Edexcel IGCSE Math A 1.8 degree of accuracy

Use accuracy questions to round values, estimate calculations and choose upper or lower bounds before giving suitable final answers.

Exam points

Round integers, decimals and significant figures to the accuracy stated in the question.
Use one-significant-figure estimates to simplify powers, roots, products and quotients.
Choose upper and lower bounds for measurements before calculating a suitable value.

Covered syllabus points

1.8.A Round integers to a given power of 10 1.8.B Rounding to significant figures or decimal places 1.8.C Upper and lower bounds 1.8.D Estimating numerical calculations 1.8.HA Upper- and lower-bound problems

[Maximum number: 4]

The weight of a cake is 2.75 kg , correct to 2 decimal places.

(a)

Write down the lower bound of the weight of the cake.

[ 1 ]

(b)

Write down the upper bound of the weight of the cake.

Penny has worked out $\frac{81.3 \times 59.2}{1.9^{2}}$ on her calculator.
Her answer is 13332.29917
Penny's answer is not sensible.

[ 1 ]

(c)

By rounding each number to one significant figure, work out a suitable estimate to show that her answer is not sensible.
Show your working clearly.

[ 2 ]

Estimate:
$\frac{80\times60}{2^2}=1200$

Final answer:
1200

Working with rounded values required.

[Maximum number: 5]

$24 D=\frac{n}{p-q}$
n=10.3 correct to 1 decimal place
p=7.24 correct to 2 decimal places
q=4.39 correct to 2 decimal places
By considering bounds, work out the value of D to a suitable degree of accuracy. Show your working clearly.

Bounds:
$10.25\le n<10.35,\quad 7.235\le p<7.245,\quad 4.385\le q<4.395$
For $D=\frac{n}{p-q}$ :
$D_{\mathrm{UB}}=\frac{10.35}{7.235-4.395}=3.644\ldots$ $D_{\mathrm{LB}}=\frac{10.25}{7.245-4.385}=3.583\ldots$
Both bounds round to:
3.6

Final answer:
$D=3.6\text{ to 1 decimal place}$

B2 for all six correct bounds. M1 for a correct upper or lower bound method. M1 for both bounds. A1 for 3.6.

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Covered syllabus points

1.8 Degree of accuracy question 1

Question (a)

Question (b)

Question (c)

1.8 Degree of accuracy question 2