O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2012 · Q1310 Marks
Answer only one of the following two alternatives. OR A function g is defined by g : x → 5x² + px + 72, where p is a constant. The function can also be written as g : x → 5(x - 4)² + q.
- (i)Find the value of p and of q.[3]
- (ii)Find the range of the function g.[1]
- (iii)Sketch the graph of the function on the axes provided.[2]
- (iv)Given that the function h is defined by h : x → ln x, where x > 0, solve the equation gh(x) = 12.[4]
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Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [1] (i) 5(x²-8x+16)+q and equate B1
- [1] p = -40 A1
- [1] q = -8 A1
- [1] (ii) g(x) ≥ -8 B1^
- [2] (iii) positive quadratic curve; correct position B1+B1
- [1] (iv) 5(lnx-4)²-8=12 B1
- [1] solve for (lnx - 4) M1
- [1] lnx = 2, 6 A1
- [1] x = 7.39 or e², x = 403 or e⁶ A1
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