The width of a field is 60 m, correct to the nearest 10 metres. Write down the lower bound and the upper bound of the width, in metres.

lower bound = 55, upper bound = 65

A and B are two measurements that have been rounded. Which calculation gives the upper bound of A B?

upper bound of A divided by lower bound of B

upper bound of A divided by upper bound of B

lower bound of A divided by lower bound of B

lower bound of A divided by upper bound of B

Are bounds and error intervals on the Foundation paper?

Error intervals from rounding and truncation (spec ref N15) are on both tiers, so a Foundation candidate can be asked to complete a statement like 23.5 x < 24.5. Applying upper and lower bounds inside a calculation, for example finding the bounds of a speed or an area, sits in N16 and is Higher tier only.

Why is the upper bound 24.5 if 24.5 rounds up to 25?

The upper bound is defined as the value the measurement must be below, not a value it is allowed to equal. That is why the interval is written 23.5 x < 24.5 with a strict inequality at the top end. Edexcel mark schemes credit 24.5; 24.49 and 24.499 are marked wrong, and they also drag rounding error into every later step.

How many marks are bounds questions worth on Edexcel Higher?

Completing an error interval is usually 2 marks. A calculation that uses bounds is typically 3-5 marks, and the version that ends 'give your answer to a suitable degree of accuracy' is often 5 marks because it needs both bound calculations and a written reason. Across a paper expect roughly 2-5 marks.

Do I need a calculator for bounds questions?

Not for the short ones. Paper 1 is non-calculator and regularly carries the write-down-a-bound and error interval questions, where all you do is halve the rounding unit. Papers 2 and 3 carry the speed, density and area versions, where the divisions are untidy and a calculator is assumed.

Bounds and Error Intervals - Edexcel GCSE Higher Maths

Q: Why is the upper bound 24.5 if 24.5 rounds up to 25?

The upper bound is defined as the value the measurement must be below, not a value it is allowed to equal. That is why the interval is written 23.5 x < 24.5 with a strict inequality at the top end. Edexcel mark schemes credit 24.5; 24.49 and 24.499 are marked wrong, and they also drag rounding error into every later step.

Q: How many marks are bounds questions worth on Edexcel Higher?

Completing an error interval is usually 2 marks. A calculation that uses bounds is typically 3-5 marks, and the version that ends 'give your answer to a suitable degree of accuracy' is often 5 marks because it needs both bound calculations and a written reason. Across a paper expect roughly 2-5 marks.

Q: Do I need a calculator for bounds questions?

Not for the short ones. Paper 1 is non-calculator and regularly carries the write-down-a-bound and error interval questions, where all you do is halve the rounding unit. Papers 2 and 3 carry the speed, density and area versions, where the divisions are untidy and a calculator is assumed.

Typically 2-5 marks per paper, more when bounds are folded into a speed or density question · Spec 1MA1

Any measurement written down after rounding hides a range of true values, and that range is what this topic tests. On Edexcel 1MA1, spec point N15 covers rounding to a stated accuracy and writing an error interval in inequality notation, including intervals produced by truncation rather than rounding. Spec point N16 asks you to apply and interpret limits of accuracy, and the upper and lower bound work inside N16 is Higher tier only. A length recorded as 24 cm to the nearest centimetre has a lower bound of 23.5 cm and an upper bound of 24.5 cm, written $23.5 \le x < 24.5$ .

Edexcel sets this on all three papers. The short version is a 2-mark fill-in: complete the error interval, or write down the upper bound. That can land on Paper 1, which is non-calculator, so you have to halve the rounding unit in your head and keep the bound exact. The longer version belongs to Papers 2 and 3, where a speed, a density, an area or a length comes from two rounded measurements and the question is worth 3-5 marks, often finishing with the instruction to give the answer to a suitable degree of accuracy and to show all working.

Two habits account for most of the lost marks. Students write the upper bound as 24.49 or 24.499 because 24.5 would round up, when the mark scheme wants 24.5 exactly; and in a division or a subtraction they pair the wrong bounds, dividing the upper by the upper instead of the upper by the lower. Practise setting out all four bounds in a small table before you touch the calculator, then ask which combination makes the answer as large as possible. Carry the bounds through unrounded and round only the final line.

Worked example

A drone flies a distance of 1860 metres, correct to the nearest 10 metres. It takes 64 seconds, correct to the nearest second. The average speed of the drone is

V

m/s. By considering bounds, work out the value of

V

to a suitable degree of accuracy. You must show your working and give a reason for your answer.

[5 marks]

Nearest 10 metres means half a unit of 5 either side, so the distance lies in $1855 \le d < 1865$ .
B1: both bounds for the distance, written exactly (not 1864.9)
Nearest second means half a unit of 0.5 either side, so the time lies in $63.5 \le t < 64.5$ .
B1: both bounds for the time
Speed is distance divided by time, so the largest speed uses the largest distance over the smallest time: $1865 \div 63.5 = 29.3700\ldots$ m/s.
M1: upper bound of $d$ divided by lower bound of $t$ , the reversal the mark scheme is looking for
The smallest speed uses the smallest distance over the largest time: $1855 \div 64.5 = 28.7596\ldots$ m/s.
M1: lower bound of $d$ divided by upper bound of $t$
To 2 significant figures both bounds give 29; to 3 significant figures they give 29.4 and 28.8, which differ. So $V = 29$ m/s, because the two bounds agree to 2 significant figures.
A1: value plus the agreement reason; the reason is part of this mark, not decoration

Practice questions

These are original questions in Edexcel 1MA1 Higher style. The short ones (write down a bound, complete an error interval, spot a truncation) are what turns up early on any of the three papers, Paper 1 included, so try those without a calculator. The longer ones combine two rounded measurements in a speed, area or density calculation and ask for a stated accuracy, which is the Higher-only part of N16.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

The length of a steel rod is 24 cm, correct to the nearest centimetre. Write down the upper bound of the length, in cm.

