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Math: Middle School: Grades 6, 7 and 8 Quiz - Numbers - Indices (Questions)

This Math quiz is called 'Numbers - Indices' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.

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Cubed and squared are types of indices. In the Powers quiz you saw how, by writing numbers as powers of a common base, multiplication and division can be turned into addition or subtraction of indices making calculations with large or small numbers easier, as long as you follow the Math rules.

1. What is the result of 16 x 64 as a power of 2?
[ ] 26
[ ] 28
[ ] 210
[ ] 212
2. What is the result of 27 ÷ 28?
[ ] 1/2
[ ] 2
[ ] -1/2
[ ] -2
3. What is the result of dividing 25 by 625?
[ ] 51
[ ] 5-1
[ ] 52
[ ] 5-2
4. What is 0.24 as a power of 5?
[ ] 5-1
[ ] 5-2
[ ] 5-4
[ ] 5-5
5. What index number must follow 3 to give 6,561?
[ ] 7
[ ] 8
[ ] 9
[ ] 10
6. What is the result of 24 x 83?
[ ] 1,992
[ ] 8,192
[ ] 65,536
[ ] 99,664
7. How many liters will fill a cube of side length 25 cm?
[ ] 1.25
[ ] 15.625
[ ] 25.125
[ ] 61.25
8. How many days are there in 29 x 33 x 54 seconds?
[ ] 30
[ ] 50
[ ] 100
[ ] 125
9. A pond plant doubles its surface area every four days. If it covered an area of 20 cm2 on 17th June, what is its area on 15th July?
[ ] 2,560 cm2
[ ] 2.56 m2
[ ] 0.256 m2
[ ] 256 cm2
10. John started a savings account with a deposit of £500 at 1.5% compound interest per year. How much (to the nearest 1p) is the account worth after three years?
[ ] £168.75
[ ] £522.84
[ ] £760.44
[ ] £1,522.50
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Math: Middle School: Grades 6, 7 and 8 Quiz - Numbers - Indices (Answers)
1. What is the result of 16 x 64 as a power of 2?
[ ] 26
[ ] 28
[x] 210
[ ] 212
16 = 24; 64 = 26; 16 x 64 = 2(4 + 6)
2. What is the result of 27 ÷ 28?
[x] 1/2
[ ] 2
[ ] -1/2
[ ] -2
2(7 - 8) = 2-1 = 1/2 since the negative power is 1 over the positive power
3. What is the result of dividing 25 by 625?
[ ] 51
[ ] 5-1
[ ] 52
[x] 5-2
25 = 52; 625 = 54
4. What is 0.24 as a power of 5?
[ ] 5-1
[ ] 5-2
[x] 5-4
[ ] 5-5
0.2 = 1/5 = 5-1
5. What index number must follow 3 to give 6,561?
[ ] 7
[x] 8
[ ] 9
[ ] 10
6,561 = 81 x 81 = 34 x 34
6. What is the result of 24 x 83?
[ ] 1,992
[x] 8,192
[ ] 65,536
[ ] 99,664
Convert 83 to a power of 2 before adding the indices
7. How many liters will fill a cube of side length 25 cm?
[ ] 1.25
[x] 15.625
[ ] 25.125
[ ] 61.25
253 ÷ 1,000 = 56 ÷ 103. Remember 1,000 cm3 = 1 liter
8. How many days are there in 29 x 33 x 54 seconds?
[ ] 30
[ ] 50
[x] 100
[ ] 125
Divide by 60 x 60 = 24 x 32 x 52 to find the hours, then divide by 24 = 23 x 31 to find days
9. A pond plant doubles its surface area every four days. If it covered an area of 20 cm2 on 17th June, what is its area on 15th July?
[x] 2,560 cm2
[ ] 2.56 m2
[ ] 0.256 m2
[ ] 256 cm2
'30 days hath September, April, June and November .......' so the plant has been growing for 28 = 4 x 7 days; 20 x 27
10. John started a savings account with a deposit of £500 at 1.5% compound interest per year. How much (to the nearest 1p) is the account worth after three years?
[ ] £168.75
[x] £522.84
[ ] £760.44
[ ] £1,522.50
After 1 year 500 x 1.015; after 3 years 500 x 1.0153
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