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Trapezium rule

Edexcel A Level Maths

Topic questions Pure mathematics Trapezium rule

Trapezium rule

31 questions · 253 marks · about 5 hours

Trapezium rule questions

TopicTrapezium rule

Edexcel 9MA0's own questions

Paper 1: Pure Mathematics 1 June 2023, Question 5 6 marks

A continuous curve has equation y = f(x).

The table shows corresponding values of x and y for this curve, where a and b are constants.

x	3	3.2	3.4	3.6	3.8	4
y	a	16.8	b	20.2	18.7	13.5

The trapezium rule is used, with all the y values in the table, to find an approximate area under the curve between x = 3 and x = 4

Given that this area is 17.59

(a)

show that a + 2b = 51

[3]

Reveal mark scheme

(b)

Given also that the sum of all the y values in the table is 97.2

find the value of a and the value of b

[3]

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Paper 2: Pure Mathematics 2 June 2022, Question 5 6 marks

Also involves Laws of logarithms

The table below shows corresponding values of x and y for y = log₃2x The values of y are given to 2 decimal places as appropriate.

x	3	4.5	6	7.5	9
y	1.63	2	2.26	2.46	2.63

(a)

Using the trapezium rule with all the values of y in the table, find an estimate for

$Question 5, shown as an image$

[3]

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(b)(i)

Using your answer to part (a) and making your method clear, estimate

$Question 5, shown as an image$

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(b)(ii)

$Question 5, shown as an image$

[3]

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Paper 1: Pure Mathematics 1 October 2021, Question 11 8 marks

Figure 2 shows a sketch of part of the curve with equation

The finite region R, shown shaded in Figure 2, is bounded by the curve, the line with equation x = 2, the x-axis and the line with equation x = 4

The table below shows corresponding values of x and y, with the values of y given to 4 decimal places.

x	2	2.5	3	3.5	4
y	0.4805	0.8396	1.2069	1.5694	1.9218

(a)

Use the trapezium rule, with all the values of y in the table, to obtain an estimate for the area of R, giving your answer to 3 significant figures.

[3]

Reveal mark scheme

(b)

Use algebraic integration to find the exact area of R, giving your answer in the form

$Question 11, shown as an image$

where a, b and c are integers to be found.

[5]

Reveal mark scheme

Paper 1: Pure Mathematics 1 November 2021, Question 11 8 marks

Also involves Definite integration

Figure 2 shows a sketch of part of the curve with equation

The finite region R, shown shaded in Figure 2, is bounded by the curve, the line with equation x = 2, the x-axis and the line with equation x = 4 The table below shows corresponding values of x and y, with the values of y given to 4 decimal places.

x	2	2.5	3	3.5	4
y	0.4805	0.8396	1.2069	1.5694	1.9218

(a)

Use the trapezium rule, with all the values of y in the table, to obtain an estimate for the area of R, giving your answer to 3 significant figures.

[3]

Reveal mark scheme

(b)

Use algebraic integration to find the exact area of R, giving your answer in the form

$Question 11, shown as an image$

where a, b and c are integers to be found.

[5]

Reveal mark scheme

Paper 2: Pure Mathematics 2 October 2020, Question 1 5 marks

$Question 1, shown as an image$

1 The table below shows corresponding values of x and y for y = $fraction$ The values of y are given to 4 significant figures.

x	0.5	1	1.5	2	2.5
y	0.5774	0.7071	0.7746	0.8165	0.8452

(a)

Use the trapezium rule, with all the values of y in the table, to find an estimate for

giving your answer to 3 significant figures.

[3]

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(b)

$Question 1, shown as an image$

[1]

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(c)

Given that

$Question 1, shown as an image$

comment on the accuracy of your answer to part (b).

[1]

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Paper 2: Pure Mathematics 2 June 2019, Question 2 4 marks

The speed of a small jet aircraft was measured every 5 seconds, starting from the time it turned onto a runway, until the time when it left the ground. The results are given in the table below with the time in seconds and the speed in m s maths symbol .

Time (s)	0	5	10	15	20	25
Speed (m s)	2	5	10	18	28	42

Using all of this information,

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(a)

estimate the length of runway used by the jet to take off.

[3]

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(b)

Given that the jet accelerated smoothly in these 25 seconds,

explain whether your answer to part (a) is an underestimate or an overestimate of the length of runway used by the jet to take off.

