YTSS 2026 Emaths Paper 1 With Ans

NAME: ( ) CLASS: SUBJECT TEACHER: __________________________________ YISHUN TOWN SECONDARY SCHOOL PRELIMINARY EXAMINATION 2026 SECONDARY 4/5 MATHEMATICS G3 PAPER 1 (4052/01) DATE : 11 August 2026 DAY : Tuesday DURATION : 2 h 15 min MARKS : 90 READ THESE INSTRUCTIONS FIRST Do not turn over the cover page until you are told to do so. Write your name, class and class index number in the spaces at the top of this page. Write in dark blue or black pen. 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. 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 of the marks for this paper is 90. MARKS OBTAINED FULL 1 2 2 3 3 1 4 2 5 2 6 2 7 3 8 4 9 2 10 4 11 2 12 3 13 3 14 3 15 3 16 6 17 3 18 6 19 3 20 7 21 5 22 8 23 6 24 7 TOTAL 90 This question paper consists of 20 printed pages. G3

2 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) [Turn over Answer all the questions. 1 Abeny, Becky and Cassidy decided to invest money in the ratio of p : 2 : 6. Becky invested $16 000 and Cassidy’s investment was 20% of the total investment. Find the value of the total investment. 2 u → $16 000 1u → $8000 6 u → $48 000 ----M1 20% → $48 000 100% → $240 000 ----A1 Answer $.................................. [2] 2 (a) Given that sin 0.8524x= , find the two possible values for angle x, where 0 180x . 58.5 (B1) or 121.5 (B1)xx==  Answer .................° or .................° [2] (b) Convert 1.54 radians into degrees. 88.2° (1 d.p.) ----B1 Answer .................................. ° [1] 3 The time taken to paint a wall is inversely proportional to the number of workers. Five workers take 14 hours. Find the number of hours it would take for 7 workers to paint the wall. 5 workers, 14 hours 1 worker, 70 hours 7 workers, 10 hours Answer .............................. hours [1]

4 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) 4 Given that ( ) 4 3 2026 20253 3 2 3n− =− , find the value of n. 4 3 2026 2025 4 3 2025 3 3 2(3 ) 3 3 (3 2) ----M1 4 3 2025 4 2028 507 ----A1 n n n n n − − =− =− −= = = Answer n = .................................. [2] 5 Mr Wong invested $15000 in a savings account that offers 2% interest per annum, compounded every 3 months. Calculate the total amount of interest Mr Wong earned at the end of 5 years. 20 20 0.0215000 1 -----M14 15000(1.005) $16573.43 Interest = 16573.43 15000 $1573.43 ----A1 A =+  = = −= Answer $.................................. [2]

5 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) [Turn over 6 (a) Given that 242 3 5nA +=   and 5 1 22 3 7nB −=   where n is a positive integer. The greatest common factor of A and B is 48. Find the value of n. 4HCF = 2 3 24 2 ----B1 n n  += = Answer n = .................................. [1] (b) Explain why 1 is not a prime number. Answer ......................................................................................................................................... ……............................................................................................................................................... [1] 7 Explain why 2 13 5 4 9 3 x xx − + +− is divisible by 10 for all integer values of x. Answer ( ) ( ) ( ) 223 5 3 4 3 3 (9) 5 3 4 3 ----M1 3 (9 5 4) -----M1 3 (10) Since it is 3 (10), 10 is a factor, it is divisible by 10. ----A1 x x x x x x x x x + +− = + − = + − = [3]

6 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) 8 (a) Factorise completely 226xx+− . (2 3)( 2) ---A2xx−+ Answer .................................. [2] (b) Hence factorise completely 22( 3) ( 4) 13yy− + + − . Write your answer as simply as possible. 2 2 2 2( 3) ( 4) 13 2( 3) ( 3 7) 13 2( 3) ( 3) 6 ----M1 sub -3 (2(y 3) 3)((y 3) 3) (2 9)( 1) ----A1 yy yy yy xy yy − + + − = − + − + − = − + − − = − − − + = − − Answer .................................. [2] 9 Cheryl went to Europe for a holiday and bought a bag for 900 Euros. She then sold the bag to her friend at a 15% profit. Given that the conversion rate between Singapore dollars ($) and Euros (€) was $1 = 0.67 (€), calculate the selling price in Singapore dollars ($). € € 1€1 0.67 1Sell Selling price ing price in S in Euros = 900 1.15 1035 -- GD = 1035 1544.78 (2 d.p.) 0. -M1 1 0.67 ---A167 SGD SGD SGD  = = = = Answer $.................................. [2]

7 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) [Turn over 10 The diagram represents a building, PQ, built on horizontal ground. The height of the building is 48 m. From a point R, the angle of elevation of the top of the tower is 40 . Point S is 18 m from R and QRS is a straight line. Calculate the angle of depression of point S from the top of the building. 1 48tan40 = ----M1 48 ----M1tan 40 48tan ----M1 18 57.204 48tan 18 57.204 32.5 RQ RQ PSQ PSQ PSQ −  =  = + =  +  =  Hence, angle of depression of point S from the top of the building is 32.5 Answer ..................................  [4] 11 Alex has 168 one-centimetre cubes. He arranges all the cubes into a cuboid. The perimeter of the top of the cuboid is 26 cm. Each side of the cuboid has a length greater than 2 cm. Find the height of the cuboid. 2( ) 26 13 ---M1 lb lb += += Checking possible pairs: 1683,10 > (rej) 30 1684,9 > (rej) 36 1685,8 > (rej) 40 1686,7 > = 4 --A142 h h h h −− = −− = −− = −− = Answer .................................. [2]

8 2026 YTSS Preliminary Examination Secondary 4/5 Mathematics G3 (4052/01) 12 (a) Express 2 6 10xx++ in the form ( ) 2 x p q++ , where p and q are constants to be found. ( ) ( ) 2 2 2 3 3 10 3 1 ----B1 yx x = + − + = + + Answer .................................. [2] (b) Write down the coordinates of the minimum point of the graph of 2 6 10y x x= + + . ( 3,1)− --- B1 Answer (................ , ..................) [1] 13 The curve 2y ax bx c= + + passes through the points ( 1, 16)−− and (1,0) . The equation of the line of symmetry of the curve is x = 2. Find the