SPS EM 2026 4G3 P2 Final

NAME FORM CLASS ACAD CLASS ST. PATRICK’S SCHOOL PRELIMINARY EXAMINATION 2026 SUBJECT : Mathematics DATE : 18 August 2026 (4052/02) LEVEL : Secondary 4EXP/5NA DURATION : 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your Name, Form Class and Acad Class in the spaces at the top of the 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 questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90 . 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. For  , use either your calculator value or 3.142. For Examiner’s Use Type of Penalties Question Number 90 Presentation 1− 2− This paper consists of 21 printed pages including this cover page and 1 blank page.

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh 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 4052/02 [Turn over 1 (a) Express 53 2 2 1xx −−+ as a single fraction in its simplest form. Answer ................................................ [2] (b) Make 𝑟 the subject of the formula 22 2 ()V h R r r= + . Answer r =............................................... [2] (c) Simplify 2 2 2 6 3 9 x xy x y x − − + − . Answer ................................................ [3] (d) Simplify ( ) ( ) 43 2 5 328x y x y−−  , giving your answer with positive indices. Answer ................................................ [2]

4 4052/02 [Turn over 2 (a) A television has a cash price of $2400. It can also be bought on hire purchase with a deposit of 20% of the cash price, followed by 24 monthly instalments of $92. (i) Calculate the total hire purchase price. Answer $ ................................................ [2] (ii) Calculate how much more the hire purchase price is than the cash price, giving your answer as a percentage of the cash price. Answer ................................................ % [2] (b) After a discount of 15%, a laptop is sold for $1734. Calculate the original price of the laptop. Answer $ ................................................ [2]

5 4052/02 [Turn over (c) Mark has a vintage watch valued at $6666. Its value appreciates at a rate of 8% per year. (i) Show that the value of the watch at the end of 2 years is $7775.22, correct to the nearest cent. Answer [2] (ii) Find the number of complete years it takes for the value of the watch to exceed $8888 and the profit Mark will make if he sells it then. Answer ..........................................years for a profit of $..................................... [3]

6 4052/02 [Turn over 3 The quadrilateral ABCD, is made up of an acute triangle ABC and an obtuse triangle ADC. AB = 11 cm, BC = 8 cm, AD = 7 cm, angle ABC = 58°, and angle ACD = 42° . Find (a) the length of AC, Answer ................................................ cm [3] (b) angle CAD, Answer ......................................... degrees [3]

7 4052/02 [Turn over (c) the length of CD, Answer ................................................ cm [2] (d) the area of quadrilateral ABCD. Answer ................................................ cm2 [2]

8 4052/02 [Turn over 4 The cumulative frequency curve shows the masses, in kilograms, of the 120 watermelons in a shipment delivered to a supermarket. (a) Use the graph to find (i) the median, Answer .................................... kg [1] (ii) the interquartile range. Answer .................................... kg [2]

9 4052/02 [Turn over (b) The supermarket can only sell watermelons with a mass between 3 kg and 6.5 kg. Watermelons with a mass outside this range are unpopular sizes and have to be sold at a discount. Find the percentage of the shipment that has to be sold at a discount. Answer .................................... % [3] (c) A second supplier delivers another shipment of watermelons. For this shipment, the smallest mass is 3 kg and the range is 4.5 kg. The lower quartile, median and upper quartile are 4 kg, 5 kg and 6.5 kg respectively. Draw a box-and-whisker diagram for this shipment on the scale below. [3] (d) Which shipment is more desirable for the supermarket? Justify your answer with reference to the acceptable range. Answer ............................................................................................................................................. ....................................................................................................................................... [2]

10 4052/02 [Turn over 5 The depth of water, d metres, at a harbour entrance is modelled by 320.1 1.2 3.3 4d t t t= − + + where t is the number of hours after 6 am, for 0 ≤ t ≤ 8. The table shows some values of d. t 0 1 2 3 4 5 6 7 8 d 4 6.2 6.6 4.4 3.0 2.2 2.6 4.8 (a) Complete the table of values. [1] (b) On the grid, draw the graph of d against t. [3] d (metres) t (hours after 6am)