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= ; 2