2023 Greendale 4NA Prelim P2

Name: ___________________________________ ( ) Class: __________. This document consists of 19 printed pages. Greendale Secondary School 2023 GREENDALE SECONDARY SCHOOL Preliminary Examination 2023 Mathematics Syllabus A 4045/02 Paper 2 15 August 2023 Secondary 4 Normal Academic 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name in the spaces at the 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. Section A Answer all the questions. Section B Answer one question. 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 number of 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 π , use either your calculator value or 3.142. Qn Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9a,b Q9c Q10 Q11 a Q11 b Q12 Strand Marks 70

Greendale Secondary School 2 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curve surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 – 2bc cos A Statistics Mean = ∑ ∑ f fx Standard deviation = 22       − ∑ ∑ ∑ ∑ f fx f fx

Greendale Secondary School 3 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 Section A (62 marks) Answer all questions in this section. 1 The diagram shows part of a n-sided regular polygon A. B is a regular hexagon and C is a square. Find n. Answer n = ..………………………… [4] B C C A

Greendale Secondary School 4 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 2 The heights of a group of 14 students were measured. The results are shown in the stem-and-leaf diagram. 15 6 16 0 2 4 7 8 17 1 2 2 4 8 18 1 3 19 0 Key 16|2 means 162 cm (a) Find the (i) range of the heights, Answer ……………………………cm [1] (ii) median height. Answer ……………………………cm [1] (b) A new student, John, joined the group and his height was measured and added to the data. As a result, his height would increase the range by 1 cm but decrease the median. What is John’s height? Answer ……………………………cm [1]

Greendale Secondary School 5 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 3 The diagram shows the cross-section of a hemispherical bowl of radius 15 cm with a divider in the middle. Water is poured into the left side of the bowl so that only half of the hemispherical bowl is completely filled with water. Find the area of the water in contact with the bowl and the divider. Answer ……………………… cm 2 [4] 15 cm

Greendale Secondary School 6 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 4 (a) Calculate 22( 6) 4( 7)− +− . Answer …………………………… [1] (b) Write the following numbers in order of size, largest first. 223.2, , , 3.1427 π−−  Answer ……… , ……… , ……… , ……… [2] largest smallest (c) The Mariana ocean trench, the world’s deepest ocean trench, has an approximate depth of 10 994 m, while the Hikurangi ocean trench has an approximate depth of 3 750 m. (i) Write 10 994 in standard form. Answer …………………………… [1] (ii) Find the difference in depth between the two ocean trenches. Give your answer in standard form. Answer ……………………… m [2]

Greendale Secondary School 7 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 5 (a) Map A is drawn to a scale of 1: 200 000 . (i) The length of a cycling path measures 3.5 km. Calculate the length of the cycling path on the map in centimetres. Answer ………………………… cm [2] (ii) The area of a forest measures 8 cm2 on the map. Calculate the actual area of the forest in square kilometres. Answer ………………………… km2 [3] (b) The actual distance representing a length on the map is 20% shorter on Map B. State the map scale of Map B in terms 1 : n. Answer 1: ……………… [1]

Greendale Secondary School 8 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 6 A is the point (−2, −2) and B is the point (6, 2). (a) Find the equation of the line AB. Answer …………………………… [1] (b) Draw the line y = 3. [1] (c) X is the point of intersection of the line AB and y = 3. (i) Write down the coordinates of X. Answer (……………, ……………) [1] (ii) Calculate the length of AX. Answer AX = ……………………… units [1] (d) C is the point (8, −2). ABCD is a rectangle. (i) Find the coordinates of D. Answer (……………, ……………) [1] (ii) Calculate the area of ABCD. Answer ………………………… square units [1] 0 y x x −1 1 −1 −2 −3 −3 3 2 2 3 1 4 5 6 8 9 7 −2 x A B

Greendale Secondary School 9 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 7 Lim runs from the park back home. The distance-time graph shows his journey. He met a friend on his way home and stopped to talk. (a) Find the number of minutes he stopped for. Answer ……………………… minutes [1] (b) Find the average speed of Lim for his whole journey in km/h. Answer ……………………… km/h [3] (c) Lim’s brother, Mark, leaves home at 0934 and runs at a constant speed to the park. He takes 25 minutes to reach the park. Complete the grid to show Mark’s journey. [1] (d) Find the distance Mark is away from the park when he passes Lim. Answer ………………………. m [1] Distance (m) Time 0 2400 3200 4000 1600 800 0950 0955 0940 0935 0930 0945 1000 Park Home

Greendale Secondary School 10 Secondary 4 Normal Academic Preliminary Examination 2023 Mathematics Paper 2 8 (a) Complete the table of values of 23y x= + . x 0.5 1 1.5 2 2.5 3 3.5 4 y 7 5 4.3 4 3.7 3.6 [2] (b) On the grid, plot the graph of 23y x= + for 0.5 4 x≤≤ . [3] (c) Use the graph to find the value of x when 5.6y= . Answer x = ……………… [1] 0 0.5 4 1 3.5 3 2.5 2 12 10 8 6 y 4 2 x 1.5