2023 S4NA Prelim MA PresHigh P1 MS

Name: Register Number: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4045/01 PAPER 1 31 July 2023 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 PRESBYTERI AN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2023 SECONDARY FOUR NORMAL PRELIMINARY EXAMINATION MARK SCHEME

Answer all the questions. 1 65% 5  0.6 0.4 5 8 Write these numbers in order of size, starting with the smallest. [2] 0.6, 5 8 , 5  , 0.4 , 65% B1 for any 2 correct 2 Find the smallest integer satisfying 4 75x− . [2] 4 75x− 318 4x− smallest integer = –18 B1 B1 3 In a class of 40 pupils, 26 are boys. 10 of the boys wear spectacles and 7 3 of the girls wear spectacles. (a) Write the ratio boys : girls in its simplest form. [1] (b) Write the ratio boys who wear spectacles : girls who wear spectacles in its simplest form. [1] boys : girls 13 : 7 B1 boys wear spec: girls wear spec 10 : 6 5 : 3 B1

4 The graph shows the number of points collected by a football team for the football league seasons in 2021 and 2022 respectively. State one feature of the graph that may be misleading and explain why. [2] Answer The vertical axis does not start from zero. It makes the difference in values on the vertical axis exaggerated./ It looks like the points collected in 2021 is triple of those collected in 2022. B1 B1 5 James bought 24 Snickers, 60 Mars and 72 M&M chocolates. If each type of chocolate is distributed equally into a number of party goodie bags, what is the greatest number of goodie bags that can be prepared? [2] 324 2 3= 260 2 3 5=   3272 2 3= 2HCF 2 3 12 bags = = B1 for any 2 prime factorisation B1 2021 2022 64 62 60 58 56 54 52 50 Points

6 Draw an enlargement of the figure using a scale factor of 3 2 . [2] 7 Figure PQRS is similar to figure ABCD. All the lengths are in centimetres. Find the value of x. [2] 21 15 10 15 210 14 BC CD QR RS x x x = = = = M1 A1 B A D C P Q R S 15 10 21 x 18

8 Given that sin y o = 0.65, find the two possible values of y. [2] 40.5416 or 180 40.5416 40.5 or 139.5 y=  −  =   B1, B1 9 The first 5 terms of a sequence are 16, 13, 10, 7, 4. (a) Write down the next two terms. [1] (b) Find an expression for the nth term of this sequence. [1] 1, –2 B1 19 3 n− B1

10 A group of students were asked to vote for their favourite T-shirt colour. The results are shown in the accurate pie chart below. The number of students who chose blue is 12 more than the number of students who chose red. Find the total number of students in the group. [3] blue 150= , red 120= 30 rep 12 students 360360 rep 12 30 144 students    = B1 for difference in angles M1 A1 Blue Red White

11 Mark’s monthly salary is $3100. In a particular month, he spent 3 10 of his salary on food, gave $150 to his parents and saved 20% of his salary. He spent the rest of his salary on outings with his friends. Mark told his friends that he spent more than 48% of his salary on outings with his friends. Is his statement correct? Justify your answer with working. [3] 3food 3100 $93010=  = 20saving 3100 $620100=  = outing 3100 620 930 150 1400= − − − = 1400% spent on outing 1003100 45.16129 45.2% = = = His statement is incorrect since 45.2% < 48%. M1 for food/ saving M1 A1 12 Given 24Q m n=− , (a) find Q when m = 3 and n = – 5, [1] (b) rearrange the formula to make m the subject. [2] 41 B1 2 2 2 4 4 4 4 Q m n m Q n Qnm Qnm =− =+ += += M1 A1

13 A heptagon has 4 interior angles that are o80 each while the remaining interior angles are o(2 5)x− , o( 30)x+ and o(3 60)x+ . Find the value of x. [2] ( ) ( ) ( ) ( ) ( )4 80 2 5 30 3 60 7 2 180 6 405 900 82.5 x x x x x + − + + + + = − += = B1 for sum of int angles A1 14 Ben invested $5000 in an account earning compound interest of r% per year. At the end of 3 years, the total amount in the account is $5329.48. Calculate r. [3] 3 3 3 3 3 5000 1 5329.48100 5329.481 100 5000 5329.481 100 5000 5329.48 1100 5000 5329.48 1 1005000 2.149978 2.15 r r r r r += += += =− = −  = = M1 M1 A1

15 M is the point of intersection of the bisector of angle BCA and the perpendicular bisector of AC. (a) By using construction, find and label M. [2] (b) Measure AM. [1] Correct perpendicular bisector/ correct angle bisector Correct location of M B1 B1 5.1 cm (range: 5.0 to 5.2 cm) B1 A B C

16 (a) Factorise 241y − . [1] (b) Hence, or otherwise, express 2 16 4 1 2 1yy +−+ as a single fraction. [3] ( )( )2 1 2 1yy+− B1 ( )( ) ( ) ( )( ) ( )( ) ( )( ) 6 2 11 2 1 2 1 2 1 2 1 1 12 6 2 1 2 1 12 5 2 1 2 1 y y y y y y yy y yy −++ − + − +−= +− −= +− M1 for LCM M1 A1