CAT HIGH 2025 EMATH PRELIM P1 MS

Name: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination Secondary 4 (O-Level Programme) Mathematics 4052/01 Paper 1 25 August 2025 2 hours 15 minutes Additional Materials: Booklets A and B Candidates answer in the space provided on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions in the space provided. 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 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. 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 Booklet A consists of 23 printed pages and 1 blank page. 90 For Examiner’s Use

MATHEMATICAL FORMULAE Compound interest n rP      + =1001 a mount Total Mensuration radians in is where,2 1 area Sector radians in is where, length Arc sin2 1 triangle a of Area 3 4 sphere a of Volume 3 1 cone a of Volume 4 s phere a of area Surface cone a of area surface Curved 2 3 2 2 θ θ θ θ π π π π r r C b aABC r h r r l r = = = = = = = Trigonometry A bc c b a C c B b A a cos2 sinsinsin 2 2 2− + = = = Statistics 22 Mean Standard deviation fx f fx fx ff ∑= ∑ ∑∑= − ∑∑ 

1 Simplify ( ) 2 5 48 2 2 x x x −+− − . ( ) ( ) ( ) 2 2 5 48 2 2 425 54 2 222 11 22 x x x x orx xxx orxx −+− − −= −+ =−− −−− =−= −− 2 Rearrange the formula to make p the subject. 261ppr p −= ( ) 2 2 61 61 1 6 ppr p pr p r −= −= =± − Answer ………………………………... [3] Answer ………………………………... [2]

3 Factorise the following expressions completely. (a) 5 2 10m n mn+−− ( ) ( ) ( )( ) ( )( ) 5 2 10 52 2 52 52 m n mn m nm nm or nm +−− = −+ − = −− = −− (b) 22 4 94x xy y+ −+ ( ) ( )( ) 22 2 449 29 23 23 x xy y xy xy xy ++− = +− =++ +− Answer ………………………………... [2] Answer ………………………………... [2]

4 The product of two numbers, x and y, is 6300 and their highest common factor is 6. Given 6 < x < y, find the value of x and the value of y. 222 2 6300 2 3 5 7 2 3 7 42 2 3 5 150 x y =××× =××= =×× = 5 Simplify 3 4 2 16 49x y −   , leaving your answer in positive indices. 3 4 242 16 6 49 343 xy yx −  = Answer x = …………………………... y = …………………………… [2] Answer ………………………………... [2]

6 (a) Express 2 8 19xx−−− in the form of ( ) 2 xp q−+ + . ( ) 2 2 8 19 43 xx x −−− = −+ − (b) Hence, on the axes below, sketch the graph of 2 8 19yx x= −−− . Answer [2] Answer ………………………………... [2] y x – 4 – 3 – 19

7 Andy places an order for some polo shirts that come in three sizes S, M and L. The ratio of the number of polo shirts S : M = 3 : 8. The ratio of the number of polo shirts S : L = 5 : 2. There are 306 more polo shirts in size M than L. Find the total number of polo shirts ordered. ( ) :: 3:8 5:2 15 : 40 15 : 6 :: 15 : 40 : 6 306Total 61 40 6 549 SM SL SML = − = 8 Solve 2 6 96p ×= . 2 6 96 2 16 4 p p p ×= = = Answer ………………………………... [2] Answer p = …………………………... [2]

9 Solve the inequality 6 3 17 32 4xx x− ≤−<− . Show your solution on the number line below. 6 3 17 32 4 3 17 6 3 17 32 4 1572 1572 xx x xx x x xx x − ≤−<− −≥ − −<− ≥< ≤< Answer [1] Answer ………………………………... [2] 7

10 The cash price of a refrigerator is $2499. The hire-purchase price of the refrigerator is $2999. The hire-purchase price is a deposit of 25% of the cash price plus 24 equal monthly payments. Calculate one monthly payment. ( )( )Remaining amount = 2999 2499 0.25 2374.25 2374.25Monthly Instalment = 98.9324 −= = Answer $ ……………………………... [2]

11 Michael deposited some money into bank A which pays a simple interest rate of 3% per annum for 18 months. If he had deposited the same amount of money with bank B, which pays a simple interest rate of 2.5% per annum for 24 months, he would receive $500 more in interest. (a) Find the amount of money he deposited. ( )( ) ( )( )2.5 2 3 1.5 500100 100 100000 PP P −= = (b) Find the amount of interest Michael would receive if he were to deposit his money into bank C which pays a compound interest of 1.9% per annum compounded every 6 months for 24 months. 4 1.9100000 1 200 103854.49 3854.49 A I = +  = = Answer $ ………………………………... [2] Answer $ ………………………………... [2]