Mathematics Mid Year Form 4 Paper 2 2010
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Mathematics Mid Year Form 4 Paper 2 2010

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    Mathematics Mid Year Form 4 Paper 2 2010 Mathematics Mid Year Form 4 Paper 2 2010 Document Transcript

    • _________________________________________________________ Mathematics Form 4 Instructions : This question paper consist of two sections. Section A and Section B. Answer all questions in Section A and four questions in Section B. The diagrams in the questions provided are not drawn to scale unless stated. The marks allocated for each question and sub-part of a question are shown in brackets. You may use a non- programmable scientific calculator. Section A [52 marks] 1. The following Venn diagram shows sets K, L and M such that the universal set ξ = K ∪ L ∪ M . On the diagram, shade the set (a) K ∩ L' (b) K ∪ L ∩ M ' [3 marks] L M L M K K Answer : (a) (b) 2. The Venn diagrams below shows the sets P, Q and R such that the universal set, ξ = P ∪ Q ∪ R . Shade the region indicated. (a) P'∪Q (b) P ∩ Q ∩ R ' [3 marks] Answer : (a) P Q R (b) P Q R 3 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 3. Solve the quadratic equation m 2 − 10 = m(1 − 2m) . [ 4 marks] Answer : 5n 2 + 3 4. Solve the equation = 2. [4 8n marks] Answer : 5. The diagram shows a composite solid formed by the combination of a cylindrical solid with a base diameter of 10 cm and a height of 21 cm and a cone that has a slant height of 13 cm. Calculate the volume, in cm3, of the combined solid. [5 marks] 13 cm 21 cm 10 cm Answer : 4 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 6. (a) Determine whether the following statement is true or false. “ 52 = 25 or 16 = 4.” (b) Complete the following statement by using the quantifier “all” or “some” to make it a false statement. “ __________ triangles are isosceles triangles.” (c) Make a general conclusion by induction for the sequence of numbers 17, 21, 33, 53, … which follows the following number pattern. 17 = 4(0)2 + 17 21 = 4(1)2 + 17 33 = 4(2)2 + 17 53 = 4(3)2 + 17  [5 marks] Answer : (a) ………………………….………….. (b) ………………………………..……. (c) ……………………………………… 7. (a) Determine whether each of the following sentences are statements or non- statement. (i) x + 7 x (ii) 2 x 2 + 5 x 2 = 7 x 2 (b) Write two implications based on the following sentence. x 3 < 0 if and only if x < 0 (c) Complete the premise in the following argument. x Premise 1 : If is a proper fraction, then x < y . y Premise 2 : …………………………………………… Conclusion : x < y. [5 marks] Answer : (a) (i) …………………………………….. (ii) ……………………………………. (b) Implication 1 : …………………………………………………………….. Implication 2 : …………………………………………………………….. 5 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 (c) ………………………………………………………………………………….. 8. In the dagram, O is the origin. The straight line RT is parallel to the x-axis and the straight line PQ and RS are parallel. The equation of RS is x + 2 y = 12 . y R T P x S Q (6, -6) (a) State the equation of RT. (b) Find the equation of PQ and hence, state its x-intercept. [5 marks] Answer : (a) (b) T 14 cm P 9. 60° O S Q 7 cm 6 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 In the diagram, TS and PQ are arcs of two different circle which have the same centre O. OQS is a straight line. 22 It is given that ∠ QOP=60º and ∠ SOT=90º. Using π = , calculate 7 (a) the perimeter, in cm, of the sector OTS, (b) the area, in cm2, of the shaded region. [6 marks] Answer : (a) (b) 10. (a) Expand ( 4 x − 1)( x + 5 ) . (b) Factorise 4 x 2 − 1 . (c) Solve the equation 2( 3 − x 2 ) = 4 x . [6 marks] Answer : (a) (b) (c) 7 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 11. (a) Complete the following statement using ‘all’ or ‘some’ to construct a true statement. ………………………… prime numbers are odd numbers. (b) Change the truth value of the following statement by using the word ‘not’. An empty set is a subset of any set. (c) Write two implications based on the following sentence. ( x − 5)( x + 3) = 0 if and only if x = 5 or x = −3 (d) 3=1+1+1 6=2+2+2 9=3+3+3  Based on the above information, form a general conclusion for the sequence 3, 6, 9, ... [6 marks] Answer : (a) ………………………………………………. (b) ………………………………………………. (c) Implication 1 : ………………………………………………….. Implication 2 : ………………………………………………….. (d) ……………………………….. Section B [48 marks] 12. The data in the diagram shows the length, in mm, of 36 leaves plucked from a tree in a garden. 