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Question 1 of 6
1. Question
(a) Simplify 7a + 2b – 4( 3a – b ) [2]
(b) Factorize completely 9y2 – 4z2 [2]
(c) Given the matrix
(i) Write down an expression in terms of y, for the determinant of A. [1]
(ii) Find the value of y given that the determinant of A is 5. [2]
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(a)
(b)
(c) (i) det A = (ii) y=
Correct 5 / 5 PointsIncorrect / 5 Points -
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Question 2 of 6
2. Question
(a) It is given that w varies directly as the square of x and inversely as y.
(i) if x = – 6, y = 12 and w = 15, find k [2]
(ii) find the value of y when x = 8 and w = 20 [2]
(b) Given that P = {x : 8x – 3 > 5x – 9, x ∈Z}, Q = {x : 7x – 2 < 3 (x + 6), x ∈ Z}, where Z is a set of integers, find n(P ∩ Q). [3]
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(a) (i) k = (ii) y =
(b) n(P ∩ Q) =
Correct 7 / 7 PointsIncorrect / 7 Points -
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Question 3 of 6
3. Question
(a) For the sequence 2, 5, 8, 11, … write down
(i) the sixth term [1]
(ii) an expression for the nth term [2]
(b) The first three terms of a geometric progression are m + 1, m – 3 and m – 1. Find
(i) the value of m [2]
(ii) the first term and the common ratio [4]
(iii) the sum to infinity [2]
write your answers in fraction form where applicable.
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(a) (i) sixth term = (ii) nth term =
(b) (i) m = (ii) a = , r =
(iii) sum to infinity =
Correct 10 / 10 PointsIncorrect / 10 Points -
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Question 4 of 6
4. Question
(a) Solve the equation 2y2 = 6y + 3 giving your answers correct to 2 decimal places [5]
(write your answers in ascending order)
(b) There are 50 green and red marbles in a bag. Given that the probability of choosing a green in a bag is 0.24 , calculate the number of red marbles in the bag [2]
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(a) y = , y =
(b) number of red mables =
Correct 7 / 7 PointsIncorrect / 7 Points -
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Question 5 of 6
5. Question
In the diagram below, O is the center of the circle ABCD AC is the diameter, AD and BC produced to meet at E. CÊD = 35o and ACB = 47o, find the angle
(i) ADC [1]
(ii) CAD [2]
(iii) DCE [2]
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(i) ADC = degrees
(ii) CAD = degrees
(iii) DCE = degrees
Correct 5 / 5 PointsIncorrect / 5 Points -
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Question 6 of 6
6. Question
(a) Given the functions
find
(i) f (–9) [1]
(ii) The value of x for which f(x) = 3g(x) [2]
(b) (i) Find the equation of the straight line passing through (– 4, 4) and is perpendicular to the straight line whose equation is y + x = 1 [3]
(ii)Find the percentage error of a bag of maize that weights 20.00kg. [2]
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(a) (i) f(-9) = (ii) x =
(b) (i) y =
(ii) percentage error =
Correct 5 / 5 PointsIncorrect / 5 Points -
