MGS 4048 02 QP

This question paper consists of 25 printed pages and 3 blank pages. Class Index Number Name : ____________________________________ METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2022 Secondary 4 Wednesday MATHEMATICS 4048/02 3 August 2022 Paper 2 2 h 30 min Candidates answer on the Question Paper. INSTRUCTIONS TO CANDIDATES Write your name, class and index number in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. Forp, use either your calculator value or 3.142, unless the question requires the answer in terms of p The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 100. 100

Page 2 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 Mathematical Formulae Compound Interest Total amount =  100 r 1 n P Mensuration Curved surface area of a cone = rlp Surface area of a sphere = 42rp Volume of a cone = hr2 3 1p Volume of a sphere = 3 3 4 rp Area of a triangle ABC = 2 1 absinC Arc length = r , where  is in radians Sector area = 21 2r, where  is in radians Trigonometry C c B b A a sin sin sin  a 2 = b 2 + c 2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22        f fx f fx

Page 3 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 1 (a) Simplify 2 4 5 3 (3 )x x  as a single fraction in is lowest term. Answer ......…………………. [2] (b) (c) Simplify 2 6 3 3 64x y     , leaving your answer in positive index. Answer ………………………. [2] Solve these simultaneous equations. 2 1 4 3 6 3 33 164 x y x y     Answer x = ................................. y = ................................. [3]

Page 4 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 (d) (i) Express 25 4 7x x  in the form 2( )a x b c  . Answer ………………………. [2] (ii) Hence, solve 25 4 9x x  . Answer ………………………. [3]

Page 5 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 2 (a) A fruit basket contains 2 apples and 2 oranges. A second bag contains 1 apple, 1 orange and 2 kiwis. Ben picks one fruit from each bag. (i) Draw a possibility diagram to show all possible outcome. Answer [2] (ii) Find the probability that Ben picks (a) two apples, Answer ………………………. [1] (b) different fruits, Answer ………………………. [1] (c) at least one orange. Answer ………………………. [1]

Page 6 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 (b) Dream Renovation Company has three different packages. The table below shows the quantity of each type of work included in the different packages. Package Plumbing Work Window Carpentry Work A 6 5 6 B 4 2 7 C 5 3 9 This information is represented by the matrix Q = 6 5 6 4 2 7 5 3 9       . The unit cost price of each work is as follows. Plumbing Work $180 Window Work $420 Carpentry Work $390 (i) (a) Write down the 3 × 1 matrix P to represent the unit cost of each work. Answer P = ……….………….[1] (b) Evaluate QP. Answer QP = …….………….. [1]

Page 7 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 (c) State what the elements of QP represent. Answer…………………………………………………………………………………….... …………………………………………………………………………………….....…. [1] (ii) A condominium’s manager, Amy, decided to engage Dream Renovation Company to do renovation works. She ordered 85 package A, 90 Package B and 85 Package C. A matrix Y when multiplied by QP, will give the total cost of this renovation. (a) State matrix Y. Answer Y= ………………………. [1] (b) Using matrix multiplication, find the total cost of this renovation. Answer $ ………………………. [2]

Page 8 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 3 In the diagram, the points A, B, C, D lie on circle I. The points A, E, D, F lie on circle II. AEC is a straight line. DF and AF are tangents to circle I. CD and AB are extended to meet at point G. ∠ECD = 67°, ∠CBD = 23° and ∠AED = 134°. (a) Stating your reason clearly, find (i) ∠AFD, Answer ∠AFD = ……………….. (ii) ∠CAD, Answer ∠CAD = ……………….. (iii) a line that has the same length as DF. Answer line ………….............… [1] [1] [2] 67° 134° A B C D E F G Circle I Circle II 23°

Page 9 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 (b) Explain why the centre of circle I lie on the circumference of circle II. [3] (c) Show that triangle BCG is similar to triangle DAG. State your working and reasons clearly. Answer [2]

Page 10 of 28 Methodist Girls’ School Mathematics Paper 2 Sec 4 Preliminary Examination 2022 4 (a) The cumulative frequency curve shows the distribution of the masses of 160 chicks from Dairy Farm. From the curve, find (i) the median mass, Answer ………………………. [1] (ii) the interquartile range, Answer ………………………. [1] Mass (g)