8 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 20 40 44 63 56 34 75 68 28 52 38 32 31 33 78 59 41 15 42 65 43 43 35 30 46 48 54 24 58 43 39 41 49 45 33 47 (a) Based on the data above and using a class interval of 10, complete the table given below. Length (mm) Frequency Cumulative Frequency Upper Boundary 0–9 0 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 [4 marks] (b) Based on the table in (a), (i) state the modal class, (ii) calculate the estimated mean of the lengths of the leaves. [4 marks] (c) For this part of the question, use the graph paper. By using a scale of 2 cm to 10 mm on the horizontal axis and 2 cm to 5 leaves on the vertical axis, draw an ogive for the data. [4 marks] Answer : (b) (i) ……………………….. (ii) 13. (a) (i) State whether the following statements is true or false. (a) 4 × 3 = 15 − 3 9 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 (b) 64 = 4 (c) 4 × 3 = 15 − 3 and 64 = 4 (d) 4 × 3 = 15 − 3 or 64 = 4 (ii) Write down two implications from the sentence given below. “ x 3 = 64 if and only if x = 4 ” (iii) Complete the premise in the following argument. Premise 1 : All acute angles are less than 90º. Premise 2 : ………………………………………. Conclusion : x is less than 90º. [8 marks] p+6 (b) Solve the equation p 2 = . [4 marks] 2 Answer : (a) (i) (a)……………………………….. (b) ………………………………. (c) ……………………………… (d) ……………………………… (ii) Implication 1 : ………………………………………………….. Implication 2 : ………………………………………………….. (iii) ……….……………………………………………… (b) 14. (a) The Venn diagram shows the sets E, F and G such that the universal set, ξ = E ∪ F ∪ G . On the diagram, shade (i) E ∩ G (ii) ( E ′ ∪ F ) ∩ G G G F F E 10 E suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 [3 marks] (b) y On the Cartesian plane, PQRS is a trapezium. PQ is parallel to RS. P(6, 10) S Q (6, 10) R(13, 2) x O Find (i) the equation of the straight line PQ, (ii) the y-intercept of the straight line PQ [6 marks] (c) Solve the equation 3n 2 + 14n − 5 = 0 . [3 marks] Answer : (b) (i) (ii) (c) 15. The data in the box below shows the marks obtained by a group of 40 pupils in a Mathematics test. 51 50 54 61 56 47 54 62 60 53 57 46 52 60 74 49 64 63 42 55 70 66 57 69 45 56 62 59 58 63 64 51 11 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 58 68 72 67 65 61 43 65 a. Using the data in the box above and a class interval of 5 marks, complete the table below. Marks Midpoint Frequency 36 - 40 38 0 41 - 45 [4 marks] b. By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 1 pupil on the y- axis, draw a frequency polygon for the data. [4 marks] c. From your frequency polygon in (b), (i) calculate the mean marks for the group of pupils, (ii) state one information which relates the marks and the number of pupils. ………………………………………………………………………………. [4 marks] 16. The data in the diagram below shows the number of SMS received per day by a group of students. 11 7 14 13 8 12 11 9 16 11 16 17 15 6 13 12 18 22 11 10 13 6 21 5 12 22 19 20 12 15 16 12 9 13 6 13 10 12 5 12 14 11 a. Using the data in the diagram above and a class interval of 5, complete the table below. 12 suesha_2010___________________________________________________________________________________
    • _________________________________________________________ Mathematics Form 4 Number of Frequency Midpoint Upper SMS received boundary 5-7 6 6 7.5 8 - 10 11 - 13 14 - 16 17 - 19 20 - 22 [4 marks] b. Based on table above, calculate the estimated mean of the SMS received per day. [3 marks] c. By using a scale of 2 cm to 3 units on the x-axis and 2 cm to 2 units on the y-axis, draw a histogram for the data. [4 marks] d. State the modal class for the data above. [1 marks] ………………………………………. 13 suesha_2010___________________________________________________________________________________