CCHM 2024 P1 Worked Solution

2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over Name: Class: Class Register Number: PRELIMINARY EXAMINATION 2024 SECONDARY 4 MATHEMATICS 4052/01 Paper 1 Friday 23 August 2024 Candidates answer on the Question Paper. 2 hours 15 minutes MARKS SCHEME This document consists of 20 printed pages.

2 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = nrP      + 1001 lr  2 4 r hr 3 1 2 3 3 4 r Cba sin 2 1 r  2 2 1 r  C c B b A a sin sin sin == Acbcba cos 2 222 −+=   f xf 22      −     f xf f xf

3 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 [Turn over Answer all the questions. 1 The length of a court is 0.028 km and the width of the court is 16 m. Express the ratio of the length to the width of the court in its simplest form. 28 :16 7 : 4 Answer ………… : ………… [1] ________________________________________________________________________________ 2 Given that 0 180x , find the possible values of x for sin 0.985x= . Give your answers correct to 1 decimal place. 11 sin 0.985 sin 0.985 or 180 sin 0.985 80.1 or 99.9 x x −− = =− = Answer x = ………..…or…………… [2] ________________________________________________________________________________ 3 (a) Simplify ( ) 34 37 4 10 ab ab , leaving your answer in positive index form. ( ) 34 12 3 3 7 3 7 9 4 4 64 10 10 32 5 ab ab a b a b a b = = Answer ………………………………... [2] (b) Given that 23x = , 27y = and 92 49 z = , use the laws of indices to find the value of 13 22. x y z−+ ( ) ( ) 1 13 32 2 3 2 2 2 2 937 49 81 49 x y z x y z−+ =   =   = Answer ………………………………... [2] Law of indices: 1: ( ) nm mnaa = 2: m n m na a a += to award M1 if student 3: m n m na a a −= show understanding of 4: 1 nnaa= either law of indices

4 2024 Preliminary Exam/CCHMS/Secondary 4/Mathematics/4052/01 4 A group of students won $ 226 in a competition and shared the amount equally, leaving $ 4 leftover. Competing for a second time , the same group of students won $ 296. They shared the $296 along with the $4 left over from the first competition equally, with no amount remaining. Assuming that each student received a whole number of dollars in both distributions, find the greatest possible number of students in the group. 222 300 2 111 150 3 37 50