5. B To determine all the holes and asymptotes of the equation: y = bdc dced f gbd

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Paulina McCarthy
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1 1. First you chck th domain of g x. For this function, x cannot qual zro. Thn w find th D domain of f g x D 3; D 3 0; x Q x x 1 3, x 0 2. Any cosin graph is going to b symmtric with th y-axis as long as it is not shiftd. 3. Monotonic mans that a function dos not chang dirction. a. y 2 (onstant) c. y 2cos (x) (Oscillating) b. y 2x (onstantly Dcrasing) d. y 2 D (onstantly Dcrasing) 4. A Sinusoidal graphs ar boundd abov and blow bcaus thy ar rstrictd by th amplituds. 5. B To dtrmin all th hols and asymptots of th quation: y bdc dd f gbd bd Dd f h Dg Dd D Dd h Dg ; Vrtical Asymptot at x 1 and hd f dh Obliqu Asymptot at y 1 4 x 1 Long Division 2 Hol at (1,0) du to th factor (x-1) canclling. You substitut in x 1 into th simplifid form of th quation to gt th y-coordinat. To gt th intrcpts, sub in x 0 and y 0 into th quation and solv. (0,0) 6. A To convrt th paramtric quations to thir artsian (rctangular) form, w will us th Pythagoran Idntity: sin x + cos x 1 x t 2cost ; cost D y t 3sint; sint ƒ D ƒ + 1 substitution. Q Q x 4 + y 9 1 c a

2 7. B To find a possibl quation: th amplitud of th graph can b sn to b 2. Thr is a point at (0,2). By substituting that valu into options B and D, you can find th only on to work to b B. y 2sin ( 1 4 x + π 2 ) 8. To find th rang of th graph of: y ˆ QDdŠ, w can considr that th only possibl valus for th cosin function ar btwn -1 and 1 inclusiv. If w find th rciprocal of thos valus, w gt, 1] [1, ) 9. D Simplifid: f DgQ ˆ D (d ˆ f D)gQ D d( ˆ f DdQ Dd) ˆ f Ddh Dd Dg Dd Dg d( Dg)( Dd) ( Dd)( Dg) d( Dg)( Dd) 2 cos x 1 ( Dd)( Dg) cos x cos 90 x (D) D D sin (x) Trigonomtric Idntity ˆ (D) D 11. B First to find th ara, us Hron s Formula: 45(25)(15)(5) 75 15, this must also qual š sin ; sin ; csc š 12. E For triangl AB with givn masurs: m A 30, b 10 cm, a 5 cm, Angl B must b 90 dgrs which maks th triangl a You can also us Law of Sins to com to th sam conclusion. 5 3 is th only option for th third sid. 13. A 1 + cot x 2 ; cot x 1 ; tan x 1 ; tanx 1 or 1; x Š h, QŠ h, Š h, x Š + Š k whr k any intgr h

14. A Th quation of th graph has a cntr at th point (-2,2) and a radius of 3 units. 3π Ara: 4 2π π 3 27π 8 15.

3 14. A Th quation of th graph has a cntr at th point (-2,2) and a radius of 3 units. 3π Ara: 4 2π π 3 27π D A parabola has a dirctrix with quation x 2 with a focus at th point (6, 3), which maks th vrtx half way btwn thos two at (2, -3). Th distanc btwn th vrtx and th focus is th a valu, so a 4. Th parabola must opn to th right bcaus th dirctrix is on th lft of th vrtx. That maks it an x quals quation. x 1 16 y **B carful that th x coordinat of th vrtx gos in th corrct plac. To find th ndpoints of th latus rctum, w can first solv for its lngth, 4(4)16. That mans thy ar 8 units abov and blow th focus. Thos will b locatd at (6,5) and (6,-11). 16. B 8 tan 65 8( š ) 17. B To find th invrs, w must first find th dtrminant and mak sur that th matrix is not singular. dt Q 18. B alinium-43 has a half-lif of 4 yars. If Evrtt starts with 100 kg of alinium-43, which of th following could rprsnt how much h has, A(t), aftr a crtain amount of tim in yars (t):

4 A t h 19. log h D ; log h D ; log D ; x h 128 ; x B To find a possibl quation for th graph that rprsnts th invrs rlation to th following graph, first w must switch th x and y variabls. Thn w will solv for th invrs quation in trms of x. y log Q (x 1) + 2 ; x log Q (y 1) + 2 ; x 2 log Q y 1 ; 3 Dd y 1 y 3 Dd + 1; Th asymptot will also b th invrs, so y D Simplify: 1 +! + h! + š Q! + b h! B To find th angl of rotation from th positiv x-axis of th graph: tan 2θ «90 ; 2θ 90 ; θ 45 3x 4xy + 3y + 2x 7y d ; tand dh 23. D To dtrmin th location of th focus (or foci) of th graph of th following quation: 32 x y ; 32 x y ; 128 x 2 y ; cntr 2, 1 of hyprbola ; c ; c 5 4 Th foci will b c away from th cntr into th curvs of th hyprbola in both th positiv and ngativ x dirction , 1 and 2 5, 1

5 24. E To idntify th phas shift and frquncy of th graph of th following quation: y 3 cos 2πx Phas shift: 1 2π and Frquncy: ±² ³ Š D To solv for th lngth of sid a us th law of cosins: a 74 70cos A To find th sum of th ara and primtr of an isoscls triangl with vrtx angl of 120 and bas of lngth 24 cm, w can first dtrmin that th two bas angls must b 30 dgrs. That maks th altitud of th triangl asy to find using th spcial right triangl rul. Altitud 4 3 which maks th lgs of th triangl both 8 3. Thus, th primtr of th Q triangl is and th ara of th triangl is Sum To dtrmin th quation of th prpndicular bisctor to th lin sgmnt with ndpoints at π, 1 and 5π, 3, w will nd to find th midpoint to hav th point th lin gos through as wll as th slop of th givn lin so that w can solv for th prpndicular slop. a. Midpoint: Šg Š, dq 3π, 1 b. Slop: dqd ŠdŠ h hš Š c. Prpndicular Slop: π (ngativ rciprocal) y π x 3π 1

6 28. I usd Elimination Mthod to solv th systm of quations. 5 3x y + 12z x 3y + 5z 25 63x 31y x + 4y 7z x 3y + 5z 25 38x y 115 y 38x x 31 38x ; x 3 y z 16; z Th answr is bcaus at pi/2, is undfind and cosin is not. 30. D sin 2x sin x 2 cos x 1 ; 2 sin x cos x sin x 2 cos x 1 ; sinx 2cosx 1 2cosx 1 ; sinx 1 2cosx 1 0 ; sinx 1 ; cosx x π 2 and x π 3

MATHEMATICS (B) 2 log (D) ( 1) = where z =

MATHEMATICS (B) 2 log (D) ( 1) = where z = MATHEMATICS SECTION- I STRAIGHT OBJECTIVE TYPE This sction contains 9 multipl choic qustions numbrd to 9. Each qustion has choic (A), (B), (C) and (D), out of which ONLY-ONE is corrct. Lt I d + +, J +