2026 Canberra E-Math Paper 2

CANBERRA SECONDARY SCHOOL 2026 Preliminary Examination Secondary Four Express/Five Normal (Academic) MATHEMATICS 14 Aug 2026 4052/02 2 hours 15 minutes 0815h 1030h 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. HOM: This question paper consists of 23 printed pages including the cover page. Setter: Ms Diyanah Marks Awarded Max Marks Total 90 O www.KiasuExamPaper.com 23 www.KiasuExamPaper.com 23

2 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) Mathematical Formulae Compound interest Total amount = Mensuration Curved Surface area of a cone = Curved surface area of a sphere = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector Area = , where is in radians Trigonometry Statistics Mean Standard deviation = www.KiasuExamPaper.com 24 www.KiasuExamPaper.com 24

3 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) [Turn Over Answer all the questions. 1 (a) Simplify , giving your answer in positive index. Answer (b) Use the laws of indices to find the value of . Answer k = www.KiasuExamPaper.com 25 www.KiasuExamPaper.com 25

4 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) (c) Simplify . Answer (d) Simplify as a single fraction in its simplest form. Answer www.KiasuExamPaper.com 26 www.KiasuExamPaper.com 26

5 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) [Turn Over 2 (a) The equation of line L is . The equation of line M is , where k is a constant. Line L and line M intersect at the point (3, p) where p is a constant. Find the value of k and the value of p. Answer k p 3] (b) A is the point (4, a) where a < 0. B is the point (16, 5). The length of line AB is 15 units. Find the value of . Answer a www.KiasuExamPaper.com 27 www.KiasuExamPaper.com 27

6 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 3 A school organized a Sports and Wellness Day for their Secondary 4 students. As part of the event, students participated in a 2.4 km run. The table below summarises the times taken by the Secondary 4 boys to complete the run. (a) Given that the estimated mean time is 15.14 min, show that the value of x is 10. [2] (b) Calculate an estimate of the standard deviation. Answer (c) The mean time for Secondary 4 girls to complete the run was 15.8 min and the standard deviation was 2.4 min. Make 2 comparisons between the times for Secondary 4 boys and girls. . . . . . [2] Time (t min) Frequency 8 22 35 25 x www.KiasuExamPaper.com 28 www.KiasuExamPaper.com 28

7 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) [Turn Over (d) At the end of the Sports and Wellness Day, each participant was allowed to select a prize voucher from a prize box. The prize box contained 8 drink vouchers, 5 snack vouchers and 7 stationery vouchers. One voucher was selected at random. Find the probability that the selected voucher was not a snack voucher. Answer (e) Two vouchers were selected at random, without replacement . Find the probability that both vouchers selected were drink vouchers. Answer 2] www.KiasuExamPaper.com 29 www.KiasuExamPaper.com 29

8 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 4 A community club is organising a sports carnival for children. Children can choose to participate in one of three events badminton, table tennis or floorball. Matrix E shows the number of boys and girls in each category for the age group 7 to 10 years old. Matrix F shows the number of boys and girls in each category for the age group 11 to 14 years old. (a) Evaluate the matrix T = E + F. Answer (b) Each participant is charged an entry fee. The entry fee is $28 for badminton, $24 for table tennis and $20 for floorball. Represent the fees in a 1 x 3 matrix C. Answer C [1] www.KiasuExamPaper.com 30 www.KiasuExamPaper.com 30

9 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) [Turn Over (c) Evalu ate the matrix M = CT and state what the elements in matrix M represent. Answer M = [2] (d) Calculate the total amount of entry fees collected for the sports carnival. Answer 1] (e) The community club has decided to organise a similar sports carnival for teenagers aged 15 to 18 years old. As compared to the fees for children aged 7 to 14 years old, the entry fees for teenagers are increased by 15% for badminton, 10% for table tennis and 20% for floorball. Using matrix multiplication, calculate the entry fees for teenagers for each category. Give your answer in matrix form. Answer www.KiasuExamPaper.com 31 www.KiasuExamPaper.com 31

10 Canberra Secondary School Mathematics 4052/02 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 5 The variables x and y are connected by the equation . Some corresponding values of x and y, correct to 1 decimal place, are given in the table below. (a) Calculate the value of p. Answer p (b) On the axes given on page 11, dra