4NA KSS Practice WA1 2025 (MS)

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 cos 35° = 13 𝑊𝑍 WZ = 13 cos 35° = 15.9° 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] sin 13 18WXY= WXY= sin-1( 13 18) = 46.2° Benny was wrong as the angle of elevation should be angle WXY and it is 46.2° 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, 228.7 4.5DC=− = 7.446 = 7.45 Answer DC = ………………….… cm [2] (b) the area of the quadrilateral ABDC. Area of 1 4.5 7.446 16.75352BCD =   = Area of 1 8.7 8.7 sin 60 32.7752ABC =    = Area of quad ABCD = 16.7535 + 32.775 = 49.5 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. 070° Answer …………………….……......... [1] (b) Calculate the bearing of A from B. angle N1BC = 110° (alt angles , // lines) bearing = 360° - 110 ° - 26 (angles at a pt) = 224° Answer ………………………….…..... [2] (c) Calculate the length of AC. 78 sin 26 sin 44 AC = 78 sin 26sin 44AC=    AC = 49.2 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. 248 2304= ; 255 3025= ; 273 5329= Since 2 2 248 55 73+= , the 3 numbers are lengths of a right -angled triangle. 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] Bearing of G from E = 360 (180 146 ) 326− −  =  (shown) (b) Find (i) ECG , 1082 1255 sin sin 78 57.491456.. 57.5 ECG ECG =  = =  Answer ………………………….……. [2] (ii) the bearing of C from G. 180 78 57.491456 44.5085..EGC = − − =  Bearing of C from G ( ) 360 44.5085 (180 146 ) 281.4915.. 281.5 1 dp = − − −  = = Answer ………………………….……. [2] (c) Find the area of triangle CEG. Area of  CEG = ( )( )1 900 1082 sin 782  = 476260 = 476 000 m2 (3 sf) 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. 80tan 894 5.11352 5.1 (1 d.p)   = = =  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. 8.5 5AE= − = 3.5 cm ; CD = 6 cm ( ) 1 3.5tan 6 3.5tan 30.2564.. 30.3 1 dp6 x x − = = = =  Answer x = …………………….……. [2] (b) Calculate the perimeter of trapezium ABCD. 226 3.5 6.94622..AB= + = Perimeter = 6.94622 8.5 6 5+ + + = 26.44622… = 26.4 cm (3 sf) 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. Range = 40 12 28−= Mode = 22 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. Based on the maximum score, 75% is 30 marks. 40 75% 30 Based on the Stem-and-leaf diagram, there are only 9 students who scored 30 marks and above. An Additional Mathematics class cannot be created. =  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 , Median time = 26.5/27 Answer ………………… minutes [1] (ii) the interquartile range. Q1 = 18 Q3 = 35 Interquartile range = 35 − 18 = 17 minutes Answer ………………… minutes [2] 0 10 20 30 40 50 60 Time (minutes) 40 80 120 160 200 240 Polling Station X Polling Station Y