[1]

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Full-course legacy questions

Core Mathematics 4 June 2019, Question 2 7 marks

Also involves Trigonometric identities · Compound and double angle formulae

Figure 1 shows a sketch of the curve with equation

$Question 2, shown as an image$

The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis and the

$Question 2, shown as an image$

The table below shows corresponding values of x and y for y = sin 2x sin x௘ maths symbol ZLWK WKH YDOXHV of y given to 5 significant figures where appropriate.

x	π 3	7π 18	4π 9	π 2
y	0.75	0.60402	0.33682	0

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(a)

Use the trapezium rule, with all the values of y in the table, to find an estimate for the area of R, giving your answer to 4 significant figures.

[3]

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(b)

$Question 2, shown as an image$

where a and b are constants to be found. (Solutions based entirely on graphical or numerical methods are not acceptable.)

[4]

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Core Mathematics 4 June 2017, Question 3 12 marks

Also involves Partial fractions · Integration by substitution

Figure 1 shows a sketch of part of the curve with equation y maths symbol $fraction$ x The finite region R, shown shaded in Figure 1, is bounded by the curve, the y-axis, the x-axis and the line with equation x = 1 The table below shows corresponding values of x and y for y = $fraction$

x	0	0.2	0.4	0.6	0.8	1
y	2		1.71830	1.56981	1.41994	1.27165

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(a)

Complete the table above by giving the missing value of y to 5 decimal places.

[1]

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(b)

Use the trapezium rule, with all the values of y in the completed table, to find an estimate for the area of R, giving your answer to 4 decimal places.

[3]

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(c)

Use the substitution u = e^x to show that the area of R can be given by

$Question 3, shown as an image$

where a and b are constants to be determined.

[2]

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(d)

Hence use calculus to find the exact area of R. [ Solutions based entirely on graphical or numerical methods are not acceptable. ]

[6]

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Core Mathematics 4 June 2016, Question 2 9 marks

Also involves Integration by parts

Figure 1 shows a sketch of part of the curve with equation y = x²ln x, x maths symbol 1 The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line x = 2 The table below shows corresponding values of x and y for y = x²ln x

x	1	1.2	1.4	1.6	1.8	2
y	0	0.2625		1.2032	1.9044	2.7726

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(a)

Complete the table above, giving the missing value of y to 4 decimal places.

[1]

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(b)

Use the trapezium rule with all the values of y in the completed table to obtain an estimate for the area of R, giving your answer to 3 decimal places.

[3]

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(c)

Use integration to find the exact value for the area of R.

[5]

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Core Mathematics 4 June 2014 (R), Question 2 9 marks

Also involves Integration by parts

Figure 1 shows a sketch of part of the curve with equation

$Question 2, shown as an image$

The finite region R, shown shaded in Figure 1, is bounded by the curve, the x- axis and the y- axis. The table below shows corresponding values of x and y for y = (2 – x)e²^x

x	0	0.5	1	1.5	2
y	2	4.077	7.389	10.043	0

(a)

Use the trapezium rule with all the values of y in the table, to obtain an approximation for the area of R, giving your answer to 2 decimal places.

[3]

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(b)

Explain how the trapezium rule can be used to give a more accurate approximation for the area of R.

[1]

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(c)

Use calculus, showing each step in your working, to obtain an exact value for the area of R. Give your answer in its simplest form.

[5]

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Core Mathematics 4 June 2014, Question 3 11 marks

The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis, and the lines with equations x = 1 and x = 4

$Question 3, shown as an image$

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(a)

Complete the table above by giving the missing value of y to 5 decimal places.

[1]

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(b)

Use the trapezium rule, with all the values of y in the completed table, to find an estimate for the area of R, giving your answer to 4 decimal places.

[3]

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(c)

By reference to the curve in Figure 1, state, giving a reason, whether your estimate in part (b) is an overestimate or an underestimate for the area of R.

[1]

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(d)

Use the substitution u = ¥ x, or otherwise, to find the exact value of

$Question 3, shown as an image$

[6]

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Core Mathematics 4 June 2013, Question 3 8 marks

Figure 1 shows the finite region R bounded by the x-axis, the y-axis, the line x maths symbol $fraction$ and the curve with equation

$Question 3, shown as an image$

(a)

Complete the table above giving the missing value of y to 6 decimal places.

[1]

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(b)

Using the trapezium rule, with all of the values of y from the completed table, find an approximation for the area of R, giving your answer to 4 decimal places.

[3]

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(c)

Region R is rotated through 2 maths symbol radians about the x-axis.

Use calculus to find the exact volume of the solid formed.

