Mock Exam 4 Paper 1. 1 Achiever. Section A(1) ab = ab. = a b. by (a), we have x < 46 (3) 25. \ The range of the values of x is x 7 3.

Transcription

1 Mock Exa Mock Exa aper Section A().. 6 ( ) 0 a b 0 ( ) a b a b n n n n. (a) 9a b ( a) ( b) ( a b)( a + b) 0 + 7x 6. (a) < 6x 0 + 7x < 66 8x 7x + 8x < 66 0 x < 6 6 x < For 7 - x 0, 7 x 0 + 7x For < 6 x, by (a), we ave x < 6. \ Te range of te values of x is x 7. \ Te greatest integer is. 7. (a) Mean Arrange te data: 8,,,,, 8 Mode 9( x y) ( x + y) [ ( x y) ( x + y)][ ( x y) + ( x + y)] ( x 6y x y)( x 6y + x + y) ( x 0y)( x y). (a) Let $x be te cost. x( + %)( - 6%) - x 7 0.0x 7 x 00 \ Te cost is $00. Selling price $00 ( + %) ( - %) $8., wic is less tan te cost. \ He will suffer a loss. Disagreed.. Let k be te volue of a solid etal spere. Ten te volue of a solid etal cylinder is k. 9(k) + (k) 0 k 0. \ Te volue of a solid etal spere (0.). Te ean age reains uncanged. Te ean age of te new ebers is. Hence te su of teir ages is 6. Tere are ore tan one ode. Te possible ages are 8 and 8, or and. 8. (a) ABE BAE 0 (base s, isos. ) BC : CD BAC : CBD (arcs prop. to s at ce ) : 0 : CBE 0 CBE CBE 60 ABC ABE + CBE AC is not a diaeter of te circle. Aciever

2 Mateatics Mock Exa ower ack (Copulsory art) Second Edition Solution Guide 9. (a) Area of te base ABCD 68 7 Section A() ( AC)( BD) ( 8 )( BD) BD 6 AC BD AB + (yt. teore) 8 6 AB + Total surface area ( + 7 ) 88 ercentage cange 00% ( A )( N )(.) ( A )( N ) 00% ( A )( N ) 0% \ His sales figure is increased by 0% in tat ont.. (a) For te frustu, 0. (a) Let A k, were k is a non-zero constant. N Wen and N, A k( 0 000) k \ A N Te required bonus $ 9 $ 00 Let A be te bonus, be te sales figure, N be te nuber of coplaints in te previous ont. A, ( A )( N N ) For te particular ont, let be te sales figure in tat ont. A N ( + %) A N. ( A )( N )(.) As sown in te figure, DACE ~ DBCD (AAA) \. \ (corr. sides, ~Ds) Te required capacity ( π)( ) ( + ) ( π)(.)() + π (. ) ( ) π Volue of te ice-crea ball ( π)( ) 6π > π Te ice-crea will overflow. Aciever

3 Mock Exa. (a) k k 0 k 0 (i) Te required percentage % () % (ii) Let be te nuber of new students % % is not a ultiple of. Te percentage of students wose drea job is banker will not be tripled.. (a) Let f(x) 8x - x + 0x -. f x is a factor of 8x x + 0x. () (i) y (x - ) + x - x (*) OC and AB can be found by substituting x 0 and x into (*) respectively. Te area of OABC {[() () + 0] + [(0) (0) + 0]} () (8 + 0) (ii) ( )( 6 + ) 0. (a) Γ is a pair of perpendicular lines, wic are te angle bisectors of te angles between L and L. () Inclination of Γ or Equations of Γ: y - 0 (x - )tan and y - 0 (x - )tan y x - and y -x + (c) Coordinates of te centre (0, ) Substituting (0, ) into y x -, L.H.S. R.H.S. 0 - L.H.S. Section B Γ passes troug te centre of te circle C. Hence, Γ bisects te circle C.. (a) Mean [0( + 0%) ] arks 0 arks () Let x arks be te exaination score and s arks be te standard deviation of te exaination scores before te score adjustent. Te standard score before te score adjustent x - 0 s Te standard score after te score adjustent [ x ( + 0 %) ] 0 s( + 0%). x -. s.( x - 0). s x - 0 s Te standard score of eac student is not canged due to te score adjustent. () \ or (rejected, D < 0) x-coordinate of B y-coordinate of B \ Coordinates of B (, ) Aciever

4 Mateatics Mock Exa ower ack (Copulsory art) Second Edition Solution Guide 6. Denote Y and G as te ball drawn is yellow and green respectively. (a) (at least two adjacent balls are of sae colour) - (any adjacent balls are of different colours) - (YGYGY or GYGYG) () (exactly yellow ball is drawn at least adjacent balls are of te sae colour) YGGGG ( ) () 7. (a) b a + () Te equation of L: y 0 (tan ) ( x 0) y x Te equation of C: (x a) + (y b) b x ax + a + y by + b b x + y ax by + a 0 Substituting y x into te equation of C, x + x ax bx + a 0 x - (a + b)x + a 0 Te x-coordinate of te id-point of Q ( a + b) a + b a + ( a + ) (by (a)) a + Te coordinates of te id-point of Q (a +, a + ) Alternative Solution Equation of L: y 0 (tan ) ( x 0) y x Te equation of te straigt line passing troug te centre of C and perpendicular to L: y b x a ( ) Substituting y x into y b x a ( ), x b (x a) x a + b x a + b a + a + (by (a)) a + Te coordinates of te id-point of Q (a +, a + ) 8. (a) In DTAC, tan8 AC AC tan8 In DTBC, tan BC BC tan In DABC, by te cosine forula, AB + BC ( AB)( BC)cos AC tan tan 8 (800) cos tan tan tan 8 0 cos ( 800) tan or (rejected) 68 (cor. to te nearest integer) Aciever

5 Mock Exa Let be te point on AB suc tat te C AB, ten C is te sorest distance between C and AB. is te greatest angle of elevation of T fro Jenny wen se walk fro A to B. 9. (a) (i) In DBC, C sin BC sin C tan tan C sin tan tan sin. (cor. to sig. fig.) Te greatest angle of elevation is.. (ii) ( ) ( ) ( ) () : b. b. or -. (rejected) Substituting b. into (), a(.) 0 80 a 000 Total weigt in te first n years ( n ) tousand tonnes n ( b - ) tousand tonnes b - ( 000)(.)[(.) n - ] tousand tonnes [(.) n - ] tousand tonnes (i) Note tat: ( + ) W( + ) 0 b 0 > b > B ( ) Te incinerator cannot burn out all te waste in eac year. (ii) ( + ) ( b ) b ( b ) b ( b ) b b b 0 b + b 6. 7 Substitute te values of a and b into te inequality and solve it:..96 or (rejected) 6.80 Te landfill will not be full in 00 after te incinerator operates. (7) Total weigt in te first years 000[(.) - ] tousand tonnes tousand tonnes tousand tonnes (cor. to te nearest tousand tonnes) (6) Aciever