O-LevelAdditional MathematicsIndices and surds4037/11 · May/June 2010 · Q88 Marks
Solve the equation (23 – 4x) (4x + 4) = 2.
- (a)Solve the equation (23 – 4x) (4x + 4) = 2.[3]
- (b)(i)Simplify √108 - 12/√3, giving your answer in the form k√3, where k is an integer.[2]
- (b)(ii)Simplify √5+3 / √5-2, giving your answer in the form a√5 + b, where a and b are integers.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2010). The mark or mark type is shown in brackets.
- [3] (a) M1 for to obtain powers of 2 (e.g. 2^(3-4x) and 2^(2x+8)); DM1 for attempt to equate powers of 2 using addition; A1 for x = 5
- [2] (b)(i) M1 for attempt to obtain each term in terms of √3; A1 for 2√3
- [3] (b)(ii) M1 for attempt to rationalise (multiply by conjugate); A1 for numerator (11 + 5√5); A1 for denominator (1) (can be implied)
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