[4]

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Core Mathematics 4 June 2013 (R), Question 5 11 marks

Also involves Area under a curve

$Question 5, shown as an image$

(a)

$Question 5, shown as an image$

3 decimal places.

[1]

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(b)

Use the trapezium rule with all the values of x in the completed table to obtain an estimate for the area of the region R, giving your to 2 decimal places. (3)

[3]

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(c)

Use calculus to find the exact value for the area of R. (6)

[6]

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(d)

Find the difference between the values obtained in part (b) and part (c), giving your to 2 decimal places. (1)

[1]

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Core Mathematics 4 January 2013, Question 4 12 marks

Figure 1 shows a sketch of part of the curve with equation y = $fraction$ . The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis, the line with equation x = 1 and the line with equation x = 4.

(a)

Complete the table with the value of y corresponding to x = 3, giving your answer to 4 decimal places.

[1]

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(b)

x	1	2	3	4
y	0.5	0.8284		1.3333

Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate of the area of the region R, giving your answer to 3 decimal places.

[3]

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(c)

Use the substitution u = 1 + maths symbol x, to find, by integrating, the exact area of R.

[8]

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Core Mathematics 4 June 2012, Question 7 11 marks

Also involves Definite integration · Integration by parts

Figure 3 shows a sketch of part of the curve with equation y = $fraction$ ln 2x. The finite region R, shown shaded in Figure 3, is bounded by the curve, the x-axis and the lines x = 1 and x maths symbol 4

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(a)

Use the trapezium rule, with 3 strips of equal width, to find an estimate for the area of R, giving your answer to 2 decimal places.

[4]

(b)

$Question 7, shown as an image$

[4]

(c)

Hence find the exact area of R, giving your answer in the form a ln 2 maths symbol b, where a and b are exact constants.

[3]

Core Mathematics 4 June 2011, Question 4 15 marks

Also involves Logarithms · Integration by parts

Figure 2 shows a sketch of the curve with equation y = x³ ln (x² + 2), x maths symbol 0. The finite region R, shown shaded in Figure 2, is bounded by the curve, the x-axis and the line x = ˲ 2. The table below shows corresponding values of x and y for y = x³ ln (x² + 2).

x	0	˲ 2 4	˲ 2 2	3˲ 2 4	˲ 2
y	0		0.3240		3.9210

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(a)

Complete the table above giving the missing values of y to 4 decimal places.

[2]

(b)

Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate for the area of R, giving your answer to 2 decimal places.

[3]

(c)

Use the substitution u = x²+ 2 to show that the area of R is

[4]

(d)

Hence, or otherwise, find the exact area of R.

[6]

Core Mathematics 4 January 2011, Question 7 14 marks

⁵

$Question 7, shown as an image$

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(a)

$Question 7, shown as an image$

x	2	3	4	5
y	0.2		0.1745

[2]

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(b)

Use the trapezium rule, with all of the values of y in the completed table, to obtain an estimate of I, giving your answer to 3 decimal places.

[4]

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(c)

Using the substitution x = maths symbol u 4² +1, or otherwise, and integrating, find the exact value of I.

[8]

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Core Mathematics 4 June 2010, Question 1 8 marks

Also involves Trigonometric ratios

Figure 1 shows part of the curve with equation y = √(0.75 + cos² x). The finite region R, shown shaded in Figure 1, is bounded by the curve, the y-axis, the x-axis and the line with

$Question 1, shown as an image$

(a)

Complete the table with values of y corresponding to x = $fraction$ and x = $fraction$

x	0	π 12	π 6	π 4	π 3
y	1.3229	1.2973			1

[2]

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(b)

Use the trapezium rule

(b)(i)

with the values of y at x maths symbol 0, x = $fraction$ and x = $fraction$ to find an estimate of the area of R. Give your answer to 3 decimal places.

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(b)(ii)

$Question 1, shown as an image$

further estimate of the area of R. Give your answer to 3 decimal places.

[6]

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Core Mathematics 4 January 2010, Question 2 13 marks

Also involves Laws of logarithms · Definite integration · Integration by parts

Figure 1 shows a sketch of the curve with equation y = x 1n x, x maths symbol 1. The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line x = 4. The table shows corresponding values of x and y for y = x 1n x.

x	1	1.5	2	2.5	3	3.5	4
y	0	0.608			3.296	4.385	5.545

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(a)

Complete the table with the values of y corresponding to x = 2 and x = 2.5, giving your answers to 3 decimal places.

