = 25  ----(2)

C + O + A + T = 29  ----(3)

Applying (2) in (3), we get

O + 25 = 29

O = 29 - 25

O = 4

We should find the value of, B + O + A + T

= (B + A + T) + O

= 17+4

= 21

So, the value of B + O + A + T is 21.

Problem 9 :

A rectangle is 6cm longer than it is wide. Its perimeter is 32cm. Find its area.

Solution :

Let x be the width of the rectangle. Then length of the rectangle will be x + 6.

Perimeter = 32 cm

2(x + x + 6) = 32

2x + 6 = 32/2

2x + 6 = 16

2x = 16 - 6

2x = 10

x = 5

Width of the rectangle = 5 cm, length of the rectangle = 11 cm

Area = length x width

= 5 x 11

= 55 cm²

Problem 10 :

On Planet Pythagoras, the people use a different money system to us. One pog is worth four pings Three pings are worth five paz Convert the following:

A. 3 pog = _____ pings

B. 40 paz = ____________ pog

C. 3 paz = ____________ pog

Solution :

1 pog is = 4 pings

3 pings = 5 paz

A)

3 pog = 3 x 4 

= 12 pings

B)

40 paz = ____________ pog

1 paz = 3/5 pings

40 paz = (3/5) x 40

= 24 pings

1 ping = 1/4 pog

24 pings = 24 x (1/4)

= 6 pog

C.

3 paz = ____________ pog

1 paz = 3/5 pings

3 paz = 3 x (3/5)

= 9/5 pings

3 pings = 5 paz

1 ping = 5/3 paz

9/5 pings = 9/5 x (5/3)

= 3 paz