Rising HONORS Algebra 2 TRIG student Summer Packet for 2016 (school year )

Transcription

1 Rising HONORS Algebra TRIG student Summer Packet for 016 (school ear ) Welcome to Algebra TRIG! To be successful in Algebra Trig, ou must be proficient at solving and simplifing each tpe of problem in this packet. This is a review of Algebra 1 and important topics in Geometr. Upon returning to school in the fall, ou are epected to have completed this assignment. We will correct and review during the first das of class, and then ou will have an assessment on this content during the first few weeks of school. Please make sure to show all work for each problem to receive full credit. Calculators are not on this assignment. TI-84 calculators will be utilized for some units during the school ear and it is highl recommended that ou have one available for use at home. Algebra Trig is an advanced diploma course and an honors course with a.5 GPA addition upon completion with units that are designed for students preparing for the Math Analsis to BC Calculus. It is important that ou maintain all pre-requisite skills. We will not have time to spend re-teaching the content in this packet. Make sure ou are comfortable with this material. Lots of space has been provided for ou. Enjo our summer and good luck! Full Name

2 Properties: Match the following properties with the eamples. The answer choices can be used once, more than once, or not at all. Write our answer on the line with a CAPITAL letter. A B C D E F G H I Commutative Propert Associative Propert Additive Identit Multiplicative Identit Distributive Propert Refleive Propert Smmetric Propert Transitive Propert Multiplicative propert of zero If m = t and t =, then m = 0 = r 0 (8)(5) = (85) If 5 = 0 then 0 = 5 ( + ) = + 6(a + 6) = 6a = 9 + = + = 9 5 = 9 5 Order of Operations: Evaluate the following epressions. All work must be documented below. 5 4 Given and 5 ( ) 5 Given 1 m ( ) Given m and 4 1 Given 5 6

3 Distribution: Simplif b distributing and collecting like terms. REMEMBER: It is epected that ou show all work and ever step all ear! (4 + 6) Distribute across,show distributive first.. cop other parts Collect like terms This is an epression, Do not use an equal sign! You cannot solve for! Not part of distribution -4, 8m bring down 7( + ) + 8 5(m + 9) 4 + 8m 6m (m 5) (4 + 4) m + (5 + m) 5m 4(m + 6) ( 5m) Substitute the given value for the variable and evaluate the epression. Use parentheses to replace our missing variable, then insert the value ( ), then enter value to reduce sign errors. = 4, =, m = 1, p = 6p + ( + 5) ( ) ( ) 6( ) + [( ) + 5( )] State whether each equation is true or false for the value of the variable given. 5 8 = for = 6 4 (5) = 1 for = 5( ) 8 = 4( ) (5) = 1 Substitute the given value for the variable and evaluate the epression. = 4, =, m = 1, p = m + ( + ) +

4 Simplif. To reduce careless errors, distribute our sign, then.. collect like terms. It is important that ou begin to show all of our work to receive credit. (z + z 4) + ( z + z ) (10b b + ) (4 b + 5b + 1) ( 4m + m 1) ( m + ) (m + 4) ( m 6m + 5) (g 4gh 10 h ) (5g gh 4 h ) Solve the equations. Show each step! 5(1 5) + 5( 8 ) = 4 8 = 1 = 4( 6 ) = Eplain and show the difference between: Make sure ou understand eponent rules! ( m )(4m ) ( m ) + (4m ) Simplif the Epressions below: a(a + 1) + (a + 1)(a 1) ( + )( + 5) (4 1)

5 Eponents: Simplif the epression. (Give answers in terms of positive eponents:) a 4ab 8b 14 7 z r w h r (6m) (m ) 4 ( z )

6 = + ; when = 6,, 0, 1 Graph the function and fill out the T-chart: show work finding (, ) Put domain in set notation: { : = } Put range in set notation: { : = } Graph the line = 5 Describe our line here: Can ou graph this on the calculator? In the table, give a sample of possible points What do ou notice? Graph the line = Describe our line here: Can ou graph this on the calculator? In the table, give a sample of possible points What do ou notice?

7 Solving the inequalit and graph. Write the solution set. 7( v) > (v 8) 4( ) > ( + 4) 9 (b 1) (b + 1) > b + 7 5( 1) 5 4 < 1 9 > 11 or 9 1 Find the slope of the line that passes through ( 4, 5) and (6, 7) Write the formula and show our work:

8 Graphing lines: Solve for first, showing all of our steps. = Solve for here: Slope = Line direction: Y intercept: Line parallel through ( 1, ) = m + b Line Perpendicular thru (,4) 4 16 Solve for here: Slope = Line direction: Y intercept: Line parallel through ( 1, ) Line Perpendicular thru (,4) 1 Solve for here: Slope = Line direction: Y intercept: Line parallel through ( 1, ) Line Perpendicular thru (,4)

9 1 Solve for here: Slope = Line direction: Y intercept: Line parallel through ( 1,)and(,5) Line Perpendicular thru ( 6,)and ( 1, 4 8 Solve for here: Slope = Line direction: Y intercept: Line parallel through ( 1, ) Line Perpendicular thru (,4) Solve for here: Slope = Line direction: Y intercept: Line parallel through ( 1, ) Line Perpendicular thru (,4)

10 Graph and solve the sstem of inequalities. Solve for, graph, dashed or solid line, shade

11 Graph and solve the sstem of inequalities Find the solution to the following sstem equations? Write as coordinate pair. 6 1 = = 16 + = 6 + = 6 + = 8 = 4 8 = 4 4 = What tpe of sstem of linear equations would be a set of parallel lines? A) Inconsistent sstem B) Consistent sstem C) Consistent, Dependent sstem

12 Find the product. ()( 6) (w 5)( w 6w 1) (k 4 g)(k 4 g) ( ) Factoring Directions: Factor completel

13 Solve b factoring. 6 = 0 5 = = = = 0 = 6 Solve using the quadratic formula. If necessar, round to the hundredths = = 0 b± b 4ac a 4 = = 0 Find the zeros of the polnomial function. m 14m w 16w 0 n n n f ( ) 5 g( ) 4 45 Find the value of the discrimant. Then use it to decide how mam different real-number roots the equation has. + = = = 0

14 Graph and illustrate our understanding of intercepts: f ( ) 10 g ( ) 5 1 h( ) 4 g() = z = 6z Solve the equation and write the answer in a solution set: + = 56 Solution Set:

15 Find the value of each variable. Write our answers in simplest radical form. Do not change an of the values to decimals. EXACT means leave it in a radical.

16 The entire fourth quarter will be dedicated to completing the trigonometr section of the course to prepare students for math analsis. It would be valuable if ou were ver familiar with the unit circle! The trig material will not be on an assessment until Quarter 4. Fill out the chart below: sin cos tan csc sec cot

17 Use reference to find EXACT value, thus no decimals! sin cos 4 4 cos 5 sin 4 5 sin 6 7 cos 4 cos 5 sin 11 sin 6 sin 7 cos 6 cos There are some good videos here. Focus on learning the ver basics and understanding wh the values what the are from our knowledge of SOH-CAH-TOA. Begin to move towards utilizing,, r values instead.

18 Enjo our summer! Algebra Trig TEAM!