[2]

(b)

Use the trapezium rule, with all the values of y in the completed table, to obtain an estimate for the area of R, giving your answer to 2 decimal places.

[4]

(c)(i)

$Question 2, shown as an image$

(c)(ii)

Hence find the exact area of R, giving your answer in the form $fraction$ a ln 2 maths symbol b), where a and b are integers.

[7]

Core Mathematics 4 June 2008, Question 1 4 marks

Figure 1 shows part of the curve with equation y = e^{0 5}^.^x². The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis, the y-axis and the line x = 2.

(a)

Complete the table with the values of y corresponding to x = 0.8 and x = 1.6.

x	0	0.4	0.8	1.2	1.6	2
y	e⁰	e^0.08		e^0.72		e²

[1]

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(b)

Use the trapezium rule with all the values in the table to find an approximate value for the area of R, giving your answer to 4 significant figures.

[3]

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Core Mathematics 4 January 2008, Question 1 6 marks

$Question 1, shown as an image$

(a)

$Question 1, shown as an image$

x	0
y	0			8.87207	0

[2]

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(b)

Use the trapezium rule, with all the values in the completed table, to obtain an estimate for the area of the region R. Give your answer to 4 decimal places.

[4]

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AS-stage legacy questions

Core Mathematics 2 June 2018, Question 1 5 marks

Figure 1 shows a sketch of part of the curve with equation

The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis and the line with equation x = 10 The table below shows corresponding values of x and y for y maths symbol $fraction$

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(a)

Complete the table, giving values of y corresponding to x= 2 and x= 6

x	−2	2	6	10
y	0			6√3

[1]

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(b)

Use the trapezium rule, with all the values of y from the completed table, to find an approximate value for the area of R, giving your answer to 3 decimal places.

[4]

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Core Mathematics 2 June 2017, Question 3 6 marks

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(a)

y = 5^x + log₂(x + 1), 0 maths symbol x ≤ 2 Complete the table below, by giving the value of y when x = 1

x	0	0.5	1	1.5	2
y	1	2.821		12.502	26.585

[1]

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(b)

Use the trapezium rule, with all the values of y from the completed table, to find an approximate value for

$Question 3, shown as an image$

giving your answer to 2 decimal places.

[4]

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(c)

Use your answer to part (b) to find an approximate value for

$Question 3, shown as an image$

giving your answer to 2 decimal places.

[1]

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Core Mathematics 2 June 2016, Question 2 6 marks

Also involves Exponential functions

The curve C has equation

(a)

Complete the table below with the value of y corresponding to x = 1

x	0	1	2	3	4
y	7.5		6	4	0

[1]

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(b)

Use the trapezium rule, with all the values of y in the completed table, to find an

$Question 2, shown as an image$

[3]

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(c)

Figure 1 shows a sketch of the curve C with equation y = 8 – 2^x^–1, 0 maths symbol x 4 The curve C meets the x-axis at the point A and meets the y-axis at the point B. The region R, shown shaded in Figure 1, is bounded by the curve C and the straight line through A and B.

Use your answer to part (b) to find an approximate value for the area of R.

[2]

Reveal mark scheme

Core Mathematics 2 June 2014, Question 1 5 marks

Figure 1 shows a sketch of part of the curve with equation y = ¥(x² + 1), x maths symbol 0 The finite region R, shown shaded in Figure 1, is bounded by the curve, the x-axis and the lines x = 1 and x = 2 The table below shows corresponding values for x and y for y = ¥(x² + 1).

x	1	1.25	1.5	1.75	2
y	1.414		1.803	2.016	2.236

(a)

Complete the table above, giving the missing value of y to 3 decimal places.

[1]

Reveal mark scheme

(b)

Use the trapezium rule, with all the values of y in the completed table, to find an approximate value for the area of R, giving your answer to 2 decimal places.

[4]

Reveal mark scheme

Core Mathematics 2 June 2013 (R), Question 2 5 marks

$Question 2, shown as an image$

(a)

Complete the table below with the value of y corresponding to x = 1.3, giving your answer to 4 decimal places.

[1]

Reveal mark scheme

(b)

x	1	1.1	1.2	1.3	1.4	1.5
y	0.7071	0.7591	0.8090		0.9037	0.9487

Use the trapezium rule, with all the values of y in the completed table, to obtain an approximate value for

$Question 2, shown as an image$

giving your answer to 3 decimal places. You must show clearly each stage of your working.

