2023 S4NA Prelim MA Preshigh P1 QP

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 PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2023 SECONDARY FOUR NORMAL PRELIMINARY EXAMINATION DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. INSTRUCTIONS TO CANDIDATES: Write your nam e, index number and class on the spaces provided abov e. Write in dark blue or black pen. You may use a n HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 70. 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 , use either your calculator value or 3.142, unless the question requires the answer in terms of . Note that all the diagrams in this paper are not drawn to scale. For Examiner’s Use Category Accuracy Symbols Others Marks Deducted Question No. Setter: Mrs Joyce Yeo Vetter: Mr Tan Chee Wee This paper consists of 17 printed pages (including this cover page) and 1 blank page. TOTAL MARKS 70

2 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard deviation = 22      −     f fx f fx

3 s 1 65% 5  0.6 0.4 5 8 Write these numbers in order of size, starting with the smallest. Answer …………. , …………. , …………., …………., …………. [2] smallest 2 Find the smallest integer satisfying 4 75x− . Answer ……………………… [2] 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. Answer ………… : ………… [1] (b) Write the ratio boys who wear spectacles : girls who wear spectacles in its simplest form. Answer ………… : ………… [1]

4 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. Answer ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………[2] 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? Answer ……………………bags [2] 2021 2022 64 62 60 58 56 54 52 50 Points

5 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. Answer x = ………………… [2] B A D C P Q R S 15 10 21 x 18

6 8 Given that sin y o = 0.65, find the two possible values of y. Answer y = ….……… or ………… [2] 9 The first 5 terms of a sequence are 16, 13, 10, 7, 4. (a) Write down the next two terms. Answer ………… , ………… [1] (b) Find an expression for the nth term of this sequence. Answer ……………………… [1]

7 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. Answer ……………………… [3] Blue Red White

8 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 s alary on outings with his friends. Is his statement correct? Justify your answer with working. Answer [3] 12 Given 24Q m n=− , (a) find Q when m = 3 and n = – 5, Answer Q = ….……………… [1] (b) rearrange the formula to make m the subject. Answer m = ….……………… [2]

9 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. Answer x = ….……………… [2] 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. Answer r = ….……………… [3]

10 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. Answer ….……………… cm [1] A B C