1 霹雳怡保培南独立中学 SM POI LAM (SUWA) IPOH SECOND MONTHLY TEST 2021 SUBJECT: MATHEMATICS TIME: 1405-1535 (1 hour 30 mins) DATE: 02-08-2021 MARKS NO.____ NAME: . REG. NO: . CLASS: J2HE / J2REN READ THESE INSTRUCTIONS FIRST Write in dark blue or black pen. Answer all 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. Use of calculator is allowed in this paper. The total number of marks for this paper is 50. 1. In the diagrams shown below ≡ . ∠ = 113°, = 18 , = 12 , = 9 , ∠ = 62° and ∠ = 74°. Find (a) the length of , (b) the length of , (c) ∠, (d) ∠. Answer: (a) cm [1] (b) cm [1] (c) ° [1] (d) ° [1] This paper consists of 8 printed pages Prepared by ： ……………………… (Ms Leow Sook Wan) Checked by： ……….……………… (Mr Ong Eik Hooi) R Q P S V U T 18 cm 12 cm 9 cm 74° 62° 113° NOT TO SCALE
2 2. In the diagram, triangle is similar to triangle . = 6.5 , = 6 , = 8 , = 2 , ∠ = 28° and ∠ = 125°. Find (a) ∠, (b) the length of , (c) the length of . Answer: (a) ° [1] (b) cm [2] (c) cm [2] NOT TO SCALE A B C G H 6 cm 8 cm 2 cm 6.5 cm 28° 125°
3 3. Two vertical posts are 14 m apart. One is 3 m high and the other 5.6 m high. Find x, the distance between the tops of the two posts, giving your answer in metres, correct to 3 significant figures. Answer: [3] 4. is a quadrilateral with sides = 4 , = 12 and diagonal = 5 as shown in the diagram below. If ∠ = ∠ = 90°, find the perimeter of the quadrilateral . Answer: Perimeter of quadrilateral = cm [3] 14 m 3 m 5.6 m x B C D 5 cm 12 cm NOT TO SCALE NOT TO SCALE 4 cm A
4 5. A map is drawn to a scale of 2 cm : 1.2 km. (a) Express the scale of the map in the form 1 : n. (b) Calculate the actual distance between two towns, in km, if their distance apart on the map is 8 cm. (c) Calculate the area of reservoir on the map, in cm2 , which represents an actual area of 16 km2 . (d) If the area of the reservoir on the second map is 4 cm2 , find the scale of the second map in the form 1 : m. Answer: (a) [2] (b) km [1] (c) cm2 [2] (d) [2]
5 6. (a) Simplify the following expressions: (i) 2 152 × 10 7 , (ii) 4+16 −2 ÷ +4 2−4 . (b) Express 3 2+ − 4 4+3 as a single fraction in its simplest form. Answer: (a)(i) [2] (a)(ii) [3] (b) [3]
6 7. (a) Make x the subject of the formula = √ 2−1 2 . (b) Hence find the value of x when = 4, = 14 and = 1. Answer: (a) [3] (b) [1] 8. In ∆, = 26 , = 20 and = 14 . Determine whether ∆ is a right-angled triangle. Answer: [2] L M N 20 cm 26 cm 14 cm NOT TO SCALE
7 9. In the diagram, ∆ is similar to ∆. = 15.6 , = 9.75 , = 6.5 , ∠ = 32° , ∠ = 90° and and intersect at . Find (a) ∠, (b) ∠, (c) the scale factor of the enlargement of ∆ to ∆, (d) the area of ∆. Answer: (a) ° [1] (b) ° [2] (c) [2] (d) cm2 [2] NOT TO SCALE B C E D X 9.75 cm 15.6 cm 6.5 cm 32° A
8 10. is a right-angled triangle where is a right angle. = (2 + 7) , = (3 + 3) and = ( + 2) . (a) Use the diagram to form an equation involving x, and show that it reduces to 2 − − 6 = 0. (b) Solve the equation 2 − − 6 = 0. (c) Calculate the area of ∆. Answer: (a) [3] Answer: (b) x = or x = . [2] (c) cm2 [2] End of paper. NOT TO SCALE Q R (2x + 7) m P (3x + 3) m (x + 2) m