[4]

Reveal mark scheme

Core Mathematics 2 June 2013, Question 4 7 marks

Reveal mark scheme

(a)

Complete the table below, giving the missing value of y to 3 decimal places.

[1]

(b)

Figure 1 shows the region R which is bounded by the curve with equation y = $fraction$ , the x-axis and the lines x = 0 and x = 3

Use the trapezium rule, with all the values of y from your table, to find an approximate value for the area of R.

[4]

Reveal mark scheme

(c)

Use your answer to part (b) to find an approximate value for

$Question 4, shown as an image$

giving your answer to 2 decimal places.

[2]

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Core Mathematics 2 January 2013, Question 9 12 marks

Also involves Indices

The finite region R, as shown in Figure 2, is bounded by the x- axis and the curve with

The curve crosses the x-axis at the points (1, 0) and (4, 0).

(a)

Complete the table below, by giving your values of y to 3 decimal places.

x	1	1.5	2	2.5	3	3.5	4
y	0	5.866		5.210		1.856	0

[2]

Reveal mark scheme

(b)

Use the trapezium rule with all the values in the completed table to find an approximate value for the area of R, giving your answer to 2 decimal places.

[4]

Reveal mark scheme

(c)

Use integration to find the exact value for the area of R.

[6]

Reveal mark scheme

Core Mathematics 2 June 2012, Question 7 6 marks

Also involves Exponential functions

(a)

Complete the table below, giving the values of y to 3 decimal places.

x	0	0.25	0.5	0.75	1
y	1	1.251			2

[2]

Reveal mark scheme

(b)

Use the trapezium rule with all the values of y from your table to find an approximation

$Question 7, shown as an image$

You must show clearly how you obtained your answer.

[4]

Reveal mark scheme

Core Mathematics 2 June 2009, Question 4 8 marks

(a)

4._x maths symbol to 3 decimal places. (a) Complete the table below, giving values of √ (2 1)

[2]

Reveal mark scheme

(b)

Figure 1 shows the region R which is bounded by the curve with equation y^x maths symbol , the

x- axis and the lines x = 0 and x = 3

Use the trapezium rule, with all the values from your table, to find an approximation for the area of R.

[4]

Reveal mark scheme

(c)

By reference to the curve in Figure 1 state, giving a reason, whether your approximation in part (b) is an overestimate or an underestimate for the area of R.

[2]

Reveal mark scheme

Core Mathematics 2 June 2008, Question 2 6 marks

y maths symbol (5^x 2)

(a)

Complete the table below, giving the values of y to 3 decimal places.

x	0	0.5	1	1.5	2
y			2.646	3.630

[2]

Reveal mark scheme

(b)

Use the trapezium rule, with all the values of y from your table, to find an approximation

$Question 2, shown as an image$

[4]

Reveal mark scheme

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Trapezium rule

Trapezium rule questions

Edexcel 9MA0 Trapezium rule 31 questions

Edexcel 9MA0's own questions

Paper 1: Pure Mathematics 1 June 2023, Question 5 Paper 1: Pure Mathematics 1 · June 2023 · Question 5 6 marks

Paper 2: Pure Mathematics 2 June 2022, Question 5 Paper 2: Pure Mathematics 2 · June 2022 · Question 5 6 marks

Paper 1: Pure Mathematics 1 October 2021, Question 11 Paper 1: Pure Mathematics 1 · October 2021 · Question 11 8 marks

Paper 1: Pure Mathematics 1 November 2021, Question 11 Paper 1: Pure Mathematics 1 · November 2021 · Question 11 8 marks

Paper 2: Pure Mathematics 2 October 2020, Question 1 Paper 2: Pure Mathematics 2 · October 2020 · Question 1 5 marks

Paper 2: Pure Mathematics 2 June 2019, Question 2 Paper 2: Pure Mathematics 2 · June 2019 · Question 2 4 marks

Full-course legacy questions

Core Mathematics 4 June 2019, Question 2 Core Mathematics 4 · June 2019 · Question 2 7 marks

Core Mathematics 4 June 2017, Question 3 Core Mathematics 4 · June 2017 · Question 3 12 marks

Core Mathematics 4 June 2016, Question 2 Core Mathematics 4 · June 2016 · Question 2 9 marks

Core Mathematics 4 June 2014 (R), Question 2 Core Mathematics 4 · June 2014 (R) · Question 2 9 marks

Core Mathematics 4 June 2014, Question 3 Core Mathematics 4 · June 2014 · Question 3 11 marks

Core Mathematics 4 June 2013, Question 3 Core Mathematics 4 · June 2013 · Question 3 8 marks

