Mathematics · May / June 2025 · Paper 22 · Question 21
0580
As printed in the paper
The question as text
NOT TO SCALE y x A Í O à Q The diagram shows the graph of y x x 3 3 Á . The graph crosses the x-axis at A, at O and at Í. The turning points of the graph are at à and at Q.
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21(a)[3]
− [A =] 3 oe [B =] 3 oe [3]
B2 for – 3 oe or 3 oe
or M1 for []( )[ ] − 2 = x 3 x 0 or better ± 2 −×−× 0 0 4 1 3 or oe ×− 2 1
21(b)(i)[2]
3 – 3x2 final answer [2]
B1 for 3 or – 3x2 correct in an expression or for correct answer spoilt
21(b)(ii)[4]
[P =] (–1, –2) and [Q =] (1, 2) [4]
B3 for (–1, –2) or (1, 2) or for two correct values of x
or M2 for x2 = 1 or for [3](1 – x)(1 + x) [= 0] oe factorised ± 2 −×−× 0 0 4 3 3 or oe ×− 2 3 OR
M1 for [3](1 – x2) [= 0] or their (b)(i) = 0 or for stating d y x = 0 d
M1 for correct method to solve their quadratic
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