Canberra EM 2024 Prelims Paper 2 QP

CANBERRA SECONDARY SCHOOL 2024 Preliminary Examination Secondary Four Express/Five Normal Academic MATHEMATICS 21 Aug 2024 4052/02 2 hours 15 minutes 0800h – 1015h Name: ______________________________________ ( ) Class: ________ READ THESE INSTRUCTIONS FIRST Write your full name, class and index number on all work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, 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. Calculators should be used 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. For  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. This question paper consists of 21 printed pages including the cover page. Setter: Ms Sim Yi Lian FOR MARKER’S USE Marks Awarded Max Marks Total 90 O

2 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic Mathematical Formulae Compound interest Total amount = 1 100 n rP+ Mensuration Curved Surface area of a cone = rl Curved surface area of a sphere = 24 r Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector Area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean fx f =  Standard deviation = 22fx fx ff  − 

3 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic Answer all the questions. 1 (a) Solve the simultaneous equations. 4 6 58 3 5 46 mn mn += += Answer m = n = [3] [Turn Over

4 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic (b) Write as a single fraction in the simplest form 2 31 2 50 5 x xx −−− . Answer [3] (c) 3 25 72 yx z= + (i) Find x when 25y= and 1z=− . Answer x = [1] (ii) Rearrange the formula to make y the subject. Answer y = [2]

5 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic (d) Solve the equation 23 20(3 1)( 1) x xx + −=+− . Answer x = or [3] [Turn Over

6 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 2 (a) The heights, in centimeters, of 100 plants of each of species A and species B are recorded. The cumulative frequency curves show the distributions of their heights. (i) Use the curve to estimate (a) the median height for species B, Answer cm [1] (b) the 40th percentile for species A, Answer cm [1] (c) the interquartile range for species A. Answer cm [2] Cumulative frequency Species A Species B 10 20 30 40 50 60 70 80 90 100 20 25 30 35 40 45 50 55 60 65 Heights

7 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic (ii) Plants from species B are used for an event. Only plants with height within 10% of 50 cm are used. Find the percentage of plants from species B which are used. Answer % [2] (b) A box has 20 pots of plants. There are 5 pink pots, 9 blue pots and the remaining pots are green. (i) Two pots are taken from the box at random, without replacement. Find, as a fraction in its simplest form, the probability that one pot is pink and the other is blue. Answer [2] (ii) These two pots are returned to the box. Three pots are taken from the box at random, without replacement. Find, as a fraction in its simplest form, the probability that only one pot is green. Answer [2] [Turn Over

8 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 3 (a) Wayne inherited a sum of money from his parents. He decided to invest 60% of the money and shares 3 4 of the remaining amount with his wife. The other $20 000 are meant for their travelling expenses. Calculate the sum of money he inherited. Answer $ [3] (b) A bank offers two investment packages. Package A Package B • Simple interest of 0.97% per annum. • One time payout of 10% of the amount of the investment. • Compound interest of 3.78% per annum. Wayne wants to invest $55 000 in one of the packages for 3 years. Which package should he choose if he wishes to reap the most benefits from the investment? [5]

9 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic (c) Wayne and his wife go on a seven days self-drive trip to Australia. They pay 150 AUD per day for car hire and 380 AUD per night for hotel. They pay using credit card and is charged with a fee of 2% for the currency conversion. The exchange rate between Singapore dollars and Australian dollars is $1 = 0.91 AUD. Calculate the total amount, including credit card fee, Wayne is charged for car hire and accommodation. Give your answer in Singapore dollars, correct to the nearest dollar. Answer $ [3] [Turn Over

10 Canberra Secondary School Mathematics 4052/02 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 4 A, B, C and D are points on a circle. Line PCQ is a tangent to the circle. Line QE bisects angle AEC and is parallel to line CD. (a) Show that EC ED= . Give a reason for each statement you make. [2] (b) Show that triangle AE