Cambridge IGCSE Mathematics Core and Extended CD-ROM
Answers to Extended revision exercises: Algebra
Worksheet 18: Curved graphs
1 (a)
x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
y –33 –22 –13 –6 –1 2 3 2 –1 –6 –13 –22 –33
(b)
x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
y 50 37 26 17 10 5 2 1 2 5 10 17 26
(c)
x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
y 4 1 0 1 4 9 16 25 36 49 64 81 100
2 (a) x = 1, x = 3 (b) x = 0, x = 4 (c) x = 4.2, x = –0.2
3 x = 1, y = 3.5
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Cambridge IGCSE Mathematics Core and Extended CD-ROM
4
x –5 –4 –3 –2 –1 1 2 3 4 5
y –0.4 –0.5 –0.67 –1 –2 2 1 0.67 0.5 0.4
x –5 –4 –3 –2 –1 1 2 3 4 5
y 0.2 0.25 0.33 0.5 1 –1 –0.5 –0.33 –0.25 –0.2
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Cambridge IGCSE Mathematics Core and Extended CD-ROM
x –1 –0.5 0 0.5 1 1.5 2 2.5 3 4
y 1 0.875 0 –0.875 –1 0.375 4 10.625 21 56
x –1 –0.5 0 0.5 1 1.5 2 2.5
y 4 4.25 2 0.25 2 3.58 5.5 7.85
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Cambridge IGCSE Mathematics Core and Extended CD-ROM
5 (a) gradient = – 4.4 (b) gradient = 13.9 (3sf)
6 (a)(i) 4 (ii) –6 (b) x = 3.8, x = –1.8
7 (a) and (c)
(b) x = 1 and x = –1.54 (answers within the range of –1.5 to – 1.6 are acceptable)
(d) (1.7, 4.4) and (–1.2, –1.4)
(e) At the points of intersection, the two equations are equal, so:
2x2 + x – 3 = 2x + 1
If you rearrange this equation, you get 2x2 – x – 4 = 0.
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Cambridge IGCSE Mathematics Core and Extended CD-ROM
8 (a) and (b)
(c) 1.41
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Cambridge IGCSE Mathematics Core and Extended CD-ROM
9 (a) and (b)
(c) x = 1
(d) It is the tangent to the curve at the point (1,1).
(e) 2
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