C1 sample A

C1/C2 material, not written in exam question style.


1  Write the terms up to x³ in the expansion of (2x – 3)                                           [4] 

2  Find the coefficient of x in the expansion of (3x – 5)                                          [3]

3  Evaluate (1/9) –3/2     and     64 - 5/6                                                                       [4]

4  Simplify  (1/a) –3/2     and     (32 a¹ b¹) - 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.

© David Scoins 2017