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AAL30_01 Question Working Answer Mark Notes 1 (a) x6−1 x5 1 B1 cao (b) y−2 + −3 y−5 1 B1 cao (c) v2 1 B1 cao (d) w 2 M1 for correct method for partial simplification A1 for w (accept w) 2 (a) 2x − 5 = 6y y = x − 2 M1 for correct method to rearrange to 6y=2x-5 or y=x+c A1 for oe (b) y = −5x + 10 y = x + c 2 M1 for correct method to find gradient of line perpendicular to 5x + y = 10 A1 for y = x + c oe 3 (a) 4a² − 4a − 3 2 M1 for 3 terms correct out of 4 terms A1 cao (b) 3cd(3cd − 8) 2 B2 for 3cd(3cd − 8) (B1 for a correct but not fully factorised expression) (c) 25(4g2 − h2) 25(2g − h)(2g + h) 2 B2 cao (B1 for 2 correct linear factors)
4 p + 5 = n2 = OR pn2 = 2 − 5n2 pn2 + 5n2 = 2 (p + 5)n2 = 2 n2 = n = ± 3 M1 for correct first operation A1 for (p + 5)n2 = 2 or n2 = A1 for n = ± 5 a = 4, b = – 6, c = 1 = = = 3 M1 for correct formula or oe M1 for A1 for oe 6 Exponential Cubic Quadratic Circular Reciprocal 3 B3 cao (B2 for 3 or 4 correct, B1 for 1 or 2 correct)) 7 3 M1 for correct method to combine the fractions M1(dep) for full simplification of the numerator A1 for or or or
8 shaded region 5 M1 for drawing line x = 3 M1 for drawing line 3x + 2y = 6 M1 for drawing line y = x + 5 A2 for fully correct region shaded (A1 for correct shading for one inequality) 9 5.55 to 5.65 3 M1 for values 3, 1.5, 1, 0.7 to 0.8, 0.6, 0.5 (condone one error) M1 (dep) for substituting ‘values’ into trapezium rule, eg × 1 A1 for 5.55 to5.65 PAPER: AAL30_01 Question Working Answer Mark Notes 10 (a) −1, 2 2 M1 for correct method to factorise x² − x − 2 A1 cao (b) (3p − 5)(p + 2) > 0 p < −2, p > 3 M1 for factorising (3p − 5)(p + 2) A1 ft for establishing the critical values, oe, −2 A1 for p < −2 (or) p > (do not accept p < −2 and p > ) OR M1 for sketching y = 3p² + p − 10 A1 ft for establishing the critical values, oe, −2 A1 for p < −2 (or) p > (do not accept p < −2 and p >)
(b) × n × (2 ×2 + (n– 1) × 5) n(5n– 1) OR × n × (2 + 5n − 3) = n(5n– 1) n(5n– 1) 2 M1 for stating or using S = n(2a + (n– 1)d) A1 ft for n(5n– 1) oe OR M1 for stating or using S =n(a + l) and l = a+(n-1)d A1 ft for n(5n– 1) oe 17 54 = k × 33 k = 2 V = 2x3 3 M1 for V x3 or V = kx3 M1 for method to establish value of k A1 for V = 2x3 18 circle drawn 2 M1 for circle centre (0, 0) drawn A1 for circle centre (0, 0), radius 6 drawn PAPER: AAL30_01 Question Working Answer Mark 19 (a) Cubic graph drawn 4 M1 for calculating points for values of x from x = –3 to +3 with at least 4 correct values of y B1 for drawing suitable axes on grid for points A1 for all points correct A1 for drawing smooth curve through the correct points (b) −2.5, 0.1, 2.4 1 B1ft for all values, accept values in the range −2.5 to −2.6, 0.1 to 0.2 and 2.3 to 2.4 (c) −2.2, 0.5, 1.6 2 M1 for equation written in the form 6x − x3 = 2x + 2or line y = 2x + 2 drawn on graph or equation y= 2x+2 seen A1 ft for all three values, accept values in the range −2.2 to −2.3, 0.5 to 0.6 and 1.6 to 1.7