SMBSS 2026 2G3 WA3 230826 updated

CANDIDATE NAME CLASS: INDEX NUMBER MATHEMATICS K310 Aug 2026 45 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. Answer all the questions. 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 of the marks for this paper is 30. 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. FOR EXAMINER’S USE TOTAL 30 Setter: Ms Isabelle Khoo This document consists of 9 printed pages and 1 blank page. [Turn over G3 SEMBAWANG SECONDARY SCHOOL WEIGHTED ASSESSMENT THREE SECONDARY TWO

2 Mathematical Formulae Compound interest Total amount = 1 100 n rP+ 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 = Cabsin2 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

3 Answer all the questions. 1 The diagram shows a right-angle triangle ABC. Write down an expression, in terms of p, q and/or r, for each of the following. (a) cos angle BAC Answer ……………….………………. [1] (b) tan angle ACB Answer ……………….………………. [1] 2 (a) 6 workers can paint 3 rooms in 2 hours. Given that all the workers paint at the same rate, find how much more time it will take two workers to paint 15 rooms. Answer ………..………………. hours [2] [Turn over p q r A B C

4 (b) Given that y is directly proportional to the cube root of x. Find the percentage change in y when the value of x is multiplied by 64 times. Answer ………..………………. % [2] 3 In the diagram, ABCD is a quadrilateral. AB = 56 cm, BC = 33 cm, AD = 63 cm and CD = 16 cm and angle ADC = 90o. Show that ABC is a right-angled triangle. Answer ...…………………………………..……………….……………… ..…………………………………..……………….……………… ..…………………………………..……………….……………… [3] A B C D 63 cm 16 cm 33 cm 56 cm

5 4 A tent pole OP, 2.4 m tall, stands vertically. Jey ties a 3.2 m long rope, AP, form the top of the pole to a peg at A. A second longer rope, BP, runs from the top of the pole to a peg at B. B lies on the same straight line as O and A, 1.8 m further from the pole than A. Calculate the angle that rope BP makes with the pole. Answer ………….………… o [3] [Turn over 2.4 m 3.2 m 1.8 m P O A B

6 5 PQR is a triangle and PT is perpendicular to QR. PT = 4.7 cm, PR = 7.8 cm and angle PQT = 68o. (a) Find the length of QT. Answer ………….………… cm [2] (b) Find angle PRT. Answer ………..………………. o [2] (c) Find the shortest (perpendicular) distance from R to PQ. Answer ………..………………. cm [2] Q T P R 68o 4.7 cm 7.8 cm

7 6 The diagram shows the cross-section of a solid formed by removing a cone from one end of a hemisphere. The hemisphere has diameter 10 cm. The cone has diameter 8 cm and height 3 cm. (a) Show that the volume of the solid is 212 cm3, corrected to 3 significant figures. Answer [2] (b) Convert 212 cm3 to m3. Answer ……………….…… m3 [1] [Turn over 10 cm 3 cm 8 cm

8 (c) The solid is made from a material with density 1.15g/cm3. Calculate the mass of the solid in kilograms. (Density = mass volume ) Answer ……………….…… kg [2] (d) The solid is melted into cubes of length 2 cm. Find the greatest number of cubes that can be formed from the solid. Answer ……………….…… cubes [2]

9 7 The diagram shows an ornament in the shape of a square pyramid. The length of the square is 6 cm and the volume of the pyramid is 108 cm3. (a) Show that the height, h, of the pyramid is 9 cm. Answer [2] (b) Find the total surface area of the pyramid. Answer ……………….………………. cm2 [3] [Turn over END OF PAPER h 6 cm 6 cm

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