O-LevelAdditional MathematicsFunctions4037/22 · May/June 2010 · Q1210 Marks
Answer only one of the following two alternatives. EITHER It is given that f(x) = 4x² + kx + k.
- (i)Find the set of values of k for which the equation f(x) = 3 has no real roots.[5]
- (ii)In the case where k = 10, express f(x) in the form (ax + b)² + c,[3]
- (iii)find the least value of f(x) and the value of x for which this least value occurs.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- M1 for Rearranges to ax² + bx + c(=0) and uses b² < 4ac
- A1 for k² - 16k + 48 < 0
- M1 for Solve 3 term quadratic
- A1 for k = 4 and 12
- A1 for 4 < k < 12
- B1+B1+B1 for (2x + 5/2)² + 15/4 or a=2, b=5/2, c=15/4 or 3.75
- B1√ for minimum 15/4 or 3.75
- B1√ for x = -5/4 or -1.25
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