4NA KSS Practice WA1 2025 (QS)

4N WA1 (2022-2024) Revision Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = r , where  is in radians Sector area = , where  is in radians Trigonometry Statistics Mean = Standard deviation = n rP      + 1001 hr 2 3 1 3 3 4 r Cabsin2 1 2 2 1 r C c B b A a sinsinsin == Abccba cos2222 −+=   f fx 22       −     f fx f fx

2 Extracted from 4NA WA1 2024 1 X, Y and Z are three points lying in a horizontal straight line. WY is a vertical flagpole. WX and WZ are supporting wires. WX = 18 m, WY = 13 m and angle YWZ = 35°. (a) Calculate WZ Answer .............................................. m [2] (b) Benny said the angle of elevation of W from X is 43.8°. Was Benny correct? Explain your answer Answer [2] W X Y Z 35° 18 m 13 m

3 2 ABC is an equilateral triangle. Angle BDC = 90° , BD = 4.5 cm and BC = 8.7 cm. Calculate (a) the length of DC, Answer DC = ………………….… cm [2] (b) the area of the quadrilateral ABDC. Answer ……………...……………. cm2 [4] A B C D 4.5 cm 8.7 cm

4 3 A, B and C are on level horizontal ground. BC = 78 m, angle ACB = 110° and angle ABC = 26°. C is due north of A. (a) Calculate the bearing of B from C. Answer …………………….……......... [1] (b) Calculate the bearing of A from B. Answer ………………………….…..... [2] (c) Calculate the length of AC. Answer ………………………….……m [3] A B C N 110 ° 26 ° 78 m

5 Extracted from 4NA WA 2023 4 Harry claims that the following three numbers could be the lengths of a right -angled triangle. 55 , 73 , 48 Justify, with clear working, whether his claim is true. Answer ….………………………………………………………………………….. ….………………………………………………………………………….. ….………………………………………………………………………….. ….………………………………………………………………………….. [2] 5 Three points, E, C and G lie on a horizontal field. EC = 900 m, EG = 1082 m, CG = 1255 m, 78CEG =  and the bearing of G from E is 146. 1082 m 1255 m E C G 78 146 North 900 m

6 (a) Show that the bearing of E from G is 326. [1] (b) Find (i) ECG , Answer ………………………….……. [2] (ii) the bearing of C from G. Answer ………………………….……. [2] (c) Find the area of triangle CEG. Answer ………………………….…. m2 [2]

7 (d) A building of height 80 m is erected at C. Calculate the angle of elevation of the top of the building when viewed from E. Answer ………………………….……. [2]

8 6 ABCD is a trapezium such that BC = 5 cm, CD = 6 cm and AD = 8.5 cm. (a) Calculate the angle x shown on the diagram. Answer x = …………………….……. [2] (b) Calculate the perimeter of trapezium ABCD. Answer ………………………….…. cm [2] 5 cm C E x B D A 6 cm 8.5 cm

9 7 The stem-and-leaf diagram below shows the first weighted assessment scores of a Secondary 2 class. There are 30 students in this class and the maximum mark of the paper is 40. (a) Find the range and the mode of the scores. Answer Range = …………….. marks Mode = …………….. marks [2] (b) A student can take Additional Mathematics in Secondary 3 if his or her score is 75% and above. An Additional Mathematics class can only be created if there are at least 10 students enrolled into it. Based on the information above, can an Additional Mathematics class be created? Show your working clearly. Answer ……………………………………..…………….……………. [2] 1 2 4 5 5 6 6 7 8 8 2 0 1 2 2 2 3 5 5 7 8 8 9 3 0 0 1 2 4 4 7 8 4 0 Key 1 | 2 means 12 marks

10 8 (a) The times taken by 240 people to cast their votes, at both polling station X and Y, in a country’s General Election is shown in the cumulative frequency curve below. Use the graph to find, for polling station X, (i) the median time , Answer ………………… minutes [1] (ii) the interquartile range. Answer ………………… minutes [2] 0 10 20 30 40 50 60 Time (minutes) 40 80 120 160 200 240 Polling Station X Polling Station Y