CHIJ STC 2024 Math Prelim P1 solutions

CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/1 Paper 1 26 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST 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 paper clips, highlighters, glue or correction fluid. Answer all 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 answers in terms of . 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 90. This document consists of 21 printed pages. CHIJ ST. THERESA’S CONVENT PRELIMINARY EXAMINATION 2024 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 2 Compound interest Total amount = P 1 100 n r+ Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 2π4 r Volume of a cone = hr 2π3 1 Volume of a sphere = 3π3 4 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== a2 = b2 + c2 − 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 3 Answer all the questions. 1 Calculate 5 326.4 14.8 4.6 3 24 +−  . Answer …………………….………… [1] 2 (a) Given that 6sin 5x= , find the two possible values for angle x, where 0 x 180 Answer x = ……………… or ……………… [2] (b) Convert 138 into radians. Answer ………………………… radians [1] 3 Solve 4 32x = . Answer x = ………….….……….……… [2] oo 6sin 5 5sin 6 56.4 or 123.6 (1 d.p.) x x x = = = 0.159 (3 s.f.) π138 138 2.41 rad (3 s.f.)180=   5 2 2 4 32 22 52 2 5 4 x x x x = = = =

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 4 4 Simplify (a) ( )5 2 4 3 x−− , Answer ……………………..………… [1] (b) 2 3 3 6 27x y −   . Answer ………………………………… [2] 5 A group of 15 adults was surveyed on the number of hours they spent in a week watching Netflix. The results of the survey were represented in the dot diagram below. (a) Write down the modal length of time. Answer …………………………… hours [1] (b) Find the median length of time. Answer …………………………… hours [1] 16 17 18 19 20 21 22 23 24 25 26 27 ( )5 2 4 3 5 8 6 8 11 xx x − − = − + =− + 22 36 33 63 4 2 27 27 9 xy yx y x −     =       = Modal length 23= Median 20=

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 5 6 (a) Factorise completely 24 16k− . Answer ………………………………… [1] (b) Expand and simplify ( ) 2 37ab− . Answer …………………….…………… [1] 7 A pencil case contains 9 black pens, 5 red pens and 6 green pens. (a) A pen is chosen at random and then replaced. What is the probability that it is not a red pen? Answer ………………….……………… [1] (b) x black pens are removed from the box. The probability of choosing a green pen is now 3 8 . Find the value of x. Answer ………………….……………… [2] ( )24 16 8 3 2kk− = − ( ) 2 223 7 9 42 49a b a ab b− = − + 9 6 3 9 5 6 4 + =++ 63 9 5 6 8 63 20 8 16 20 4 x x x x =− + + =− =− =

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 6 8 Rearrange the formula 23 51 xy x += − to make x the subject. Answer …………………..…..………… [3] 9 Express 83 3 2 2 1xx −−+ as a single fraction in its simplest form. Answer ……………….………………… [3] ( ) ( ) 23 51 5 1 2 3 5 2 3 5 2 3 5 2 3 3 52 xy x y x x xy y x xy x y x y y yx y += − − = + − = + − = + − = + += − ( ) ( ) ( )( ) ( )( ) ( )( ) 83 3 2 2 1 8 2 1 3 3 2 3 2 2 1 16 8 9 6 3 2 2 1 7 14 3 2 2 1 xx xx xx xx xx x xx −−+ + − −= −+ + − += −+ += −+

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 7 10 The mean weight of a group of athletes is 72 kg. There are 6 more male athletes than female athletes in the group. The mean weight of the female athletes is 60.8 kg. The mean weight of the male athletes is 80.4 kg. Calculate the total number of athletes in the group. Answer ………………………………… [3] ( ) ( ) ( ) Let the number of female athletes be . the number of male athletes is 6. 60.8 80.4 6 72 6 60.8 80.4 482.4 144 432 2.8 50.4 50.4 182.8 total number of athletes 18 18 6 42 x x x x x x x x x x x + + + = + + + + = + − =− − = =−  = + + = ( ) ( ) ( ) Alternative solution: Let the number of male athletes be . the number of female athletes is 6. 60.8 6 80.4 72 6 60.8 364.8 80.4 144 432 2.8 67.2 67.2 242.8 total number of athletes 24 x x x x x x x x x x x − − + = + − − + = − − =− − = =−  = + ( )24 6 42−=

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 8 11 The pie chart below shows the sales for four different brands of potato chips. (a) State one misleading feature of the pie chart. Answer…………………………………………………………………………………….. …………………………………………………………………………………………….. …………………………………………………………………………………………….. ……………………………………………………………………………………….. [1] (b) Explain how this feature affects the reader’s interpretation of the pie chart. Answer…………………………………………………………………………………….. …………………………………………………………………………………………….. …………………………………………………………………………………………….. …………………………………………………………………………………………….. ……………………………………………………………………………………….. [1] 34% Brand D Brand B 10% Brand A 22% Brand C Brand B is the Best Seller! % of Brand 100% 22% 34% 10% 34% Brand and Brand have equal percentages but their proportions in the pie chart are not equal. OR The title is biased B BD = − − − = It may mislead readers into believing that Brand is selling better than Brand . OR It does not allow the reader to make his/her own judgement. BD

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2024 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 9 12 Factorise 29 6 8xx−− . Answer …………………………………… [2] 13 Cerra is thinking of two numbers. If she triples the first number and subtracts from it twice the second number, the answer is 6. If she multiplies the first number by 5 and a