O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2023 · Q610 Marks

ABCD is a rectangle with area 30cm². AB = x cm. Rectangle DEFG is removed from the corner of rectangle ABCD. AE = CG = 2 cm.

(a)Write down an expression for BC in terms of x.[1]
(b)Show that the shaded area, y cm², is given by y = 2x + 60/x - 4.[3]
(c)Complete the table for y = 2x + 60/x - 4. Write your answer correct to 1 decimal place.[1]
(d)Draw the graph of y = 2x + 60/x - 4 for 2 ≤ x ≤ 14 .[3]
(e)The shaded area is 24 cm². The length of AB is less than the length of BC. Use your graph to find the dimensions of rectangle ABCD.[2]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

[1] (a) 30/x
[3] (b) Correct unexpanded expression for shaded area e.g. [y=]30-(x-2)(30/x-2) or [y=]2(x-2)+2x+2(30/x-2) or [y=]2x+2(30/x)-2 or [y=]2(x-2)+2(30/x)
[3] (b) B1 for (x-2) or (their 30/x-2) seen
[3] (b) Correct expansion of brackets and rearrangement to y = 2x + 60/x - 4 A1 A0 if any errors or omissions
[1] (c) 28.3
[3] (d) Correct smooth curve
[3] (d) B2 FT for 7 or 8 points correctly plotted or B1 FT for 5 or 6 points correctly plotted
[2] (e) FT reading the two values from their graph at y = 24
[2] (e) B1 FT for one correct
[2] (e) B1 FT for second value = 30 ÷ their first value or for their second value at y = 24

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