2022 Sec 3 Express A Math EOY Beatty Secondary with Answer

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BP-34 BEATW SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2022 SECONDARY THREE EXPRESS CANDIDATE NAME CLASS REGISTER NUMBER ADDITIONAL MATHEMATICS Paper t h,,,,." ilr ltcl. Setter Ms Joanna Chong HY Candidates answer on the Question Paper Additional Materials: Nil 4049 {0 Octobor 2022 2 hours 15 minuteg READ THESE INSTRUCTIONS FIRST Write your name, class and r€ister number in the spaces at the top of this page Write in da* blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or conection fluid. Answer all the questions. Given non-exact numerical answers conecl to 3 sbnificant 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 scientmc calarlator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question The total of the marks for this paper is 90. For Examiner's Use This document consists of lE printed pages and 0 blank pages. PartnerlnLearning 32 r I

I Find the range ofvalues ofp for which y = xl + p(x-1)+4-x is positive for all real values of .r, BP-36 t4l t3l) Given that J1 Q, * z) = z(t -2) , express ft in the form a + DJ7 ParlnerlnLeaming 34

BP-37 3 (r) By completing the sqrnre, prove that the minimum value of y=gaz+4x-7is t3l (b) Two statements are made about a quadratic expression f(r) Statement I : The graph of f(x) has a turning point at (-3, 5). Statement B : f(x) cannot be expressed as f(x\ = a1r- 011, - q) where a, p arrd q are real numbers State whether each ofthe following is true, false, or ifthere is insufficient information to conclude. Justi$ your answer with reasons. (D f(x)=212g1312 *5. t2) (ii) (-3,5) is a minimum point. t2) PartnerlnLeaming ) J 35

4 Solve each ofthe following equations for ()" < lr< 36()". (a) I sin(d-25") =; (b) zle:l. o-t=sserce. BP- 38 t3l tsl PartnerlnLeaming 36

5x2 -3x+8 2 3x+l BP-39 tzt tsl 5 A student claimed that (i) (ii) Express (.r-l)(x'?+4) = _+ : x-l x'+4 , x*1. Without finding the partial fiactions o1 J'':I1t and without substituting(.x-l)(x'+4) any values ofx, show that the student's answer is wrong 5.r'-Jr+t( (, -rX7 +4) as a sum of two partial fractions. PartnerlnLeaming 37

6 (a) Solve 32' + l8:3'-'] (b) Solve the following equation logr.( I5,r* 6) - - =los (r- l) BP-40 t3l t4llogr5 PartnerlnLeaming 38

7 Given that f(x)=2xt +(a-4)x2 +ax-6a, (D show that .:r - 2 is a factor of f(x), (ii) find the other quadratic factor in terms of a and x (iii) If f(x) has three real roots, find the range ofvalues ofo. BP-41 tll 14) t2) PartnerlnLeaming 39

8 The diagram shows the curve ]:asin bx+c for 01xa t radians. The curve has a maximumpointat (f ,r) *0"-,nimumpointat (+ --) BP-42 l2l t2) v 2 G o 7t (+ -, (i) Explain why b = 2. (ii) Find the equation ofthe curve. On the sarne axes, draw the graph of y = 4ss52, + 2 .l-abel the y-intercept and the coordinates of minimum point(s) on the graph clearly. PartnerlnLeaming 40 (iii) t3l

9 Concentric circles are circles which have the same centre The diagram shows two concentric circles C, and Cr. PR is a trngent to the ctcle Crat P (l,7). The equation of C, is x2 + yz +4x-6y+4=0. (D Show that the centre of C, is (-2,3) and find the radius of C, 8P.43 t3l t2l C P(1. ?) rR (ii) Find the equation of Cr. PartnerlnLeaming 41 I C