Pre-AP Secondary Math 2 Summer Assignment Name:_____________________________

Due Date: First day of school- August 12, 2019

SUMMER ASSIGNMENT: The topics in this assignment should be a review of already mastered skills. This assignment does NOT reflect the difficulty level of the course. We strongly suggest that you take this assignment seriously. If you have difficulty with a question, DO NOT SKIP IT – RESEARCH IT. In addition to the Schoology course listed above, you may also refer to the websites below as a resource.

http://www.khanacademy.org http://www.regentsprep.org http://purplemath.com http://mathwarehouse.com http://mathopenref.com http://hippocampus.org http://mathisfun.com http://mathbitsNotebook.com http://tutorvista.com http://mathworld.wolfram.com http://nlvm.usu.edu/en/nav/vlibrary.html Directions for Completion: 1. Students are to complete these assignments individually

2. All answers must be exact, do NOT round unless specifically directed to do so on the assignment.

3. Copying from another student or from the internet, having someone else complete the problems, or getting specific answers from the internet will result in a ZERO for the assignment.

4. Showing your thinking is mandatory & work should be organized and clear. DO NOT create an answer column, the answer should be with the required work. If you do not have enough space on the worksheet to show your work, write the problem and work on binder or graph paper. If you use binder/graph paper, each section should be on a separate page with the title of the section at the top & each problem numbered. Answers without supporting work will result in a maximum of half credit.

5. Where no answer space is provided, answers must be clearly indicated by being either circled or boxed.

6. A ruler must be used to graph all lines.

Check off each completed section and write down any specific problem numbers on which you may have had difficulty. This is your opportunity to ensure that you have mastered the necessary prerequisite skills to be successful in this class. “I don’t get it”, “I didn’t learn this before”, “This is hard”, etc. are not acceptable excuses. It is your responsibility to review and learn material that you do not understand.

Assignments: Questions Score (for teacher use)

� Computation Review pg. 1 _____________ _______

� Properties of Exponents/Interval Notation pg. 2 _____________ _______

� Solving Equations pg. 3 _____________ _______

� Graphing Functions pg. 4-6 _____________ _______

� Representations of Functions pg. 7 _____________ _______

� Function Notation pg. 8-10 _____________ _______

� Arithmetic and Geometric Sequences pg. 11-12 _____________ _______

� Linear and Exponential Functions pg. 13-15 _____________ _______

� Triangle Congruence pg. 16-17 _____________ _______

SUMMER ASSIGNMENT TEST: You will be tested on the topics from the Summer Assignment on Friday, August 16th. There will be NO RETAKES for a poor score, so get any help that you require prior to this test. The test will assess mastery & retention of the prerequisite math skills needed to succeed in Pre-AP SM2.

Page | 1

Computations Review- No Calculators Should be Used!

Evaluate the following expressions:

1. 4 5 42+ − 2. 6 2 6

3+ 3. 43

4 2−

− 4. 81 4

4+ −

Find the distance between each pair of points:

5. ( ) ( )5, 5 ; 5,0− − − 6. ( ) ( )5,8 ; 2,5− 7. ( ) ( )4,8 ; 6,2 8. ( ) ( )1,3 ; 6, 4− −

Solve each system by Substitution:

9. 2 2 108 23

x yx y− =+ = −

10. 3 2 17 13

x yx y− + =− = −

Solve each system by Elimination:

11. 9 2 2

18 10 10x y

x y− = −

− + = 12. 9 6 24

8 9 3x y

x y− =

− + = −

Find the missing side length of each triangle. Leave your answers in simplest radical form.

13. 14. 15. 16.

17. 5, ?, 14a b c= = = 18. ?, 8, 16a b c= = = 19. 13, ?, 14a b c= = = 20. 11, 13, ?a b c= = =

Page | 2

Properties of Exponents/Interval Notation- No Calculators Should be Used!

Fill in the blanks to expand each expression:

1. 34 = 2. 5 a = 3. ( )33 d = 4.