Your answer (fractions like 1/2 are fine)
Question 2 Warm-up [2 marks]

The width of a field is 60 m, correct to the nearest 10 metres. Write down the lower bound and the upper bound of the width, in metres.

lower bound = upper bound =
Question 3 Exam pace [2 marks]

$A$ and $B$ are two measurements that have been rounded. Which calculation gives the upper bound of $A \div B$ ?

Answer options for question 3
upper bound of $A$ divided by lower bound of $B$ upper bound of $A$ divided by upper bound of $B$ lower bound of $A$ divided by lower bound of $B$ lower bound of $A$ divided by upper bound of $B$
Question 4 Exam pace [3 marks]

A square has sides of length 6.2 cm, correct to 1 decimal place. Work out the lower bound of the area of the square, in $\text{cm}^2$ .

Your answer (fractions like 1/2 are fine)
Question 5 Exam pace [2 marks]

The value of $y$ is 0.007, truncated to 1 significant figure. Which inequality is the error interval for $y$ ?

Answer options for question 5
$0.007 \le y < 0.008$ $0.0065 \le y < 0.0075$ $0.006 \le y < 0.008$ $0.007 < y \le 0.008$
Question 6 Stretch [5 marks]

The time period $T$ seconds of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$ , where $L = 1.36$ correct to 2 decimal places and $g = 9.8$ correct to 1 decimal place. Work out the upper bound of $T$ . Give your answer correct to 3 significant figures.

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Writing the upper bound of a 24 cm length (nearest cm) as 24.49 or 24.4999, on the grounds that 24.5 would round up to 25.

Write 24.5. The upper bound is the value the measurement must stay below, and Edexcel mark schemes state it exactly. Record the interval as $23.5 \le x < 24.5$ : the strict inequality at the top is what excludes 24.5, not a shaved-off digit.
Dividing upper bound by upper bound for a largest speed. With 84 km to 2 significant figures over 1.2 hours to 1 decimal place, that gives $84.5 \div 1.25 = 67.6$ instead of $84.5 \div 1.15 = 73.5$ km/h.

Ask what makes a fraction large: a big numerator over a small denominator. Upper bound of the distance over lower bound of the time, and the other way round for the lower bound. List all four bounds before choosing.
Subtracting upper from upper for a largest difference, so cutting 0.85 m (nearest 0.01 m) from a 2.4 m plank (nearest 0.1 m) gives $2.45 - 0.855 = 1.595$ m rather than 1.605 m.

For the maximum of $A - B$ use the upper bound of $A$ and the lower bound of $B$ ; swap both for the minimum. The amount taken away has to be as small as possible when you want a big answer.
Treating a truncated value as a rounded one, so 6.73 m truncated to 2 decimal places is given the interval $6.725 \le d < 6.735$ .

Truncation cuts digits off and never rounds up, so the original value is at least the number written: $6.73 \le d < 6.74$ . A truncated value always sits at the bottom of its own interval, and phrases like 'the first three digits of the display' signal truncation.
Answering a suitable degree of accuracy question with the mean of the two bounds, or with the unrounded upper bound, and giving no reason.

Round the lower bound and the upper bound to 1 significant figure, then 2, then 3, and stop at the last place where they still match. Quote that agreement as your reason; the final mark on these questions is for the justification.

Frequently asked questions

Are bounds and error intervals on the Foundation paper?: Error intervals from rounding and truncation (spec ref N15) are on both tiers, so a Foundation candidate can be asked to complete a statement like $23.5 \le x < 24.5$ . Applying upper and lower bounds inside a calculation, for example finding the bounds of a speed or an area, sits in N16 and is Higher tier only.
Why is the upper bound 24.5 if 24.5 rounds up to 25?: The upper bound is defined as the value the measurement must be below, not a value it is allowed to equal. That is why the interval is written $23.5 \le x < 24.5$ with a strict inequality at the top end. Edexcel mark schemes credit 24.5; 24.49 and 24.499 are marked wrong, and they also drag rounding error into every later step.
How many marks are bounds questions worth on Edexcel Higher?: Completing an error interval is usually 2 marks. A calculation that uses bounds is typically 3-5 marks, and the version that ends 'give your answer to a suitable degree of accuracy' is often 5 marks because it needs both bound calculations and a written reason. Across a paper expect roughly 2-5 marks.
Do I need a calculator for bounds questions?: Not for the short ones. Paper 1 is non-calculator and regularly carries the write-down-a-bound and error interval questions, where all you do is halve the rounding unit. Papers 2 and 3 carry the speed, density and area versions, where the divisions are untidy and a calculator is assumed.

Bounds and Error Intervals - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics