2026 Canberra E-Math Paper 1

CANBERRA SECONDARY SCHOOL 2026 Preliminary Examination Secondary Four Express/Five Normal (Academic) MATHEMATICS 13 Aug 2026 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 19 printed pages including the cover page. Setter: Mr Edwin Cheong Marks Awarded Max Marks Total 90 O www.KiasuExamPaper.com 3 www.KiasuExamPaper.com 3

2 Canberra Secondary School Mathematics 4052/01 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 sin sin sin a b c A B C Statistics Mean Standard deviation = www.KiasuExamPaper.com 4 www.KiasuExamPaper.com 4

3 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) Answer all the questions. 1 Represent the inequality , on the number line below. [1] 2 Simplify (a) , Answer [1] (b) Answer [3] [Turn over www.KiasuExamPaper.com 5 www.KiasuExamPaper.com 5

4 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 3 The cash price of a computer is $3000. Adeline buys the computer on hire purchase. She pays a deposit of $2000 plus 36 equal monthly payments of $34.50. (a) Calculate the total cost Adeline has to pay by hire purchase. Answer [1] (b) Find the rate of simple interest charged per annum. Answer [2] 4 Consider the pattern: Row Mathematical sentence Sum No. of odd integers 1 1 + 3 4 2 2 1 + 3 + 5 9 3 3 1 + 3 + 5 + 7 16 4 4 1 + 3 + 5 + 7 + 9 25 5 : : : n k S (a) Is it possible to have a sum of 200? Explain your answer. [1] www.KiasuExamPaper.com 6 www.KiasuExamPaper.com 6

5 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) (b) Express k in terms of n. Answer [1] (c) How many odd integers are there from 1 to 49? Answer [1] 5 (a) Answer [2] (b) Answer [2] [Turn over www.KiasuExamPaper.com 7 www.KiasuExamPaper.com 7

6 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 6 (a) Find y when and . Give your answer to 2 significant figures. Answer [2] (b) Rearrange the formula to make x the subject. Answer [3] 7 The dimensions of a rectangular box are 60 cm by 54 cm by 42 cm. The box is to be filled with identical cubes of k cm so that there will be no empty space. (a) Find the largest value of k. Answer k = cm [2] www.KiasuExamPaper.com 8 www.KiasuExamPaper.com 8

7 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) (b) Using your answer in (a), find the total number of cubes the box can hold. Answer [2] 8 (a) Express in set notation, the region shaded in the Venn diagram below. Answer [1] (b) A and B are subsets of . The number of elements in the subsets is shown in the Venn diagram. Given that n( ) = 35, find the value of x. Answer [1] 9 Answer [2] A B [Turn over x www.KiasuExamPaper.com 9 www.KiasuExamPaper.com 9

8 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 10 The diagram represents a scale drawing of a plot of land, ABCD. CD is 12 km. (a) Express the scale of the map in 1 : n. Answer [1] (b) The area of the lake on the map is 1.65 cm2. Calculate the actual area of the lake in km2. Answer 2 [2] 11 Solve these simultaneous equations. You must show your working. Answer x y [3] A D C B www.KiasuExamPaper.com 10 www.KiasuExamPaper.com 10

9 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 12 The circular arc BC is part of a circle centre A. The centre of semicircle ACD is O. The diameter of the semicircle, AC is 13 cm. radians. (a) Show that the arc length BC is 12.48 cm. [1] (b) Find the perimeter of ABCD. Answer cm [2] 13 (a) The total population of Singapore is estimated to be 5906000 in 2026. Express this number in standard form. Answer [1] (b) The Gross Domestic Product (GDP) of Singapore in 2026 is estimated to be 659.6 billion dollars. Express this figure in standard form. Answer [1] (c) The GDP is the average income per person multiply by the total population. Calculate the average income per person correct to the nearest hundred dollars. Answer [1] A C B D O 13 cm [Turn over www.KiasuExamPaper.com 11 www.KiasuExamPaper.com 11

10 Canberra Secondary School Mathematics 4052/01 2026 Preliminary Examination Secondary 4 Express / 5 Normal (Academic) 14 In the diagram , Find (a) the area of Answer [1] (b) the numerical value of Answer [2] 15 Solve the equation by completing the square. Give your solutions correct to 2 decimal places. Answer x [3] B C A 4 cm 5 cm www.KiasuExamPaper.com 12 www.KiasuExamPaper.com 12