Pre-Calculus TMTA Test 2018

Transcription

1 . For the function f ( x) ( x )( x )( x 4) find the verge rte of chnge from x to x. ) logb 8. If logb.07, logb 4.96, nd logb.60, then ) For, ) sec (sin ) is equivlent to 4. The sum of the first n terms of n rithmetic series is n th the k term. ) k k 4 6k 6k 4 9k n. Find n expression for

2 . Let ) 0 4 x A B ( x )( x 4) x x 4. Wht is A B? 6. A seventh-degree polynomil is known to hve roots i nd i. Wht is the mximum number of distinct rel zeros tht the polynomil could hve? ) In how mny wys cn kindergrteners sit in circle? ) If tn( ) ) 7 7 nd tn( ), wht is tn( )? 9. In the given tringle, 60 C. Find the length b. )

3 0. Given the vectors u, nd v 4, wht is the mgnitude of u - v? ) If the determinnt of ) b c d e f g h k is 0, wht is the determinnt of 6b c g h k d g e h f k. Find the domin of the function ) (,) (,) (, ) (,) (, ) [,) [,) (,) (, ) (, ) f( x) ( x ) 9 x x x 6. Wht is the period of the trigonometric function cot ) x

4 4. Simplify sin cos csc tn ) sin tn csc sec 7. If ( x y z ) is expnded, the coefficient of the ) x y z term will be 6. Convert sincos r to rectngulr form. ) x x y y 0 x x y y 0 x x y y 0 x x y y 0 x y x y 0 7. For the polynomil x 9x 8, find the sum of the possible positive roots given by the Rtionl Root Theorem. ) The function f( x) x x 6 x hs s n oblique symptote, the line ) y 0 y y x y x y x 4 4

5 9. Compute 4 ) 0 0 n n 0. Given tht the eqution of the circle is x y nd the ngle between OF nd the x- xis is, wht is the re of isosceles tringle EFG? ) cos sin cos sin cos cos sin cos sin. Wht is )

6 . If ) sin 0 wht is sin? You hve two investment choices: Invest your money t 7% compounded continuously, or invest your money t 7.% compounded dily (ssume 6 dys in yer). How mny more dys will it tke your money to double if you choose the 7% investment? ) The mth club consists of 6 girls nd 8 boys. If members re chosen t rndom, wht is the probbility tht exctly re girls? )

7 . Using the digrm, find ll vlues of g(x) if f(x)=4. ),, 4 4, 4 6. If sin nd is in qudrnt III, wht is the vlue of sec? ) 7. Find ll solutions to the following system of equtions: ) 9 9, 7 7, ,,, ,,,, ,,, ,,,,,,, x y x y 7

8 8. Write i i in stndrd form. ) i i i i 0 0 i 9. Which of the following functions is one to one, nd thus is invertible? ) x x x e x 4 x x x 0. A fixed point for function f(x) is number d such tht f(=d. Find ll fixed points for the function ) (, ) (, ) (, ) (, 0) (, ) f( x) x x. The distnce from the point (0, ) to the line x y = 7 is pproximtely: )

9 . The conjugte xis of hyperbol runs long the x-xis, nd the trnsverse xis hs length of 4 nd runs long the line x=. If one of the symptotes mkes 0-degree ngle with the x-xis, wht is the eqution of the hyperbol? ) ( x ) y 4 x y 4 y ( x ) 4 y ( x ) 4 y ( x ) Wht is the reminder when x 7x x is divided by x? ) Two gers, with rdii R = 0 nd r = 6, re connected by chin belt. If the lrger ger spins t 00 rottions per minute, wht is the ngulr speed of the smller ger in rdins per second? )

10 . Solve x b c 8 ) c c, b 4 b 4,, b 4 c b 4 c, c c, b 4 b 4, c c b 4, b 4 b 4 c, b 4 c 6. An re is contminted with cesium-7 nd now hs ten times the norml level of this rdioctive mteril. If the hlf-life of cesium-7 is yers, how mny yers will it tke until the level returns to norml? ) A regulr dodecgon (-sided figur is circumscribed bout circle of rdius. How long re its sides? ) 4 0

11 8. Find ll solutions to the eqution ) 4,,, cos 6 cos 4 cos in the intervl [0, ) 7,,, ,,,,, ,,,,, ,,,,,,, Find the minimum vlue of the prbol f ( x) x bx 4 ) b 4 b 4 8 b b Fctor x 4 x x ) 0 6 x ( x ) x x ( x ) ( x ) ( x )( x )( x i)( x i) ( x )( x )( x i)( x i)