What is N14: Estimation?

An estimate replaces the original inputs with nearby values that are easy to calculate, often by rounding each to one significant figure. Carry out the operation on those rounded inputs and use ≈, because the result is not exact.

How many marks are N14 questions worth?

In verified past-paper appearances, N14 questions on Edexcel GCSE Maths 1MA1 have been worth 3–6 marks.

Which past exam papers has N14 appeared in?

N14 has appeared in 12 verified past-paper questions indexed on this page, with direct links to the official question paper and mark scheme for each.

N14

Estimate answers; check calculations using approximation and estimation, including answers obtained using technology

Estimation

Worked answers, methods and verified real exam appearances for N14 on Edexcel GCSE Maths 1MA1.

Explanation

An estimate replaces the original inputs with nearby values that are easy to calculate, often by rounding each to one significant figure. Carry out the operation on those rounded inputs and use $\approx$ , because the result is not exact.
Estimation checks whether a calculator answer has a sensible size, sign and decimal position; it should be an independent calculation, not a rounding of the calculator display.
Choose compatible approximations, especially for division, so mental arithmetic stays simple.
If the exact answer differs by about a factor of $10$ or $100$ , suspect a place-value entry error.
Examiners require both the estimate and a clear comparison when asked to comment.

Worked example

A calculator gives $931.24$ for $\dfrac{598.4\times0.0317}{0.204}$ . Use an estimate to decide whether it is reasonable.

1.Round inputs to convenient values: $598.4\approx600$ , $0.0317\approx0.03$ , $0.204\approx0.2$ .
2.Estimate $\dfrac{600\times0.03}{0.2}=90$ .
3.Compare $931.24$ with $90$ : the display is roughly ten times too large.

Answer: The display is not reasonable.

Common mistakes

Don't round only the final calculator answer instead of estimating from the inputs.
Don't use $=$ rather than $\approx$ between an expression and its estimate.
Don't round a small decimal such as $0.0317$ to zero.

Exam tip

In a “check using estimation” question, state whether the given answer is reasonable and support the decision with your rounded calculation.

Worked practice

Tier 1 · Easy

Estimate the value of

19.8\times0.49

(1)

(Total for Question 1 is 1 mark)

Mark scheme

Mark scheme for question 1
Question	Answer	Mark	Mark scheme
1	$10$	1	Use convenient one-significant-figure values: $19.8\approx20$ and $0.49\approx0.5$ . Then $20\times0.5=10$ .

Tier 2 · Standard

Estimate

\dfrac{48.7\times0.203}{0.098}

(2)

(Total for Question 2 is 2 marks)

Mark scheme

Mark scheme for question 2
Question	Answer	Mark	Mark scheme
2	$100$	2	Round to convenient values: $48.7\approx50$ , $0.203\approx0.2$ and $0.098\approx0.1$ . Then $\dfrac{50\times0.2}{0.1}=\dfrac{10}{0.1}=100$ .

Tier 3 · Hard

A calculator display gives

931.24

for

\dfrac{598.4\times0.0317}{0.204}

. Use an estimate to decide whether this display is reasonable. Give a reason.

(3)

(Total for Question 3 is 3 marks)

Mark scheme

Mark scheme for question 3
Question	Answer	Mark	Mark scheme
3	The display is not reasonable. An estimate is $90$ , so the displayed answer is about ten times too large.	3	Use $598.4\approx600$ , $0.0317\approx0.03$ and $0.204\approx0.2$ . This gives $\dfrac{600\times0.03}{0.2}=\dfrac{18}{0.2}=90$ . Since $931.24$ is near $900$ rather than $90$ , it is not reasonable and likely has a decimal-place error.

Tier 1 · Easy

By rounding each number to

1

significant figure, estimate the value of

72.4+26.3

(1)

(Total for Question 4 is 1 mark)

Mark scheme

Mark scheme for question 4
Question	Answer	Mark	Mark scheme
4	$100$	1	Round each number to $1$ significant figure: $72.4\approx70$ and $26.3\approx30$ . Then $70+30=100$ .

Tier 2 · Standard

Estimate the value of

9.8^2+51

by rounding each number to

1

significant figure.

(2)

(Total for Question 5 is 2 marks)

Mark scheme

Mark scheme for question 5
Question	Answer	Mark	Mark scheme
5	$150$	2	Use $9.8\approx10$ and $51\approx50$ . Then $10^2+50=100+50=150$ .

