 Form 3 Mathematics
A variable P varies directly as t3 and inversely as the square root of s. When t = 2 and s = 9, P = 16. Determine the equation connecting P, t and s, hence find P when s = 36 and t=3.
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Form 3 MathematicsGiven that Cos 2x0 = 0.8070, find x when 00 < x < 3600 ( 4 marks)
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Form 3 MathematicsFind, without using Mathematical Tables the values of x which satisfy the equation Log2 (x2 – 9) = 3 log2 (2 + 1) (4 marks)
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Form 3 MathematicsThe first three consecutive terms of a geometrical progression are 3, x and 5 1/3. Find the value of x. ( 2 marks)
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Form 3 MathematicsThe points P, Q, R and S have position vectors 2p, 3p, r and 3r respectively, relative to an origin O. A point T divides PS internally in the ratio 1:6 (a) Find, in the simplest form, the vectors OT and QT in terms P and r ( 4 marks) (i) Show that the points Q, T, and R lie on a straight line ( 3 marks)
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Form 3 Mathematics
Without using mathematical tables or a calculator, evaluate sin 30°-sin60 °/tan60°
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Form 3 Mathematics(a) (i) Complete the table below for the function y = x3 + x2 – 2x (2 marks) 
(ii On the grid provided, draw the graph of y = x3 + x2 – 2x for the values of x in the interval – 3 ≤ x ≤ 2.5 (2 marks) (iii) State the range of negative values of x for which y is also negative (1 mk) (b) Find the coordinates of two points on the curve other than (0,0) at which x- coordinate and y- coordinate are equal (3 marks)
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Form 3 MathematicsA bank either pays simple interest as 5% p.a or compound interest 5% p.a on deposits. Nekesa deposited Kshs P in the bank for two years on simple interest terms. If she had deposited the same amount for two years on compound interest terms, she would have earned Kshs 210 more. Calculate without using Mathematics Tables, the values of P ( 4 marks)
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Form 3 MathematicsPoint T is the midpoint of a straight line AB. Given the position vectors of A and T are i-j + k and 2i+ 1 ½ k respectively, find the position vector of B in terms of i, j \ and k. ( 3 marks)
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Form 3 MathematicsIn this question Mathematical Tables should not be usedThe base and perpendicular height of a triangle measured to the nearest centimeter are 6 cm and 4 cm respectively. Find (a) The absolute error in calculating the area of the triangle (2marks) (b) The percentage error in the area, giving the answer to 1 decimal place (2mks)
Answers
Form 3 Mathematics
(a) The 5th term of an AP is 82 and the 12th term is 103.
Find: (i) the first term and the common difference; (ii) the sum of the first 21 terms. (b) A staircase was built such that each subsequent stair has a uniform difference in height. The height of the 6th stair from the horizontal floor was 85 cm and the height of the 10th stair was 145 cm. Calculate the height of the 1st stair and the uniform difference in height of the stairs.
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