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GCSEMathsOCRExam Questions4. Approximation & EstimationUsing a Calculator

Using a Calculator (OCR GCSE Maths)

Exam Questions

57 mins26 questions
Easy
Medium
Hard
1a
Sme Calculator2 marks

Use your calculator to work out  fraction numerator 38.5 space cross times space 14.2 over denominator 18.4 space minus space 5.9 end fraction 

Write down all the figures on your calculator display.
You must give your answer as a decimal.

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1b
Sme Calculator1 mark

Write your answer to part (a) correct to 1 significant figure.

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2
Sme Calculator2 marks

Use a calculator to work out

fraction numerator square root of 20.4 end root over denominator 6.2 cross times 0.48 end fraction

Write down all the figures on your calculator display.
Give your answer as a decimal.

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3a
Sme Calculator2 marks

Use your calculator to work out   fraction numerator square root of 7056 over denominator 0.35 cross times 12.8 end fraction

Write down all the figures on your calculator display.
You must give your answer as a decimal.

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3b
Sme Calculator1 mark

Write your answer to part (a) correct to 1 significant figure.

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4a
Sme Calculator2 marks

Calculate.

square root of fraction numerator 4.8 squared plus 3.6 squared over denominator 4 end fraction end root

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4b
Sme Calculator2 marks

fraction numerator 1 over denominator open parentheses 2 cross times 10 to the power of 4 close parentheses plus open parentheses 5 cross times 10 cubed close parentheses end fraction

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5
Sme Calculator2 marks

Work out left parenthesis 5.6 cross times 10 to the power of 6 right parenthesis space plus space left parenthesis 2.3 cross times 10 to the power of 5 right parenthesis.

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6
Sme Calculator1 mark

Work out the square root of 100 million.
Circle your answer.

1000 10 000 100 000 1 000 000

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7
Sme Calculator2 marks

Work out   fraction numerator square root of 17 plus 4 squared end root over denominator 7.3 squared end fraction

Write down all the figures on your calculator display.

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8
Sme Calculator2 marks

Work out  4.2 cross times 10 cubed plus 5.3 cross times 10 squared


Give your answer in standard form.

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9
Sme Calculator1 mark

Calculate fraction numerator 4 over denominator square root of 0.0025 end root end fraction.

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10
Sme Calculator1 mark

Calculate.

5 over 8 plus cube root of 340

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11
Sme Calculator1 mark

Calculate.

fraction numerator 5.39 minus 0.98 over denominator 0.743 minus 0.0743 end fraction

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12
Sme Calculator1 mark

Calculate square root of 2.38 plus 6.4 squared end root, writing down your full calculator display.

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1
Sme Calculator2 marks

Calculate the value of square root of fraction numerator tan space 60 to the power of ring operator space plus space 1 over denominator tan space 60 to the power of ring operator space minus space 1 end fraction end root

Write down all the figures on your calculator display.
You must give your answer as a decimal.

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2a
Sme Calculator2 marks

Use your calculator to work out   fraction numerator square root of 70.25 end root over denominator 4.2 minus 2.37 end fraction

Write down all the figures on your calculator display
You must give your answer as a decimal.

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2b
Sme Calculator1 mark

Write your answer to part (a) correct to 4 decimal places.

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3
Sme Calculator2 marks

Use your calculator to work out fraction numerator 1.45 squared over denominator 3.89 minus space square root of 5.75 end root end fraction

Write down all the figures on your calculator display.
You must give your answer as a decimal.

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4a
Sme Calculator2 marks

Use your calculator to work out   square root of fraction numerator sin 25 to the power of ring operator plus space sin 40 to the power of ring operator over denominator cos 25 to the power of ring operator minus space cos 40 to the power of ring operator end fraction end root

Write down all the figures on your calculator display.

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4b
Sme Calculator1 mark

Write your answer to part (a) correct to 2 decimal places.

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5
Sme Calculator2 marks

Work out fraction numerator 5.6 space cross times space 10 to the power of 4 space end exponent plus space 7 space cross times 10 cubed over denominator 2.8 cross times 10 to the power of negative 3 end exponent end fraction

Give your answer in standard form.

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6
Sme Calculator2 marks

Work out  fraction numerator 3 cross times 10 to the power of 5 space minus space 2.7 space cross times 10 to the power of 4 over denominator 6 cross times 10 to the power of negative 2 end exponent end fraction

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7
Sme Calculator2 marks

An approximation for the value of pi is given by

4 open parentheses 1 minus 22 over 57 plus 22 over 85 minus 22 over 105 plus 22 over 117 minus 22 over 242 close parentheses


Use your calculator to show that this approximation is within 0.1 of 3.14

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8
Sme Calculator2 marks

Work out   fraction numerator 3.2 cross times 10 cubed plus 5.1 cross times 10 to the power of negative 2 end exponent over denominator 4.3 cross times 10 to the power of negative 4 end exponent end fraction

Give your answer in standard form, correct to 3 significant figures.

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1a
Sme Calculator1 mark

Find the reciprocal of 2.5

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1b
Sme Calculator2 marks

Work out    cube root of fraction numerator 4.3 space cross times space tan space 39 to the power of ring operator over denominator 23.4 space minus space 6.06 end fraction end root

Give your answer correct to 3 significant figures.

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2
Sme Calculator2 marks
i)
Find the value of fifth root of 3.2 cross times 10 to the power of 11 end root
[1]
ii)
Find the value of 10 to the power of 3 over 4 end exponent
Give your answer correct to 1 decimal place.
[1]

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3
Sme Calculator2 marks

Work out                          square root of fraction numerator 2.5 space cross times space sin space 43 to the power of ring operator over denominator 8.2 squared space minus space 50.5 end fraction end root

Give your answer correct to 3 significant figures.

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4a
Sme Calculator1 mark

Use your calculator to work out 19.42 squared space – space cube root of 1006 space divided by space 4.95

Write down your full calculator display.

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4b
Sme Calculator2 marks

Use approximations to check that your answer to part (a) is sensible.

You must show your working.

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5
Sme Calculator3 marks

Use the formula  x subscript n plus 1 end subscript equals cube root of 10 minus 2 x subscript n end root  to find the values of x subscript 1, x subscript 2 and x subscript 3 to 3 decimal places
Start with x subscript 0 equals 2

x subscript 1 equals space......  
x subscript 2 equals space......  
x subscript 3 equals space.....  

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6a
Sme Calculator2 marks

Use your calculator to work out fraction numerator 29 squared minus 4.6 over denominator square root of 35 minus 1.9 cubed end root end fraction

Write down all the figures on your calculator display.

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6b
Sme Calculator1 mark

Write your answer to part (a) correct to 4 significant figures.

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