O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2023 · Q611 Marks

Simplify 3u - 6w - 5u+9w.

(a)Simplify 3u - 6w - 5u+9w.[2]
(b)Emilio buys m pencils at 40 cents each and 12 pens at 85 cents each. He pays $20 and receives $2.20 change. Form an equation in m and solve it to find the number of pencils Emilio buys. Show your working.[4]
(c)y is directly proportional to the cube of (x – 2). When y = 12, x = 4. Find y when x = 5.[2]
(d)Write as a single fraction in its simplest form. (3/(x-1)) - (4/(2x+1))[3]

Mark scheme

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

[2] (a) 3w – 2u final answer B1 for 3w - 2u seen or answer 3w + ku or kw - 2u
[2] (b) 40m + 12 x 85 = 2000 – 220 or 40m = 2000-220-12 × 85 or 0.4m + 12 × 0.85 = 20 – 2.20 or 0.4m = 20-2.20 – 12 × 0.85 B2 B1 for 40m + 12 × 85 oe or 0.4m + 12 x 0.85 oe or 1780 or 17.8[0] seen
[2] (b) 19 B2 M1 for correctly rearranging their linear equation to m = ...
[2] (c) 81/2 or 40.5 B1 for k = 3/2 oe or M1 for y/(5-2)³ = 12/(4-2)³ oe or M1 for y = their k × (5 – 2)³
[3] (d) (2x+7)/((x-1)(2x+1)) or (2x+7)/(2x²-x-1) final answer B1 for 3(2x + 1) −4(x – 1) oe isw B1 for denominator (x – 1)(2x + 1) oe isw

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