Summer Work Packet for MPH Math Classes

Transcription

1 Summer Work Pcket for MPH Mth Clsses Students going into Pre-clculus AC Sept. 018 Nme:

2 This pcket is designed to help students sty current with their mth skills. Ech mth clss expects certin level of number sense, lgebr sense nd grph sense in order to be successful in the course. These problems need to be completed in the spce provided nd hnded in for grde by September 7 th. Be sure to show ll work. Plese emil me t dmeehn@mphschool.org with ny questions. ************************************** ** You will need TI-84 clcultor for this clss.** ********************************************

3 Liner Functions & Inequlities 1. Given: 6x 4y = 1. A. Find the coordintes of the x-intercept: nd y-intercept:. B. Use these to clculte the slope. m = C. Write the eqution of line prllel to the given line nd going through the point (0, ). D. Grph both lines below.

4 . Given: m = ½ nd A (, 5) A. Write the eqution of the line in point-slope form: B. Write the eqution of the line perpendiculr to the given line going through the point (4, 5) in point-slope form.. Given: (y ) = ¾(x + 5) A. Nme point on the line. P (, ) B. Find the slope. m = C. Find f( 9). f( 9) = 4. Grph the inequlities. Nme the points of intersection. Lbel the solution re. Show your check to verify the shded re is correct. y > ⅔x nd y x nd x <

5 System of Equtions Solve for the vribles using the elimintion method. Check. 1. 5k + 9h = 1. + b + c = 6 6k + 4h = + b c = b + c = Solve for the vribles using the substitution method. Check.. y = 5x 1 5x y = 14

6 Algebr Review: Simplify completely x 1 4x. 1 b b x y 16x y 4x y 4 4x y

7 4. (y 108)( y y 4y) y( y 1y 6)(y 0y 7) (Leve your nswer in fctored form.) 5. m 4 m m 1 m 1 (Leve your nswer in fctored form.) 6. b c bc bc

8 7. m n n m n m n m (Leve your nswer in fctored form.) (Leve your nswer in fctored form.) b b b b b b b b b b b (Leve your nswer in fctored form.)

9 10. 6x 4y x x x d d 4 11d x 1 1 x x 1

10 Algebr Review: Solve nd check. 14. w + 8w + 7 = b + 1b = 7b 16. p + p 8p 4 = h 18. c c c c c c c

11 Functions Fill in the blnks with rule to represent different situtions. Write two tht represent function nd one tht do not. Explin why ech is or is not function. Ex. 1: The number of lods of lundry I do is function of the number of people t home during the week. Ex. : The frction of the pool tht is filled with wter is function of the mount of time the hose hs been filling it. Ex. : The ge of ech person in the clss is dependent on the numbers 15, 16 nd 17. (More thn one person could be ech ge, or someone could be different ge.) 1. is Function? Yes or No? Why?. is Function? Yes or No? Why?. is Function? Yes or No? Why?

12 Odd nd Even Functions Prove lgebriclly tht the function is odd, even or neither. Choosing numericl vlue for x does NOT prove odd/even. It must be shown true for ALL vlues of x. Follow the exmple. Definition: f(x) is odd, if f ( x) = f (x). f(x) is even, if f ( x) = f (x). Otherwise, the function is neither odd nor even. Exmple: f(x) = 4x 5x Find f( x): f( x) = 4( x) 5( x) = 4x + 5x. Thus, f( x) f(x). Find f(x): f(x) = (4x 5x) = 4x + 5x. Thus, f(x) = f( x) nd the function is ODD. 1. f(x) = 6x 4. f(x) = 1 4x. f(x) = x 4 5. f(x) = x 1 x. f(x) = (x 5) 6. f(x) = x x + x 1

13 Qudrtic Inequlities nd Sign Ptterning Use the number lines to indicte the sign of ech fctor. From this, determine the intervls of x vlues which mke the inequlity true. x( x ) ( x ) EXAMPLE 1: 4x 4x + 4x EXAMPLE : 0 4x 4x 4x 0 4x (x x 6 ) 0 4x (x )(x + ) 0 Use the sme number lines becuse multipliction nd division with negtive numbers hve the sme rules. fctor vlue: negtive negtive 0 positive positive fctor 4x x vlues: - 0 negtive negtive negtive 0 positive (x ) - 0 negtive 0 positive positive positive (x + ) - 0 expression: negtive *0 positive 0 negtive 0 positive x(x )(x + ) - 0 Therefore, the solution set for Exmple 1 is {x x 0 or x }. Therefore, the solution set for Exmple is {x x < or 0 < x < }. (Exmple is undefined t x =.*)

14 Find the solution set using the sign ptterning method. Grph the solution on number line. 1. w 7w < 0 k 6 k c c 0 5 x x x g g 8 g ( p)(4 p)(7 p) > 0

15 Logrithms-Solve & check. Show work. 1. log 4 ( x 1) 4. log 5( x 4) log 5(x). log ( x ) 5 5. log( x 1) log( x ) 1. log 5( x ) log 5(4x 6)

16 Reference Angles & Trig Functions 1) Using the unit circle, give the exct vlue of ech trigonometric expression. Py ttention to the sign of the nswer (no clcultor). ) On the unit circle mrk the letter of ech problem in the correct ngle position. Letter is done for you. ) sin(π) 0 b) cos(5π/4) c) tn(11π/6) d) cot(π/) e) sec(1π/) f) csc(8π) g) sin(41π/6) h) tn( 7π/) i) csc( 19π/4) j) cos(14π) k) sec(1π/4) l) tn(19π/) m) cot( 17π) n) sin(47π/) o) cos( 11π/6) p) sin( 7π/4)

17 Grphing Functions Grph the following functions on the grph below. Be sure to lbel your xes nd identify the scle on ech xis. Do ech pir in the question on the sme set of xes. 1. y = x y = ½ x. y = x y = x

18 . y = x y = x 4. y = log (x) y = log (x) +

19 5. y = sin(x) y = cos(x) Grph from π to π. Use 6 BLOCKS = π on the x-xis nd BLOCKS = 1 on the y-xis. (If you use your clcultor, be sure to put it in rdin mode nd use ZOOM TRIG for the window.)