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 4
1. Question
(a) Given that ,
(i) Write down in terms of k, the determinant of A, [2]
(ii) Given that the determinant of A is 1, find the value of k, [2]
(b) Solve the equation 2m² – 5 + m = 0 , giving your answers correct to 2 decimal Places [5]
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(a) (i) Det A =
(ii) k =
(b) smaller value of m =
bigger value of m =
Correct 8 / 8 PointsIncorrect / 8 Points -
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Question 2 of 4
2. Question
The Venn diagram below shows the number of pupils who eats Mangoes (M), Guavas (G) and Tangerines (T).
(a) If the total number of 40 pupils eats at least one of the three fruits, find the value of x. [3]
(b)Find the number of pupils who eats
(i) Two different types of fruits only, [1]
(ii) One type of fruit only, [1]
(iii) Guavas or Tangerines but not Mangoes. [1]
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(a) x =
(b) (i) Ans = (ii) Ans = (iii) Ans =
Correct 6 / 6 PointsIncorrect / 6 Points -
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Question 3 of 4
3. Question
(a) Insert two geometric means between 243 and 9 [4]
(b) Given that the sum to infinity of a geometric progression is 64 and the common ratio is 0.75.
(i) find the first term [2]
(ii) write down the first four terms of this geometric progression in descending order [4]
(iii) find the sum of the first 7 terms. correct to two decimal places [3]
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(a) T2 = , T3 =
(b) (i) a =
(ii) First four terms = , , ,
(iii) Sum of 7 terms =
Correct 11 / 11 PointsIncorrect / 11 Points -
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Question 4 of 4
4. Question
(a) The diagram below shows the location of three secondary schools in Kitwe district, Mindolo (M), Chibote (C) and Parklands (P). M is 34km from C, P is 24 km from M and C is 42 from P.
(i) Calculate angle CMP (correct to 1 d.p) [4]
(ii) Calculate the area of triangle CMP (correct to 2 d.p) [2]
(iii) Calculate the shortest distance from M to meet PC (correct to a whole number). [2]
(b) Solve the equation 3tanθ – 2 = 1 for 0° ≤ θ ≤ 360° . write your answers in ascending order [2]
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(a) (i) Angle CMP =
(ii) Area of triangle CMP =
(iii) Shortest distance =
(b) θ = degrees and degrees
Correct 11 / 11 PointsIncorrect / 11 Points -
