Edexcel IALMathematicsGeneral Applications7 Marks
Given that for all real values of x, 3x² + bx + 10 = A(x-2)² + C, where A, b and C are constants.
- (a)Find the value of A.[1]
- (b)Find the value of b and the value of C.[6]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- (a) B1 for A = 3 (by comparing coefficients of x² on both sides)
- (b) M1 for expanding A(x-2)² + C to A(x² - 4x + 4) + C (or their A)
- (b) A1 for 3x² - 12x + 12 + C (after substituting A=3)
- (b) M1 for comparing coefficients of x: b = -12 (from their expansion)
- (b) A1 for b = -12
- (b) M1 for comparing constant terms: 10 = 12 + C (from their expansion)
- (b) A1 for C = -2
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