Core Mathematics 4 June 2013 (R), Question 5 Core Mathematics 4 · June 2013 (R) · Question 5 11 marks

Core Mathematics 4 January 2013, Question 4 Core Mathematics 4 · January 2013 · Question 4 12 marks

Core Mathematics 4 June 2012, Question 7 Core Mathematics 4 · June 2012 · Question 7 11 marks

Core Mathematics 4 June 2011, Question 4 Core Mathematics 4 · June 2011 · Question 4 15 marks

Core Mathematics 4 January 2011, Question 7 Core Mathematics 4 · January 2011 · Question 7 14 marks

Core Mathematics 4 June 2010, Question 1 Core Mathematics 4 · June 2010 · Question 1 8 marks

Core Mathematics 4 January 2010, Question 2 Core Mathematics 4 · January 2010 · Question 2 13 marks

Core Mathematics 4 June 2008, Question 1 Core Mathematics 4 · June 2008 · Question 1 4 marks

Core Mathematics 4 January 2008, Question 1 Core Mathematics 4 · January 2008 · Question 1 6 marks

AS-stage legacy questions

Core Mathematics 2 June 2018, Question 1 Core Mathematics 2 · June 2018 · Question 1 5 marks

Core Mathematics 2 June 2017, Question 3 Core Mathematics 2 · June 2017 · Question 3 6 marks

Core Mathematics 2 June 2016, Question 2 Core Mathematics 2 · June 2016 · Question 2 6 marks

Core Mathematics 2 June 2014, Question 1 Core Mathematics 2 · June 2014 · Question 1 5 marks

Core Mathematics 2 June 2013 (R), Question 2 Core Mathematics 2 · June 2013 (R) · Question 2 5 marks

Core Mathematics 2 June 2013, Question 4 Core Mathematics 2 · June 2013 · Question 4 7 marks

Core Mathematics 2 January 2013, Question 9 Core Mathematics 2 · January 2013 · Question 9 12 marks

Core Mathematics 2 June 2012, Question 7 Core Mathematics 2 · June 2012 · Question 7 6 marks

Core Mathematics 2 June 2009, Question 4 Core Mathematics 2 · June 2009 · Question 4 8 marks

Core Mathematics 2 June 2008, Question 2 Core Mathematics 2 · June 2008 · Question 2 6 marks

Certified Maths memes. Peer-reviewed by nobody.

Paper 1: Pure Mathematics 1 June 2023, Question 5 6 marks

Paper 2: Pure Mathematics 2 June 2022, Question 5 6 marks

Paper 1: Pure Mathematics 1 October 2021, Question 11 8 marks

Paper 1: Pure Mathematics 1 November 2021, Question 11 8 marks

Paper 2: Pure Mathematics 2 October 2020, Question 1 5 marks

Paper 2: Pure Mathematics 2 June 2019, Question 2 4 marks

Core Mathematics 4 June 2019, Question 2 7 marks

Core Mathematics 4 June 2017, Question 3 12 marks

Core Mathematics 4 June 2016, Question 2 9 marks

Core Mathematics 4 June 2014 (R), Question 2 9 marks

Core Mathematics 4 June 2014, Question 3 11 marks

Core Mathematics 4 June 2013, Question 3 8 marks

Core Mathematics 4 June 2013 (R), Question 5 11 marks

Core Mathematics 4 January 2013, Question 4 12 marks

Core Mathematics 4 June 2012, Question 7 11 marks

Core Mathematics 4 June 2011, Question 4 15 marks

Core Mathematics 4 January 2011, Question 7 14 marks

Core Mathematics 4 June 2010, Question 1 8 marks

Core Mathematics 4 January 2010, Question 2 13 marks

Core Mathematics 4 June 2008, Question 1 4 marks

Core Mathematics 4 January 2008, Question 1 6 marks

Core Mathematics 2 June 2018, Question 1 5 marks

Core Mathematics 2 June 2017, Question 3 6 marks

Core Mathematics 2 June 2016, Question 2 6 marks

Core Mathematics 2 June 2014, Question 1 5 marks

Core Mathematics 2 June 2013 (R), Question 2 5 marks

Core Mathematics 2 June 2013, Question 4 7 marks

Core Mathematics 2 January 2013, Question 9 12 marks

Core Mathematics 2 June 2012, Question 7 6 marks

Core Mathematics 2 June 2009, Question 4 8 marks

Core Mathematics 2 June 2008, Question 2 6 marks