Greenridge Sec 2024 4NA MA Prelims P1-vetted

[Turn over This paper consists of 14 printed pages, including this cover page. GREENRIDGE SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY 4 NORMAL (ACADEMIC) CANDIDATE NAME CLASS - INDEX NUMBER MATHEMATICS SYLLABUS A 4045/01 Paper 1 5 August 2024 Setter: Mrs Goh-Kok Mei Leng 2 hours Candidates answer on the Question Paper. Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. 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 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. For Examiner’s Use Total 70

2 Mathematical Formulae Compound interest Total amount = n rP       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 [Turn over Answer all the questions. 1 It is given that 78.9 24.05 7.85 m  . (a) Without the use of a calculator, estimate the value of m. Show your working clearly. Answer …………...………………… [1] (b) Use your calculator to find the value of m, leaving your answer to 2 decimal places. Answer …………...………………… [1] 2 The weight of a golf ball is 0.0459368 kg. (a) Write this weight correct to 3 significant figures. Answer …………...………………… [1] (b) Write your answer in part (a) in standard form. Answer …………...………………… [1] 3 Find the least integer value of x satisfying 5 21x .

4 Answer …………...………………… [2] 4 3, 8, 13, 18, 23, … (a) Find an algebraic expression for the nth term in the sequence. Answer …………...………………… [1] (b) Show that 403 is a term in the sequence. Answer [2] 5 (a) Find the obtuse angle of A such that sin 0.8667A . Answer A = ……...…………..…….. [1] (b) Write the following in order of size, starting with the smallest. 32.5% 0.3255 0.32  64 625

5 [Turn over Answer ………… , ...……..… ,.. .……… , ……………… smallest [2] 6 (a) Write 4255 5  as a single power of 5. Answer …………...………………… [2] (b) Given that 1 232 m , find the value of m. Answer m = ……...………………… [1] 7 Factorise (a) 2 6 3ap bp aq bq   , Answer …………...………….……... [2] (b) 22 10xx .

6 Answer …………...………….……... [1] 8 In a sale, the price of a watch was reduced by 30% of its original price to $385. Find the original price of the watch. Answer $ ….………...………….… [2] 9 Draw a reduction of this quadrilateral using the scale factor of 1 2 . [2] 10 If Jenny buys x kg of sugar at the price of 99 cents, how much will y kg of sugar cost in dollars? Express your answer in terms of x and y.

7 [Turn over Answer $ ………...………………… [2] 11 Quadrilateral WXYZ is a reduction of quadrilateral EFGH. XW = 3 cm, EF = 6 cm and EH = 8.6 cm. Angle ο60FEH , angle 130 FGH and angle 90WZY . Find (a) the scale factor, Answer …………...………………… [1] (b) WZ, Answer WZ = …………...……. cm [1] (c) Angle WXY . Answer Angle WXY = ...…………… [1] 12 Tim scored 16 out of 20 marks in Test A and 49 out of 56 marks in Test B. In which test did Tim do better? Justify your answer. Answer E F G H W Z Y X 3 cm 6 cm 8.6 cm 60 130

8 [2] 13 Solve these simultaneous equations. 5 2 16 37 xy xy    Answer x …….… , y = ……… [3] 14 Three bells ring every 15 minutes, 21 minutes and 25 minutes respectively. (a) Given that they rang together at 08 30, when will they next ring together again? Answer …………...………………… [2] (b) How many times will they ring together over a period of 19 hours?

9 [Turn over Answer …………...………………… [1] 15 (a) Express 2 62xx in the form 2()x a b . Answer …………...………………… [1] (b) Hence solve 2 6 2 0xx   . Answer …………...………………… [3] 16 p is inversely proportional to the square of x. When x = 3, p = 20. (a) Show that 2 180p x . Answer [2] (b) Find the values of x when p = 7.2.

10 Answer x = …………. or ………….. [2] 17 (a) Show that the point (1, 2) lies on the line 3 2 4yx . Answer [1] (b) Find the coordinates of the y-intercept of the line 3 2 4yx Answer ( ……..….. , ……….…... ) [1] 18 (a) The ratio of Peter’s age to his father’s age is 2 : 7. Peter is 14 years old now. How old is his father? Answer …………...………………… [1] (b) The ratio of George’s age to his mother’s age is 3 : 8. The total of their ages is 66 years. (i) How old is George? Answer …………...………………… [2]