C1/C2 material, not written in exam question style.
1 Write the terms up to x³ in the expansion of (2x – 3)⁷ [4]
2 Find the coefficient of x⁴ in the expansion of (3x – 5)⁶ [3]
3 Evaluate (1/9) –3/2 and 64 - 5/6 [4]
4 Simplify (1/a⁴) –3/2 and (32 a¹⁰ b¹⁵) - 3/5 [4]
5 (i) Simplify √125 + √5 [2]
(ii) Express 48 / (5 - √13) in the form a + b √13, where a & b are integers. [3]
6 (i) Simplify √108 + √48 [2]
(ii)Express 45 / (4 + √11) in the form a + b √11, where a & b are integers. [3]
7 Find the gradient and intercepts of the line 2x + 7y =12 [4]
8 The middle of three consecutive integers is 2n. Write down the other two. Prove that the sum of the three integers is divisible by 3. [3]
9 The simplest model for disease has the rate of infection proportional to the numbers of those with the disease and of those free of the disease. Write a suitable differential equation to represent this situation. [3]
10 I have a race coming up. There is a special award for beating 4 hours for 56km. Given that I have always run 21.1km (the half marathon) inside 90 minutes, express an opinion (showing your argument) on the prospect of making the special award. I have run one marathon inside three hours; twenty five years ago; does this affect your answer? [5]
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Q10’s race was the Old Comrades in Cape Town. I did the Half-marathon instead. They started less than hour apart and shared a lot of the route.
