MSHS 2026 Prelim Math P1 Solution

This document consists of 22 printed pages. [Turn over For Examiner’s Use Subtotal Statement Presentation Units Rounding off Class/ Index Number Centre Number/ ‘O’ Level Index Number Name / / MARIS STELLA HIGH SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR MATHEMATICS 4052/1 Paper 1 17 August 2026 Candidates answer on the Question Paper. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. 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. 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. 90

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 A a sin = B b sin = C c sin 2 2 2 2 cosa b c bc A= + − Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 Answer all the questions. 1 (a) Solve the inequalities 7 6 2(3 1) 5( 1) 2x x x−  −  − + . Answer ............................................. [2] (b) Represent your answer to part (a) on this number line. [1] 2 Expand and simplify (3 2 )( 4 )x y x y−+ . Answer ............................................. [2] 3 Given that 3 2 1729 9 x= , find the value of x. Answer x = .................................... [2] – 2 –3 0 2 1 4 3 6 5 7 x 7 6 6 2xx−  − and 6 2 5 5 2xx−  − + 4x and 1x− 1x− ( ) 36433 x−= 4 18x=− 14 2x=− 223 12 2 8x xy xy y+ − − 223 10 8x xy y= + − –1

4 4 Jonathan has $10 000 to invest. A bank offers an interest of 1.95% per annum, compounded monthly for 8 years. Calculate the total amount of interest he will receive after 8 years if he invests in the bank. Give your answer correct to the nearest cent. Answer $ .................................... [3] 5 (a) The sets  , P and Q satisfy the conditions n( ) 50 = , n( ) 10P = and n( ) 38Q = . Find the smallest possible value of n( )'PQ . Answer ............................................. [1] (b) On the Venn diagram, shade the region which represents ( ) 'XY . [1] The smallest possible value of n( )'PQ is when n( )PQ is the largest, when n( ) 10 38 48PQ = + = . The smallest possible value of n( )' 50 48 2PQ = − = .  X Y Total interest 8 12 1.95 /12$10000 1 $10000100  = + −  = $1686.78

5 6 The Marist Football Team plays home and away matches in a weekend league that comprises 14 teams. The dot diagram below represents the total number of goals scored in these matches. (a) Johnson said that the modal and median number of goals scored are the same. Do you agree with Johnson? Explain your answer. ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. [1] (b) Johnson did not include all the 3 matches which ended goalless, as he reckoned that there are zero goals anyway. He calculated the mean number of goals scored as: Mean ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 5 3 8 4 5 5 2 6 1 3.132 5 8 5 2 1  +  +  +  +  + == + + + + + (3 s.f.) Do you agree with his method of computation? Explain your answer. ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. [1] 0 1 2 3 4 5 6 No, I disagree with him. By excluding the matches which ended goalless, the 3.13 goals calculated is larger than the actual mean (of 2.77 goals). Yes, I agree with him. The modal goals is 3 goals and the median goals is the mean of the 13th and 14th value = 3 goals. Hence they are the same.

6 7 Express as a single fraction in its simplest form 30 6 1 (2 3)( 5) 3 2 a a a a + −− + − . Answer ............................................. [3] 8 It takes 2 painters 6 hours to paint the interior of 1 flat. Each painter can work for 8 hours a day. (a) Calculate the number of days it takes 1 painter to paint 6 flats. Answer ....................................... days [2] (b) Calculate the number of painters needed to paint 36 flats in 6 days. Answer ............................... painters [2] ( ) ( )( ) 65 1 2 3 5 2 3 a a a a + +− + − ( )( ) 30 6 5 2 3 5 (2 3)( 5) aa a a a a ++ +− + − + ( ) ( ) 61 2 3 2 3aa=+ −− or ( )( ) 7( 5) 2 3 5 a aa += −+ 7 23a= − 7 23a= − 2 painters can paint 1 flat in 6 hours. 1 painter can paint 1 flat in 6 2 12= hours. 1 painter can paint 6 flats in 12 6 72= hours 72 8=  = 9 days. 1 painter can paint 1 flat in 12 hours. 1 painter can paint 36 flats in 12 36 432= hours. To paint 36 flats in 6 days (48 hours), 432 48 9= painters are needed.

7 9 Maya records the monthly sales figures (in thousands of dollars) for her shop over one year. She presents the graph below to her investors. (a) Estimate her monthly sales figure for January. Answer $ .................................... [1] (b) Explain why the graph may not show the true trend in sales over the year. ……………………………………………………………………………………….. ……………………………………………………………………………………….. ……………………………………………………………………………………….. [1] (c) (i) State one misleading feature of the graph. ………………………………………………………………………………… ……………………………………………………………………………….. [1] (ii) Explain how this feature affects the reader's interpretation of the graph. ………………………………………………………………………………… ……………………………………………………………………………….. [1] 4700 4800 4900 5000 5100 5200 5300 December January Monthly Sales Figure The graph only shows two months’ sale, so fluctuations between other months are not captured. The vertical-axis does not start at zero This makes small differences appear much larger, misleading the reader into thinking sales varied far more than they actually did. 5220 000-5240 000.

8 10 In the triangle, KM = 4.5 m and angle 57KML= . Given that the area of the triangle = 10.4 m2, calculate the distance LM. Answer …..........................................m [2] 11 A patient has to take three types of pills at regular intervals. Pill A once every 4 hours, Pill B once every 6 hours and Pill C once every 8 hours. He started taking all three pills at 0800 hours At what time will he take all three pills together again? Answer ........................................ hours [2] M K 4.5 m L 57° Area of triangle = 1 (4.5)( )sin 572 LM  10.4 2.25sin 57LM =  = 5.51 m (3s.f) LCM of 4, 6 and 8 32 3 24=  = hours He will take all 3 pills at 0800 + 24 hours = 0