Question 5 — IGCSE 0580 May/June 2024 Paper 42
Cambridge IGCSE Mathematics 0580, Extended tier, calculator. Topic: Algebra · Basic algebra. Worth 18 marks.
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Question text
5 (a) Simplify 25x6 2.
` j
................................................. [2]
(b) These are the first five terms of a sequence.
1
1 6 36 216
6
Find the nth term of the sequence.
................................................. [2]
(c) Expand and simplify.
(x+4)(x-3)(3x-1)
..................................................................... [3]
© UCLES 2024 0580/42/M/J/24
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(d) (i) Show that (3x+5)+ = x simplifies to 2x2+x-3 = 0.
x-2
[4]
(ii) Solve by factorisation 2x2+x-3 = 0.
x = ................. or x = ................... [3]
(e) A solid cylinder has base radius x and height 3x.
The total surface area of the cylinder is the same as the total surface area of a solid hemisphere of
radius 5y.
75y2
Show that x2 = .
8
[The surface area, A, of a sphere with radius r is A = 4rr2.]
[4]
© UCLES 2024 0580/42/M/J/24 [Turn over
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