3 7x =

Fill in the blanks to evaluate each expression:

5. ( )333 − = = = 6. ( )2

25 6

−− = = =

Simplify each expression:

7. 08x 8. 25− 9. yx 214 −− 10. ( )325x−

11. ( )45 23x y− 12. 7

3

xx

13. 3

265

xyx y−

14. ( )321

2323cbacba

−

−

15. 32 5 4 ⋅− 16. 36

3 543

x yx y

17. 9

3

4

23

1215

98

xyx

yyx −

− ⋅ 18. 03−

Rewrite the inequality in interval notation:

19. 3x > − 20. 2 8x< ≤ 21. 5x <

22. 1 6x− ≤ ≤ 23. 4 14x< < 24. 2 or 3x x≤ − >

Page | 3

Solving Equations

Solve each equation, showing each step and justifying your work:

Example:

1. 99x

= 2. 2 16m− − = −

3. 38 19 n− = − − 4. 219n=

5. 16 17 m= + 6. 40 2n− =

7. ( )7 1 2 119x− = 8. ( )128 2 8 1 2b b− = − + −

9. ( )3 5 7 111m− − − = − 10. ( )103 5 4 6 3k= − + − −

Properties of Equality:

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Graphing (use a ruler for lines)

Page | 5

Graphing (continued)- Use a table as needed

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Graphing (continued)- Use a table as needed

Page | 7

Multiple Representations of Functions

Page | 8

Function Notation

Page | 9

Function Notation (continued)

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Function Notation (continued)

Page | 11

Arithmetic & Geometric Sequences

Use the diagram below to answer questions 1-4

1. What type of sequence is represented?

2. What is the recursive function for the sequence above?

3. The explicit function for the sequence above is ________________?

4. How many dots would there be on day 5?

5. If 𝑓𝑓(1) = 6, 𝑓𝑓(𝑥𝑥) = 𝑓𝑓(𝑥𝑥 − 1) × 3, write the first 5 terms of this sequence

____________ , ___________ , ___________ , ___________ , __________

6. If 𝑓𝑓(𝑥𝑥) = −3𝑥𝑥 + 9, then f (-2) = ____________

Use the sequence below to answer questions 7 - 10. Let f (1)=2

2 , 5 , 8 , 11 , 14 , …

7. The sequence above is a(n) _____________________________ sequence.

8. Write the recursive function for the sequence above. ______________________________

9. Write the explicit function for the sequence above. _________________________________

10. Find the 100th term of the sequence. _________________

Page | 12

Arithmetic & Geometric Sequences (continued)

11. What is the recursive function for the sequence 1 , 5 , 9 , 13 , 17 , … ?

12. Which explicit function best matches the recursive function

𝑓𝑓(1) = −4 ,𝑓𝑓(𝑥𝑥) = 𝑓𝑓(𝑥𝑥 − 1) + 4 ?

a. 𝑓𝑓(𝑥𝑥) = −4𝑥𝑥 + 4 c. 𝑓𝑓(𝑥𝑥) = 4𝑥𝑥

b. 𝑓𝑓(𝑥𝑥) = 4𝑥𝑥 − 4

d. 𝑓𝑓(𝑥𝑥) = 4𝑥𝑥 − 8

13. Write the first five terms of the sequence represented by the equation 𝑓𝑓(𝑥𝑥) = 3𝑥𝑥 − 4.

14. Write the explicit equation for the sequence 1 , 2 , 4 , 8 , 16 , …

Use the following information to answer questions 15-17:

Today I have $500 and put it on my credit card. My card has an interest rate of 12% each month. The interest is added to my debt at the end of each month.

15. Write a recursive equation that best describes the situation above.

16. Write an explicit equation that best describes the situation above.

17. If I don’t make a payment on my credit card, and just let the debt build up, how much debt will I have on my card after 6 months?

Page | 13

Recursive Rule: Graph

Explicit Equation:

Table:

Recursive Rule: Graph

Explicit Equation: 12xy −=

Table:

Story Context:

Linear & Exponential Functions

You are given one representation, fill in the remaining four:

1. Linear:

2. Exponential:

Page | 14

Linear & Exponential Functions (continued)

Page | 15

Linear & Exponential Functions (continued)

Page | 16

Triangle Congruence

Page | 17

Triangle Congruence (continued)