SHSS 2022 MA S4E5N Prelim QP P1

This question paper consists of 20 printed pages including the cover page. [Turn Over Name: Class: Index Number: ST. HILDA’S SECONDARY SCHOOL 2, TAMPINES STREET 82, SINGAPORE 528986, TEL: 6305 5277 FAX: 6786 5011 ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL ST. HILDA’S SECONDARY SCHOOL PRELIMINARY EXAMINATION 2022 Mathematics 4048/01 Paper 1 Date of Exam: 24 August 2022 Level: Secondary 4 Express & 5 Normal Academic Duration: 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class register number and class 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 questions. 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 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 . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 80. Set by: Mrs Diane Ang Checked by: Mr Clarence Lim For Examiner’s Use Total 80

2 2022/Prelim/4Exp5NA/Mathematics/4048/01 Mathematical Formulae Compound interest Total amount = P 1+ r 100 æ èç ö ø÷ n Mensuration Curved surface area of a cone = p rl Surface area of a sphere = 4pr 2 Volume of a cone = 1 3p r 2h Volume of a sphere = 4 3 p r 3 Area of triangle ABC = 1 2 absinC Arc length = rq , where q is in radians Sector area = 1 2 r 2q , where q is in radians Trigonometry a sin A = b sin B = c sinC a2 = b2 + c2 - 2bccos A Statistics Mean = å fx å f Standard deviation = å fx 2 å f - å fx å f æ èç ö ø÷ 2

3 2022/Prelim/4Exp5NA/Mathematics/4048/01 Answer all the questions. 1 Write down a possible equation for each of the following graphs. (a) Answer ..……………………… [1] (b) Answer ..……………………… [1] 2 Simplify 2 6 3 9 p r −   . Answer ..……………………… [2] y x O −2

4 2022/Prelim/4Exp5NA/Mathematics/4048/01 3 (a) On the Venn diagram, shade the region which represents AÇ B' . [1] (b) Use set notation to describe the shaded region. Answer ..……………………… [1] 4 The highest common factor and lowest common multiple of two numbers, m and n, are 117 and 222 3 13 respectively. Given than m is an even number and m < n, find the values of m and n. Answer m = …………………… n = …………………… [2] A B

5 2022/Prelim/4Exp5NA/Mathematics/4048/01 5 Two jugs are geometrically similar. The bigger jug has a capacity of 3.2 litres and the smaller jug has a capacity of 1.35 litres. Given that the height of the larger jug is 27 cm, calculate the height of the smaller jug. Answer …………………… cm [2] 6 y is inversely proportional to nx and y is 1 16 of its original value when x is increased by 100%. Calculate the value of n. Answer n = …………………… [3]

6 2022/Prelim/4Exp5NA/Mathematics/4048/01 7 The first 4 terms of a sequence are 33, 25, 17 and 9. (a) Find an expression, in terms of n, for the nth term of the sequence. Answer ……………………… [1] (b) Explain whether −101 is a term in the sequence Answer …………………………………………………………………………………… …………………………………………………………………………………… [2] 8 A map of Singapore is drawn to the scale of 1 : n. The 12-km long Kallang-Paya Lebar Expressway (KPE) is represented by a line of length 6 cm on the map. (a) Find the value of n. Answer n = …………………… [1] (b) The area on the map that represents the Jurong Bird Park is 0.05 cm2. Calculate the actual area, in square kilometres, of the park. Answer ……………………. km2 [2]

7 2022/Prelim/4Exp5NA/Mathematics/4048/01 9 The table shows the heights of a group of 25 boys. Height h (cm) Frequency 140 150h 1 150 160h 3 160 170h 5 170 180h 14 180 190h 2 (a) Calculate an estimate for (i) the mean height of the boys, Answer …………………… cm [1] (ii) the standard deviation of their heights. Answer …………………… cm [1] (b) Find the probability of selecting a boy whose height is below 170 cm. Answer ………………………… [1] 10 DEF is a triangle. 6 2DE = − , 3 .7DF −=  Calculate the length of EF. Answer …………………… units [3]

8 2022/Prelim/4Exp5NA/Mathematics/4048/01 11 (a) Simplify 3(2 ) 5( 2 )b d b d+ − − . Answer ………………………… [1] (b) Write as a single fraction in its simplest form 2 41 (5 3 ) 5 3xx −−− . Answer ..……………………… [2] 12 (a) Express 2 67xx −+ in the form ( ) 2 x p q++ . Answer ……………………… [2] (b) Write down the coordinates of the minimum point of the graph of 2 67y x x= − + . Answer ( ………… , ………… ) [1]

9 2022/Prelim/4Exp5NA/Mathematics/4048/01 13 The times taken, in minutes, for 30 students to complete a Mathematics assignment were recorded. The results are shown in the stem-and-leaf diagram. Stem Leaf 1 2 5 5 6 8 8 2 0 p 4 5 5 8 9 3 0 0 2 3 3 4 6 9 4 2 5 5 7 7 7 8 5 2 4 Key: 1|2 represents 12 minutes (a) Write down the median time taken. Answer …………………… minutes [1] (b) The interquartile range of the times is 22 minutes. Find p. Answer p = …………………… [2]

10 2022/Prelim/4Exp5NA/Mathematics/4048/01 14 The diagram represents a plot of land, WXYZ, which is used for a garden. (a) Construct the perpendicular bisector of WX. [1] (b) Construct the angle bisector of XYZ. [1] (c) A fountain F is to be built in the garden, nearer to W than to X and nearer to YZ than to XY. Shade the region where the fountain is to be built. [1] X Y W Z