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1. An arithmetic progression has first term 4 and common difference 1 2. State the 100th term. 2. A geometric series has first term 6 and common ratio 3. Find the sum of the first 10 terms. 3. A = 1 −7 , B = 3 7 , C = 1 0 −1 2 −1 0 −1 1 Find: a) BC, b) 5A − 2C, c) A + C, 4. Find the inverse of A = −2 1 5 −3 5. Use matrices to solve the following simultaneous equations: 2x + 3y = 10 x − 2y = −9 6. Find the gradient function of y = 3x3 − 9x + 2. Find the value of the gradient function at x = 1, x = 0 and x = −1. 7. A particle moves along a coordinate axis. Its position at time t is given by s(t) = t3 − 9t2 + 24t + 4. Find: (a) What is the velocity of the ball ? (b) What is the acceleration of the ball? (c) Find the speed. (d) what is the velocity at t = 3. (e) What is the acceleration at t = 3. 8. Find the area under y = 1t between t = 1 and t = 5
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