IGCSE Mathematics (9–1) 0980 · Algebra and graphs · 10

0580.E2.2.01 — ax + bx + kay + kby.: past paper questions

25 real questionsasked in 7 of the last 10 exam series2019–2025usually: Find, Solve, Show, Complete

Real questions on 0580.e2.2.01 — ax + bx + kay + kby.

The newest 20 of 25 written questions. Open one to see it on the real paper.

0980/22 · May/June 2025 · Q19b[2]
19 Write as a single fraction in its simplest form. (b) $\frac{p}{2} + \frac{3 t}{4}$ See it on the paper →
0980/21 · October/November 2024 · Q22a[2]
22 The graph of $y = (x + 2) (x - 1)^{2}$ is shown on the grid. [Diagram: A graph of a cubic function on a grid. The x-axis is marked from -2 to 2, and the y-axis is marked from -1 to 4. The curve passes through $(- 2, 0)$ , has a local maximum near $x = - 0.5$ , passes through $(0, 2)$ , touches the x-axis at $(1, 0)$ , and rises st...See it on the paper →
0980/32 · May/June 2024 · Q2c(i)[2]
(c) The time, $T$ minutes, to cook a chicken with a mass of $m$ kg is $T = 35 m + 20$ . (i) Make $m$ the subject of the formula.See it on the paper →
0980/32 · May/June 2024 · Q2d[3]
(d) Solve these simultaneous equations. You must show all your working. $5 x - 6 y = 24$ $15 x + 8 y = 33$ See it on the paper →
0980/21 · October/November 2023 · Q5a[2]
5 Factorise completely. (a) $42 mk - 35 m$ See it on the paper →
0980/41 · October/November 2023 · Q2e[2]
(e) Factorise completely. $6 pq - 4 q - 3 p + 2$ See it on the paper →
0980/41 · October/November 2023 · Q9a(i)[1]
9 \quad f(x) = (3x+1)(x+5)(x-4) \quad g(x) = 2x-3 \quad h(x) = 4^{2x-1} (a) Find (i) \quad f(0)See it on the paper →
0980/41 · October/November 2023 · Q9a(ii)[2]
$f (x) = (3 x + 1) (x + 5) (x - 4)$ $g (x) = 2 x - 3$ $h (x) = 4^{2 x - 1}$ (a) Find (ii) $g^{- 1} (x)$ See it on the paper →
0980/41 · October/November 2023 · Q9a(iii)[2]
9 $f (x) = (3 x + 1) (x + 5) (x - 4)$ $g (x) = 2 x - 3$ $h (x) = 4^{2 x - 1}$ (a) Find (iii) $g h (2)$ .See it on the paper →
0980/41 · October/November 2023 · Q9b[2]
$f (x) = (3 x + 1) (x + 5) (x - 4)$ $g (x) = 2 x - 3$ $h (x) = 4^{2 x - 1}$ (b) $g (2 x) = 7$ Find the value of $x$ .See it on the paper →
0980/41 · October/November 2023 · Q9c[3]
9 $f (x) = (3 x + 1) (x + 5) (x - 4)$ $g (x) = 2 x - 3$ $h (x) = 4^{2 x - 1}$ (c) Simplify $g (x^{2}) + g g (x) + 1$ .See it on the paper →
0980/41 · October/November 2023 · Q9d[2]
$f (x) = (3 x + 1) (x + 5) (x - 4)$ $g (x) = 2 x - 3$ $h (x) = 4^{2 x - 1}$ (d) Find $h^{- 1} (16)$ .See it on the paper →
0980/31 · October/November 2022 · Q7c[2]
(c) Factorise completely. $14 x^{3} + 49 x$ See it on the paper →
0980/41 · October/November 2022 · Q10a(i)[1]
The diagram shows a sketch of the graph of $y = f (x)$ for $- 1.5 ⩽ x ⩽ 6$ . The coordinates of five points on the graph of $y = f (x)$ are shown on the diagram. [Diagram: A graph of a function $y = f (x)$ on a Cartesian plane. The curve starts at point $A (- 1.5, 7.9)$ , dips to a local mi...See it on the paper →
0980/41 · October/November 2022 · Q10a(ii)[2]
The diagram shows a sketch of the graph of $y = f (x)$ for $- 1.5 ⩽ x ⩽ 6$ . The coordinates of five points on the graph of $y = f (x)$ are shown on the diagram. [Diagram: A graph of a function $y = f (x)$ on a Cartesian plane. The curve starts at point $A (- 1.5, 7.9)$ , dips to a local minimum at $B (- 1, 7)$ , ri...See it on the paper →
0980/41 · October/November 2022 · Q10b[5]
(b) Find the coordinates of the two stationary points on the graph of $y = x^{6} - 6 x^{5}$ . You must show all your working.See it on the paper →
0980/21 · October/November 2021 · Q8[3]
Solve the simultaneous equations. You must show all your working. $4 x - 2 y = - 13$ $- 3 x + 4 y = 11$ See it on the paper →
0980/21 · October/November 2021 · Q22c[3]
(c) Solve. $3^{3 x} \times (\frac{1}{9})^{4 - 3 x} = 3$ See it on the paper →
0980/31 · October/November 2021 · Q3d(i)[1]
360 people go on a school trip to one of four places. Some of the information is shown in the table. | | Adventure park | Botanic gardens | Wildlife centre | Red castle | Total | |---|---|---|---|---|---| | Boys | 65 | 12 | | 36 | | | Girls | | 9 | 62 | | 163 | | Staff | 15 | 3 | | | 37 | | Total | 144 | 24 | 121 | 71...See it on the paper →
0980/42 · May/June 2021 · Q3d(ii)[2]
(d) Factorise the following completely. (ii) $7 (a + 2 b)^{2} + 4 a (a + 2 b)$ See it on the paper →

What examiners said

The vast majority started the question correctly by multiplying one or both equations to equalise coefficients and then use the elimination method, and many showed full and clear working for this. However, many struggled to add (or subtract) their two equations consistently and so were unable to gain the method mark and therefore the answer marks. A large number of these nevertheless gained a spec...
— Examiner report, May/June 2024, 0980/32 Q2(d) (Cambridge)

This part was answered very well as most candidates gave a correct full or partial factorisation. A few candidates left the m in the second term, so they wrote 7 m (6 k – 5 m).
— Examiner report, October/November 2023, 0980/21 Q5(a) (Cambridge)

This question had a mixed response. Many candidates successfully factorised 6 pq − 4q − 3 p + 2 to ( 3 p − 2)( 2q − 1) or equivalent but many others did not know what to do with this sort of expression. When first factorising, many candidates did not realise they needed to have the same expression within the two brackets if they were to factorise further. This was generally due to not being able t...
— Examiner report, October/November 2023, 0980/41 Q2(e) (Cambridge)

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