2022 pearson june booklet + mark scheme Edexcel International GCSE 4PM1/01 Further Pure Mathematics PAPER 1

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Answer all TEN questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 Given that 2 3 4 3 3 5 − + can be written in the form a + b 3 where a ... and b are integers, find, without using a calculator, the value of a and the value of b Show your working clearly. 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(Total for Question 1 is 3 marks)4 *P71661A0432*  2 Diagram NOT accurately drawn A 3xcm ycm 5xcm G L D E N FM P V QU B R T C 3xcm ycm 5xcm 3xcm ycm 3xcm 3xcm ycm 3xcm Figure 1 Figure 1 shows the design for a flag consisting of a white cross on a grey background. AEFG and DLMN are squares with sides of length 3xcm. BPQR and CTUV are rectangles with sides of length 5xcm and 3xcm. The width of the cross is ycm. The total area of the flag is Hcm2 (a) Write down an expression, in terms of x and y, for H. (1) Given that the area of the cross is Kcm2 (b) show that K = 14xy + y2 (3) The total area of the flag is to be 3432cm2 and the area of the cross is to be 1080cm2 (c) Find the value of x and the value of y (5) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. ............................................................................................................. 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