PHS 2022 S4NA Prelim MA P1 MS

Name: Index No.: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4045/01 PAPER ONE 25 July 2022 Monday 2 hours PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL SECONDARY FOUR NORMAL (ACADEMIC) PRELIMINARY EXAMINATIONS MARK SCHEME

2 Presbyterian High School 4045/01/4NA Prelim/2022 Answer all the questions. 1 (a) 2 11.75 1.3 1 3−− Write these numbers in order of size, starting with the smallest. Answer 211 , 1.3,1.75 ,3 −− [B1] [1] (b) Express 73.4% as a fraction. 73.4 367 100 500= Answer 367 500 [B1] [1] 2 Adult Child (Ages 4 – 12) One-Day Admission Ticket $68 $58 Universal Express Pass $50 $50 (Source: www.rwsentosa.com) The table shows the cost for one-day admission ticket to Universal Studio. The Universal Express Pass can be purchased to skip the queue at participating rides and shows. Mr and Mrs Teo bought one -day admission tickets for themselves and their son (12 years old) and daughter (13 years old). They also bought Universal Express Passes for each of their two children. Calculate the total cost of the tickets. ( ) ( )cost = 68 3 58 50 2 [M1 - cost of admission tic kets/ cost of universal pass] 362  + +  = Answer $ 362 [A1] [2] 3 Solve 4 352x =− . ( ) 4 352 3 5 2 4 [M1] 15 6 4 15 10 2 3 x x x x x =− −= −= = = Answer x = 2 3 [A1] [2]

3 Presbyterian High School 4045/01/4NA Prelim/2022 [Turn over 4 The diagram shows a regular octagon ABCDEFGH. Calculate y. ( )8 2 180each int = 135 [M1 either]8 180 135 22.52y −   =  − − = =  Answer y = 22.5 [A1] [2] 5 p is inversely proportional to q2. When p = 3 when q = 2. Find the value of p when q = 10. 2 2 2 3 [M1] 2 12 12 3 or 0.122510 kp q k k p = = = == Answer p = 3 25 or 0.12 [A1] [2] 6 (a) Given that 6 30 5 5 55 v − =  , find v. ( ) 6 30 63 9 5 5 55 55 55 v v v − −− =  = = Answer v = 9 [B1] [1] (b) Given that 1 464 w= , find w. 3 3 1 464 1 4 4 44 3 w w w w − = = = =− Answer w = – 3 [B1] [1] A B C D E F G H yo

4 Presbyterian High School 4045/01/4NA Prelim/2022 7 (a) The diagram shows the sketch of 2y x k=− + . State a possible value of k. Answer k = 1 [B1] [1] [Accept any value above 0] (b) State the equation of the line of symmetry of this graph of a quadratic function. 37 2 2 x x −+= = Answer 2x= [B1] [1] 0 y x –21 y x –3 7

5 Presbyterian High School 4045/01/4NA Prelim/2022 [Turn over 8 In the diagram, AB is parallel to CD and EF. Angle 40ABC= and angle 135CEF = . Calculate angle BCE . ( ) ( ) 40 alt , / / 180 135 45 int , / / 40 45 85 BCD AB CD DCE CD EF BCD  =    = − =    = + =  [M1 – int angle] Answer 85 [A1] [2] 9 (a) sin 0.6m= Given that m is an obtuse angle, find m. ( )1180 sin 0.6 143.13 m −= − = Answer m = 143.1 [B1] [1] (b) cos 133 cos n=−  Given that n is an acute angle, find n. 180 133 47 m= −  = Answer n = 47 [B1] [1] 40o 135o A B C D E F

6 Presbyterian High School 4045/01/4NA Prelim/2022 10 On the grid below, draw a reduction of figure P using a scale factor of 1 3 . P [B2 – 4 correct sides, B1 – 2 correct sides] [2] 11 A car is travelling at a constant speed of 90 km/h. (a) How many minutes does the car take to travel 105 km? 105time [M1]90 7 h6 = 70 min = = Answer 70 minutes [A1] [2] (b) Convert 90 km/h to m/s. 90 1000 251 3600  = Answer 25 m/s [B1] [1]

7 Presbyterian High School 4045/01/4NA Prelim/2022 [Turn over 12 In 2021, Jane’s annual salary was $22 140. This was an increase of 2.5% on her annual salary in 2020. (a) Calculate her annual salary in 2020. 22140annual salary 100% [M1]102.5 21600 = = Answer $ 21 600 [A1] [2] (b) The income tax rates for 2021 were: Chargeable Income Income Tax Rate (%) Gross Tax Payable ($) First $20 000 0 0 Next $10 000 2 200 (Source: www.iras.gov.sg) Calculate the amount of income tax she paid in 2021. tax payable 2140 2% $42.80 = = Answer $ 42.80 [B1] [1] 13 Express 2 51 39 xx + +− as a single fraction, in its simplest form. ( )( ) ( )( ) ( )( ) ( ) ( )( ) ( )( ) ( )( ) 2 2 5 1 5 1 [M1 - 9 3 3 ]3 3 3 39 135 [M1 - common denominator]3 3 3 3 53 33 2 33 x x xx x x xx x x x x x x xx x xx + = + − = + −+ + − +− −=+ + − + − +−= +− += +− Answer ( )( ) 2 33 x xx + +− [A1] [3]

8 Presbyterian High School 4045/01/4NA Prelim/2022 14 ABCD is a quadrilateral and E is a point on AD. BC = CD and BE is parallel to CD. Angle 124ABC = , angle 110BCD= and angle angle 85CDA= . (a) Find angle BAD . 360 110 85 124 41 BAD = − − −  = Answer 41 [B1] [1] (b) Find angle BDE . 180 110 35 [M1]2 85 35 50 CDB BDE −  = =   = − =  Answer 50 [A1] [2] 15 (a) Jerry deposits $60 500 in a bank at 1.2% per annum interest for 3 years. Calculate the simple interest earned for 3 years. 60500 1.2 3interest 100 2178 = = Answer $ 2178 [B1] [1] (b) Tom invests $12 000 for 4 years. He receives compound interest at 1.15% per year. How much is the investment worth at the end of the four years? Give your answer to the nearest cent. 4 1.15Amt 12000 1 [M1]100 12561.595 =+  = Answer $ 12561.60 [A1] [2] A B C E D 124o 110o 85o

9 Presbyterian High School 4045/01/4NA Prelim/2022 [Turn over 16 A cone has a vertical height of 11.5 cm, radius r cm and volume 434 cm3. Calculate r. ( ) ( ) ( ) 2 2 1 11.5 434 [M1]3 434 [M1]1 11.53 434 1 11.53 6.00318 r r r    = = = = Answer r = 6.00 [A1] [3] 11.5 r

10 Presbyterian High School 4045/01/4NA Prelim/2022 17 The scale of the map is 1 : 40 000. (a) The distance between two police stations on the map is 35 cm. Find the actual distance. Give your answer in kilometres. 1cm : 40000 cm 1 cm : 0.4 km actual distance 35 0.4 [M1] 14 = = Answer 14 km [A1] [2] (b) The area of a forest has an area of 4.8 km2. Calculate the area of the forest on the map. Give your answer in cm2. ( ) ( ) ( ) 22 2 1 cm : 40000 cm 1 cm : 0.4 km [M1] 4.8area on map 0.4 30 = = Answer 30 c