KSS 2021 P1 (QP)

Name: ___________________________( ) Class: ______ KRANJI SECONDARY SCHOOL Preliminary Examination Secondary 4 Normal (Academic) MATHEMATICS 4045/01 PAPER 1 Wednesday 28 July 2021 2 hours KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI READ THESE INSTRUCTIONS FIRST Write your class, index number and name in the spaces on top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all 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 80. 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 your answers in degrees to one decimal place. For 𝜋, use either your calculator value or 3.142. Setter : Mrs Lee Siew Ling This question paper consists of 20 printed pages, including the cover page. [Turn over FR2 For Examiner’s Use Total 80

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = prl Surface area of a sphere = 4pr2 Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = rq , where q is in radians Sector area = , where q is in radians Trigonometry Statistics Mean = Standard deviation = n rP ÷ ø öç è æ+1001 hr2 3 1p 3 3 4rp Cabsin 2 1 q2 2 1r C c B b A a sinsinsin == Abccba cos2222 -+= å å f fx 22 ÷÷ ø ö çç è æ - å å å å f fx f fx

3 1 By writing each number correct to 1 significant figure, estimate the value of . Answer .……………………………. [2] ______________________________________________________________________________________ 2 Find the smallest prime number x satisfying > 10. Answer x = …………………………. [2] _______________________________________________________________________________________ 3 The line crosses the y-axis at the point A. Find (a) the coordinates of the point A, Answer (…….……… , ……..…….) [1] (b) the gradient of the line. Answer .……………………………. [1] _______________________________________________________________________________________ 4.26 8.53 97.1 ´ 23x+ 32 8xy+=

4 4 A sum of money was divided among Andy, Ben and Charles in the ratio 3 : 4 : 5. If the sum of money had been divided equally among the 3 boys, Andy would have received an extra $30. Find the sum of money. Answer $……………………..……. [2] ______________________________________________________________________________________ 5 Simplify . Give your answer as a single fraction in its simplest form. Answer ……………………………. [2] _______________________________________________________________________________________ 4 32 35 5 12 6 pr r pp q÷

5 (Sec 4 Topic) 6 The diagram shows a circle, centre O and radius 15 cm. A and B are points on the circumference and angle AOB = 110°. Find the perimeter of the major sector. Leave your answer in the simplest form in terms of π. Answer ………………………… cm [2] _______________________________________________________________________________________ O A B 110º 15

6 7 In the diagram, ABCD is a square of sides 30 cm. The ratio of the length of CM to MD is 1 : 2 and angle MAD = angle CMN. (a) Find the exact value of tanMAD. Answer ….…………………………. [1] (b) Hence or otherwise, find the length of CN. Answer ….………………………cm [2] _______________________________________________________________________________________ 8 Write these numbers in order, starting with the smallest. -3 3.03 Answer ……….…. , …….……. , …….……. , ……….…. [1] _______________________________________________________________________________________ Ð 13 3- 133 smallest t B C D M N 30 A

7 9 The line graph shows the prices of petrol in the last 6 months of 2018. (a) Between which two months did the price of petrol have the greatest decrease? Answer ……………….…… and ……………………. [1] (b) Find the percentage increase in the price of the petrol from August to September. Answer .………………………….% [2] _______________________________________________________________________________________ Month Price of 1 litre of petrol

8 10 (a) On the grid below, draw a reduction of figure PQRST using a scale factor of . [1] (b) ABC and ECD are similar triangles with all the lengths given in centimetres. (i) ∆ECD is an enlargement of ∆ABC. Find the scale factor. Answer ….…………………………. [1] 23 A B C D E 10 4 y 18 22

9 (ii) Find y. Answer y = ………………………cm [1] _______________________________________________________________________________________ 11 (a) Simplify . Answer ………………………………. [1] (b) Simplify . Answer ……………………………. [2] _______________________________________________________________________________________ 41 036yx y x-- + 25 3 25 xx--

10 12 A number of students were asked to name their favourite subject. The results of the survey is shown in the pie chart. One sixth of the students chose Science. 45 students chose Mathematics. (a) How many students chose Science? Answer ………………………………. [1] (b) How many students chose English? Answer ………………………………. [2] ______________________________________________________________________________________ 180º Mathematics 2qº qº pº History Science English