2023 S4NA Prelim MA P2 MS

Name: Register Number: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4045/02 PAPER 2 1 August 2023 Tuesday 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 PRESBYTERI AN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2023 SECONDARY FOUR NORMAL (ACADEMIC) PRELIMINARY EXAMINATION MARK SCHEME

Section A (62 marks) Answer all the questions in this section. 1 (a) Work out (i) 2212 ( 9) ( 6)− − − − , [1] (ii) 292.195.17 2031.0 3 + . [1] (b) (i) Write 29.951 correct to 3 significant figures. [1] (ii) Write 4.523 million to the nearest ten thousand. [1] 18.5 B1 0.0519 B1 0.00201 B1 4520000 B1 2 (a) Given that 1 3 43 81 3 m= , find the value of m. [2] (b) Simplify 7 3 9a a . [2] ( ) 1 3 4 1 34 4 31 4 3 81 3 3 3 3 3 3 3 33 4 m m m m m = = = = = M1: 481 3= A1 ( ) 1 77 2 33 1 4 2 2 99 9 3 aa aa a a = = = M1: 4a /fractional indices A1

3 (a) p is directly proportional to q3. Given that p = 24 when q = 2, find (i) the formula connecting p and q. [2] (ii) the value of q when p = 192. [1] (b) 5 men can paint a house in 6 days. The house was painted in n days. Write down an expression, in terms of n, for the number of men needed to paint the house. [2] ( ) 3 3 24 2 3 p kq k k = = = Eqn is 33pq= M1 for finding constant A1 3 3 192 3 64 3 4 q q q = = = B1 1 man takes 30 days 30 d s requir ney sae mn n M1 A1

4 (a) Find 130% of 2 litres in millilitres. [1] (b) A map is drawn to a scale of 1 : 50000. (i) The perimeter of a reservoir on the map is 22.8 cm. Find the actual perimeter, in kilometres, of the reservoir. [2] (ii) The actual area of a plantation is 46 km2. Calculate the area, in square centimetres , of the plantation on the map. [2] 2600ml B1 1 cm : 50000cm 1 cm : 0.5 km actual perimeter 0.5 22.8 11.4 km = = M1 A1 ( ) ( ) 22 22 1 cm : 0.5 km 1 cm : 0.25 km 2 46map area 0.25 184 cm = = M1: area scale A1

5 The diagram shows the speed-time graph of a particle over a period of 60 seconds. (a) Describe what is happening between t = 20 and t = 60. [1] (b) Calculate the acceleration of the particle in the first 20 seconds. [1] (c) Calculate the speed of the particle at t = 45. [2] (d) The area under the graph represents the total distance travelled. Calculate the total distance travelled by the particle. [2] The particle is decelerating. B1 2 24 16acceleration 20 0.4 m/s −= = B1 15 24 40 15 2440 9 m/s v v = = = M1 A1 ( )( ) ( )( )11total distance 16 24 20 40 2422 880 m = + + = M1: area of triangle/ trapezium A1 Speed (v) in m/s Time (t) in seconds 0 16 24 20 60

6 In the diagram, angle AEC = angle ACB = angle CAD = 90  . Angle EAC = 55 , AC = 4.1 cm and CD = 5.4 cm. Calculate (a) the length of AD, [2] (b) the length of AB, [2] (c) the angle ADC. [2] 225.4 4.1 3.51425 3.51 cm AD=− = = M1 A1 4.1cos 55 4.1 cos 55 7.1481 7.15 cm AB AB = =  = = M1 A1 1 4.1sin 5.4 4.1sin 5.4 49.3989 49.4 ADC ADC − = =  = = M1 A1 D A E C 4.1 5.4 B

7 The table shows the number of times students of a class were late for school in a month. Number of times 0 1 2 3 4 Number of students 6 12 3 8 p (a) State the largest value of p if the mode is 1. [1] (b) Find the value of p if the probability of choosing a student who was late more than 2 times is 0.5. [2] (c) It is given that p = 11. (i) Find the mean. [2] (ii) A student’s record was left out of the table. This student was late 3 times in a month. The table is now updated to include this student’s record. Without calculation, explain how the mean will be affected. [1] 11 B1 ( ) 81 29 2 2 8 29 16 2 29 13 p p pp pp p + =+ + = + + = + = M1 A1 ( ) ( ) ( ) ( ) ( )0 6 1 12 2 3 3 8 4 11mean 40 86 40 2.15 + + + += = = M1 A1 The mean will increase as the student’s record of 3 times is more than the mean. B1

8 (a) Lightning strikes the earth approximately 1.4 billion times per year. (i) Write 1.4 billion in standard form. [1] (ii) Calculate the average number of times the lightning strikes the earth in a day, assuming there are 365 days in a year. Write your answer in standard form, correct to 3 significant figures. [2] (b) Solve the simultaneous equations. [3] 5 2 16 37 xy xy −= + =− (c) Solve 0153 2 =−− xx . Give your answers correct to 2 decimal places. [3] 91.4 10 B1 9 6 1.4 10 365 3.84 10  = M1 A1 ( ) ( ) ( ) ( ) 2 : 7 3 3 subs 3 into 1 xy=− − ( )5 7 3 2 16 35 15 2 16 17 51 3 yy yy y y − − − = − − − = −= =− ( )7 3 3 2x=− − − = M1 A1 A1 ( ) ( ) ( )( ) ( ) 2 5 5 4 3 1 23 1.8471 or 0.18046 1.85 or 0.18 x x − −  − − −= =− =− M1 A1, A1

9 (a) Complete the table of values for 3 9y x x=− . [2] x –3 –2 –1.5 –1 0 1 1.5 2 3 4 y 0 10 8 0 –8 –10.125 0 28 (b) On the gri