Tier 3 · Hard

Each pack of seed covers

2.9

^2

. A garden has area

118

^2

. Use an estimate to decide whether

35

packs will cover the garden. Give a reason.

(3)

(Total for Question 6 is 3 marks)

Mark scheme

Mark scheme for question 6
Question	Answer	Mark	Mark scheme
6	No; about $40$ packs are needed, so $35$ packs will not cover the garden.	3	Use $118\approx120$ and $2.9\approx3$ . The estimated number of packs is $120\div3=40$ . Since $35<40$ , $35$ packs will not cover the garden.

Tier 2 · Standard

By rounding each number to

1

significant figure, estimate the value of

\dfrac{31.2\times197}{0.62}

(3)

(Total for Question 7 is 3 marks)

Mark scheme

Mark scheme for question 7
Question	Answer	Mark	Mark scheme
7	$10\,000$	3	$31.2\approx30$ , $197\approx200$ and $0.62\approx0.6$ . The estimate is $\dfrac{30\times200}{0.6}=\dfrac{6000}{0.6}=10\,000$ .

Tier 3 · Hard

The value of

\dfrac{498\times19.6}{0.204}

lies in one of these intervals. A:

400

600

. B:

4000

6000

. C:

40\,000

60\,000

. Use an estimate to choose the correct interval. Write down the letter of the interval.

(3)

(Total for Question 8 is 3 marks)

Mark scheme

Mark scheme for question 8
Question	Answer	Mark	Mark scheme
8	C $40\,000$ to $60\,000$	3	$498\approx500$ , $19.6\approx20$ and $0.204\approx0.2$ . The estimate is $\dfrac{500\times20}{0.2}=50\,000$ , which lies in interval C.

Tier 3 · Hard

Replace all three numbers by their

1

-significant-figure approximations to estimate

\dfrac{76.2\times0.384}{2.17}

. State whether the estimate is an overestimate or an underestimate, and give a reason.

(4)

(Total for Question 9 is 4 marks)

Mark scheme

Mark scheme for question 9
Question	Answer	Mark	Mark scheme
9	$16$ ; it is an overestimate.	4	$76.2\approx80$ , $0.384\approx0.4$ and $2.17\approx2$ , giving $\dfrac{80\times0.4}{2}=16$ . Both numerator factors were rounded up while the denominator was rounded down, so these changes all increase the value. The estimate is therefore an overestimate.

Q10

Tier 3 · Hard

A packing line seals

293

cartons in

8.2

minutes. It has

60

minutes to seal

2050

cartons. Use an estimated sealing rate to decide whether the available time should be enough.

(4)

(Total for Question 10 is 4 marks)

Mark scheme

Mark scheme for question 10
Question	Answer	Mark	Mark scheme
10	Yes; the estimated capacity is $2250$ cartons, so the time should be enough.	4	Use $293\approx300$ and $8.2\approx8$ , giving an estimated rate of $300\div8=37.5$ cartons per minute. In $60$ minutes the line should seal about $37.5\times60=2250$ cartons. This exceeds the target by $200$ cartons, about $9.8\%$ of $2050$ , so the estimate supports the decision that the time should be enough.

Verified exam appearances

Series	Paper	Question	Marks	Calculator	Tier	Links
2022-06	1F	Q15	3	Non-calculator	Foundation	QP MS
2023-06	1F	Q11	6	Non-calculator	Foundation	QP MS
2024-06	1H	Q5	4	Non-calculator	Higher	QP MS
2023-11	1F	Q26	3	Non-calculator	Foundation	QP MS
2024-11	1F	Q22	4	Non-calculator	Foundation	QP MS
2021-11	1H	Q10	4	Non-calculator	Higher	QP MS
2024-06	1F	Q24	4	Non-calculator	Foundation	QP MS
2019-06	3F	Q11	4	Allowed	Foundation	QP MS
2019-11	1F	Q12	5	Non-calculator	Foundation	QP MS
2019-11	3F	Q23	3	Allowed	Foundation	QP MS
2019-06	1H	Q8	4	Non-calculator	Higher	QP MS
2024-11	1H	Q5	4	Non-calculator	Higher	QP MS

Other points in N Number

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