Math 151 Project 1 (60 points) Due Thursday 20 th September
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1 Mat 151 Project 1 (60 points) Due Tursday 0 t September Students Name: Tis Project is to elp you to review some of te concepts from Precalc I and II tat you will use in tis class. Tese questions need to be done by and but you may ask te Tutors and your fellow students to elp you solve any of tese problems, but it is important tat you are able to do all of tese types of questions on your own as we will be using all of tem at some point during te course. Section I- Multiple Coice 1. Te epression wen factored fully is:- A. (3 1)( 3) B. (3 1)( + 3) C. (3 + 1)( 3) D. (3 + 1)( + 3). Te epression 100y 00 wen factored fully is:- A. 100(y ) B. 100(y + )(y ) C. (y + 0)(y 0) D. Can t be factored 3. Te epression a b 3 8a 3 b 3 wen factored fully is:- A. a b 3 (1 a) B. a b 3 ( a) C. a b 3 ( 8a) D. ab(ab a b ) E some oter answer. Te epression wen factored fully is:- A. (3 + 8)( + ) B. (3 )( + ) C. (3 )( ) D. (3 + )( + ) E some oter answer 5. Simplify A 16 B C 1 D 6. Add and simplify te following epression A 1 B 1 C D
2 7. Te equation of te line tat passes troug te points A(1,7) and B(,1) is A. y 5 B y ½ + C y + 5 D y ½ Simplify te following radical epression 8 A. B C. 1 D Te quadratic equation as te following number of real number solutions A 0 solutions B 1 solution C solutions D 3 solutions 10. Te solution(s) to te quadratic equation is:- A 5 and 5 B. 65 C. 5 D 1.5 and 1.5 Section II 1. Evaluate te following functions Give your answer as an eact value in its simplest form (a) For f() + 7 evaluate f( 10) (b) For g() 1 evaluate g() (c) For () sin cos cos() evaluate ( ) (d) For () (e sin )(e + cos ) evaluate (0)
3 . For te function f() (a) Find an epression for f(a) (b) Find an epression for f(a + ) (c) Find and simplify an epression for f ( a ) f ( a) 3. For te function f() 3 (a) Find an epression for f(a) (b) Find an epression for f(a + ) (c) Find and simplify an epression for f ( a ) f ( a)
4 . Te following question is for a graping calculator. No working is needed. For te function f() 3 + using -values in te interval (-10,10) answer te following questions. (i) List te intercepts? Answer -intercepts are.. (ii) List te y intercept. Answer y-intercept is.. (iii) Give te coordinates of any local minimums (if tey eist). Answer. (iv) Give te coordinates of any local maimums (if tey eist). Answer. 5. Find te quotient and remainder for te division divided by + 1
5 6. Factor eac of te following epressions as muc as possible. (a) (b) 9 (b) Solve te equation cos 3cos (Give all solutions in te range 0 ) 8. Verify te identity (sin t cos t) sec t csc t
6 Mat 151 Project 1 Solutions Section I 1. A. B 3.A.B 5.B 6.B 7.C 8.D 9.A 10. A Section II 1. Evaluate te following functions Give your answer as an eact value in its simplest form (a) For f() + 7 evaluate f( 10) f( 10) ( 10) ( 10) (b) For g() g() 1 () evaluate f() (c) For () sin cos cos() evaluate ( ) ( ) sin cos cos( ) + 0 undefined (d) For () (e sin )(e + cos ) evaluate (0) (0) (e 0 sin 0)(e 0 + cos 0) (1 0)(1 + 1) (1)()
7 . For te function f() (a) Find an epression for f(a) a a (b)find an epression for f(a + ) (a + ) (a + ) a + a + a (d) Find and simplify an epression for f ( a ) f ( a) a +a+ a (a a) a +a+ a a +a a+ (a+ ) a + 3. For te function f() 3 (a) Find an epression for f(a) a 3 (b) Find an epression for f(a + ) f(a + ) (a + ) 3 (a + )(a + ) (a + )(a + a + ) a 3 + 3a + 3a + 3 (c) Find and simplify an epression for f ( a ) f ( a) f ( a ) f ( a) a 3 +3a +3a + 3 a 3 3a +3a + 3 (3a +3a+ ) 3a + 3a +
8 . Te following question is for a graping calculator. No working is needed. For te function f() 3 + using -values in te interval (-10,10) answer te following questions. (i) List te intercepts? Answer -intercepts are (0,0) and (1,0) (ii) List te y intercept. Answer y-intercept is (0,0) (iii) Give te coordinates of any local minimums (if tey eist). Answer (1,0) (iv) Give te coordinates of any local maimums (if tey eist). Answer (0.333,0,18) 5. Find te quotient and remainder for te division divided by Quotient Remainder Note: Remember tat we get by subtracting ( ) 6. Factor eac of te following epressions as muc as possible. (a) ( 5 + 6) ( 3)( ) (b) 9 ( + 3)( 3) (c) ( )( ) ( + )( ) ( + )( ) ( + ) ( ) 7 Solve te equation cos 3cos (Give all solutions in te range 0 ) cos 3cos (cos 1)(cos 1) 0 cos 1 0 and cos 1 0 cos ½ cos 1 π 3 5π 3 Quadrant I Quadrant IV 0 and π Solutions in te range 0 are 0, π, 5π 3 3 and π
9 (sin t cos t) 8. Verify te identity sec t csc t LHS (sin t cos t) sin t cos t sin t cos t 1 1 sin t cost sec t csc t RHS
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