mock as level

AS LEVEL MOCK MOCK MOCK PURE MATHMATICES TIME 1.30 HR Hp HUNDRED PERCENTILE Shaping Future Adeptness BY Prof. Hansraj Singh (B.Tech, CSE) MATHEMATICS ,PHYSICS ,COMPUTING,CHEMISTRY IB (HL,SL ,STUDIES) , CIE(AS,AL) IGCSE(MYP), SAT 1,2 ersingh@hotmail.com ,09890408588 1. f(x) = 5sin3x, 0  x  180. (a) Sketch the graph of f(x), indicating the value of x at each point where the graph intersects the x-axis (b) Write down the coordinates of all the maximum and minimum points of f(x). (c) Calculate the values of x for which f(x) = 2.5 2. A mechanist has spherical ball of brass of diameter x cm the ball is placed in the lathe and machined into a cylinder (a) If the cylinder has the radius x cm, show that cylinder’s volume is given by V(x) = πx2 (100-4x2 )1/2 (b) Hence, find the dimension of largest volume which can be made 3. The shape of a badge is a sector ABC of a circle with centre A and radius AB, as shown in Fig 1. The triangle ABC is equilateral and has a perpendicular height 3 cm. (a) Find, in surd form, the length AB. (b) Find, in terms of , the area of the badge. A B C 3 cm Hp HUNDRED PERCENTILE Shaping Future Adeptness BY Prof. Hansraj Singh (B.Tech, CSE) MATHEMATICS ,PHYSICS ,COMPUTING,CHEMISTRY IB (HL,SL ,STUDIES) , CIE(AS,AL) IGCSE(MYP), SAT 1,2 ersingh@hotmail.com ,09890408588 (c) Prove that the perimeter of the badge is )6(332 cm. 4. The ninth, thirteenth and fifteenth terms of an arithmetic progression are the first three terms of a geometric progression whose sum of infinity is 80. The sixteenth term of an arithmetic progression is equal to the fourth term of the geometric progression. Calculate the sum of the first sixteen terms of the arithmetic progression 5. Fig. 1 Figure 1 shows the curve with equation y = 5 + 2x  x2 and the line with equation y = 2. The curve and the line intersect at the points A and B. (a) Find the x-coordinates of A and B. A B O R y x y = 2 y = 5 + 2x  x2 Hp HUNDRED PERCENTILE Shaping Future Adeptness BY Prof. Hansraj Singh (B.Tech, CSE) MATHEMATICS ,PHYSICS ,COMPUTING,CHEMISTRY IB (HL,SL ,STUDIES) , CIE(AS,AL) IGCSE(MYP), SAT 1,2 ersingh@hotmail.com ,09890408588 The shaded region R is bounded by the curve and the line. (b) Find the area of R. 6. The diagram shows a parallelogram OPQR in which = , = (a) Find the vector . (b) Use the scalar product of two vectors to show that cos = – (c) (i) Explain why cos = –cos (ii) Hence show that sin = . (iii) Calculate the area of the parallelogram OPQR, giving your answer as an integer. 7. OP37OQ.110yxPOQRORQPˆO.75415RQˆPQ.PˆO R Q ˆP 75423Hp HUNDRED PERCENTILE Shaping Future Adeptness BY Prof. Hansraj Singh (B.Tech, CSE) MATHEMATICS ,PHYSICS ,COMPUTING,CHEMISTRY IB (HL,SL ,STUDIES) , CIE(AS,AL) IGCSE(MYP), SAT 1,2 ersingh@hotmail.com ,09890408588 The coefficient of x in the expansion of is . Find the possible values of a. 8. In the rectangle ABCD, B and D have coordinates (5,3) and (0,3). Given that the equation of BC is y = -2x + 13, find the (i) equation of CD (ii) coordinates of C (iii) coordinates of A. 9. Find all values of  in the interval 0   < 360 for which (a) cos ( + 75) = 0.5, (b) sin 2  = 0.7, giving your answers to one decima1 place. 10. 721axx37Hp HUNDRED PERCENTILE Shaping Future Adeptness BY Prof. Hansraj Singh (B.Tech, CSE) MATHEMATICS ,PHYSICS ,COMPUTING,CHEMISTRY IB (HL,SL ,STUDIES) , CIE(AS,AL) IGCSE(MYP), SAT 1,2 ersingh@hotmail.com ,09890408588 (a) Prove, by completing the square, that the roots of the equation x2 + 2kx + c = 0, where k and c are constants, are k ± (k2  c). The equation x2 + 2kx +81 = 0 has equal roots. (b) Find the possible values of k.