DHS Math 2 MYE 2021

L Name Register Number DUNMAN HIGH SCHOOL Mid-Year Examination Year 4 DHP MATHEMATICS 2 Additional Materials: Answer Sheet Insert A READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/tape. Answer all questions. Write your answers on the separate answer paper provided. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. Class 11 May 2021 2 hours 30 minutes Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded on the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. This document consists of 6 printed pages.

1. ALGEBRA Quadratic Equation For the equation ax2 +bx+ c = 0, -b± ✓b 2 -4ac x=------ 2a Binomial Expansion ( a + b )" = a' + (: }•- 1 b + (; }•- 2 b 2 + ... + (;) r b' + .. • + b' , (n) n I n( n-1) ... ( n-r + 1) where n is a positive integer and = { · ) = , · r r!n-r! r. Identities Formulae for MBC 2. TRIGONOMETRY sin2 A+cos 2 A=l sec 2 A = I+ tan 2 A cosec2 A = I + cot 2 A sin (A± B) = sin A cos B ± cos A sin B cos(A±B) = cosAcosB+sinAsinB tan(A±B)= tanA±tanB I+tanAtanB sin2A = 2sinAcosA cos2A=cos 2 A-sin 2 A=2cos 2 A-l=l-2sin 2 A tan 2A = _2_t_an_A_ I-tan 2 A a b C --=--=--sin A sin B sin C a2 = b 2 + c 2 - 2bc cos A Area oft:,.= ½ab sin C

j Answer all the questions 1 Find the range of values of m for which the line 4 y = ( m - 2) x intersects the curve y = -2-. x+l [4] 2 Given that the curve y = ax2 + Sx- c lies completely above the line y = c, find the condition(s) that must be applied to constants a and c. [4] 3 Find the x-coordinates of the points on the curve y = ex+ sin2x, 0::; x::; 1t, at which the gradient 1s zero. [4] 4 2x 2 +x-5 Express 2 in partial fractions. (x-l) [4] 5 Solve log5 x 2 = 3 log✓x 5 -1. [5] 6 (i) Explain why 12x - 3x2 -16 < 0 for all real values of x. [3] (ii) (7 x-3)(x+ 5) Hence, solve 2 > 0 . 12x-3x -16 [2] 7 (i) 5x dy 5 ( ax 2 + b) Given that y = 3 , find the values of a and b such that - = 5 • [3] ( ✓1 - x 2 ) dx ( ✓1 - x 2 ) ( 2) dy y (ii) Hence, show that 1- x dx - --:; = 2,;\,y . [1]

4 8 Mary collected some data from a science experiment to verify an equation 1- by = axy · She plotted a graph of.!. against x and obtained the straight line graph below. 9 y 1 y (4, 19) (l,y --0-=+-