Duration: 1:30 minutes
Instructions:
Answer all the questions in this paper
Write your final answers in the spaces provided
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Question 1 of 7
1. Question
(a) The points A and B have coordinates (–2, 15) and (3, 5) respectively. The perpendicular
to the line AB at the point A (–2, 15) crosses the y-axis at the point C. Find the coordinates of C [4]
(b) The line x – y = 2 intersects the curve x2 + 4xy = 4 at the points A and B. Find the coordinates of A and of B [5]
A (has the smallest value of x)
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(i) C = ( , )
(ii) A = ( , ) B = ( , )
Correct 8 / 8 PointsIncorrect / 8 Points -
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Question 2 of 7
2. Question
Solve the simultaneous equation
2x + y – 3z = – 2
3x + y + 2z = 1
x – 2y – 4z = – 16
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x = , y = , z =
Correct 6 / 6 PointsIncorrect / 6 Points -
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Question 3 of 7
3. Question
A function is defined by f:x→(3x-1)/2 . Find
(i) The value of a given that ff(a)=5/8 [3]
(ii) The value of x such that f -I(x)=f(x) [3]
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(i) a =
(ii) x =
Correct 6 / 6 PointsIncorrect / 6 Points -
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Question 4 of 7
4. Question
(a) Express 2 – 3x – x2 in the form q + a(x + p)2 where a, p and q are constants. Hence, find the values of a, p and q, the
coordinates of the turning point and stating whether it is maximum or minimum [6]
(b) Find the range of values of k for which the equation x2 – 4x – 10 = k has real roots. [3]
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(i) a = , p = , q =
the T.P = ( , )
(ii) the range is
Correct 6 / 6 PointsIncorrect / 6 Points -
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Question 5 of 7
5. Question
(a) The sixth term of an arithmetic progression is – 7 and the sum of the first 10 terms is – 60. Calculate;
(i) The first term and the common difference [3]
(ii)The 20th term [2]
(b) Given that the 2nd and 5th term of a geometric progression are 10 and 5/4 Find
(i) The first term and the common ratio [4]
(ii) The sum of the first six terms [3]
(iii) The sum to infinity of this geometric progression [2]
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(a) (i) a = , d =
(ii) The 20th term =
(b) (i) The first term (a) = , the common ratio (r) =
(ii) The sum of the first six terms =
(iii) The sum to infinity =
Correct 16 / 16 PointsIncorrect / 16 Points -
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Question 6 of 7
6. Question
(a) The first three terms in the expansion of (1 + ax)n in ascending powers of x are 1 – 12x + 63x2.
Find the values of a and n. [5]
(b) Find the term independent of x in the expansion of (2x3 + 1/x)n [4]
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(i) a= , n =
(ii) answer =
Correct 10 / 10 PointsIncorrect / 10 Points -
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Question 7 of 7
7. Question
The diagram shows a triangle ABC in which A is (3, -2) and B is (15,22). The gradients of AB, AC and BC are 2m, -2m and m respectively, where m is a positive constant.
(i) Find the gradient of AB and deduce the value of m [2]
(ii) Find the coordinates of C [4]
The perpendicular bisector of AB meets BC at D
(iii) Find the coordinates of D [4]
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(i) m =
(ii) The coordinate of C= ( , )
(ii) D = ( , )
Correct 10 / 10 PointsIncorrect / 10 Points -
