Canberra EM 2024 Prelims Paper 1 QP

CANBERRA SECONDARY SCHOOL 2024 Preliminary Examination Secondary Four Express/Five Normal Academic MATHEMATICS 20 Aug 2024 4052/01 2 hours 15 minutes 1130h – 1345h Name: ______________________________________ ( ) Class: ________ READ THESE INSTRUCTIONS FIRST Write your full name, class and index number on all work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the 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. Calculators should be used 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 90. This question paper consists of 21 printed pages including the cover page. Setter: Mr Ng Chuen Joo FOR MARKER’S USE Marks Awarded Max Marks Total 90 O

2 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic Mathematical Formulae Compound interest Total amount = 1 100 n rP+ Mensuration Curved Surface area of a cone = rl Curved surface area of a sphere = 24 r Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector Area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean fx f =  Standard deviation = 22fx fx ff  − 

3 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic Answer all the questions. 1 Solve 19 252 x−= . Answer x = [1] 2 Ahmad, Simon and Bala share a sum of money in the ratio 3 : 2 : 5. If Bala has $900 more than Simon, what is the sum of money being shared by the three of them? Answer $ [2] 3 Write as a single fraction in its simplest form 32 2 1 1 2aa −−− . Answer [2] [Turn Over

4 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 4 Five positive integers have a mean of 5, median of 4, mode of 3 and a range of 7. Find the five numbers. Answer [2] 5 (a) On the Venn diagram, shade the region that represents AB . (b) Use set notation to describe the shaded region. [1] Answer [1] A B A B

5 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 6 The quadratic curve 2 4 21y x x= + − can be written as ( )( )y x a x b= − + . (a) Find the value of a and the value of b, where a and b are positive integers. Answer a = [1] b = [1] (b) Explain why y will not have a value smaller than 25− . Answer [1] 7 (a) Expand and simplify ( )( )3x y y x−+ . Answer [2] (b) Factorise completely 23 12 a− . Answer [2] [Turn Over

6 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 8 (a) Given that 3 1xa a a  = , find the value of x. Answer [1] (b) Simplify 2 4 2 x −  , giving your answer in positive index. Answer [2] 9 (a) 2 10 27xx−+ can be expressed in the form ( ) 2 x p q++ . Find the value of p and the value of q. Answer p = [1] q = [1] (b) Hence write down the coordinates of the minimum point of the graph of 2 10 27y x x= − + . Answer ( , ) [1]

7 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 10 In the diagram, O is the centre of the circle and ABCD is a cyclic quadrilateral. Angle AOB = angle ADC 70= . Explain why triangle ABC is an isosceles triangle. Give reasons for each step of your working. [3] 70° O 70° B C D [Turn Over A

8 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 11 (a) The angles of a quadrilateral taken in order are 3x, 6x, 5x and 4x. Find the value of x. Answer x = [1] (b) Explain whether the quadrilateral is a parallelogram or a trapezium. because [2]

9 Canberra Secondary School Mathematics 4052/01 2024 Preliminary Examination Secondary 4 Express / 5 Normal Academic 12 13 A square pyramid P has base with side x m, height y m and a volume of 300 3m. Find (a) the volume of a similar square pyramid, which has a height double that of the pyramid P. Answer 3m (b) the volume of another square pyramid with side 3x m and height 2 3 y m. Answer 3m The following stem-and-leaf diagram shows the scores of students in a math test. Stem Leaf 6 8 9 7 0 2 3 3 4 4 4 7 8 8 3 4 5 6 7 7 9 9 1 3 7 Find (a) the median score, Answer (b) the interquartile range. Answer [1] [2] [1] [2] 6 8 represents 68 marks [Turn Over

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