Algebra 2 Mid-Year Exam Name



Camden Catholic High School

Incoming Pre-calculus Course Number 327

Summer Math Practice 2020

This packet is designed to review and refresh previously learned material from Algebra I and Algebra 2. This packet should be handed in on the first day of class and you will be tested on this material within the first week of the school year. It is highly recommended that you not only put your best effort and show all work, but make note of topics that you still have difficulty with so you can seek help and clarification from your instructor. Please see the following pages.

PART 1 – Mark each Question as True or False. If False, state the reason why or show a counter example.

1. – 4.5 [pic] – 4

2. [pic]

3. [pic]

4. [pic] is an example of the Distributive Property

5. [pic]

6. [pic] is equivalent to – 3 < x – 1 < 3

7. The slope(m) of the line 2x + 3y = 6 is [pic]

8. [pic]

PART 2 – Multiple Choice. Choose the letter that represents the best answer.

_______ 1. Evaluate: x ( y – 1 ) 2 if x = 3 , y = 4

A. 11 B. 27 C. 51 D. 81

_______ 2. Which absolute value inequality represents numbers at least 5 units from 1 ?

A. [pic] B. [pic] C. [pic] D. [pic]

_______ 3. Find the slope of the line containing the points ( 4 , – 3 ) and ( – 2 , 5 ).

A. [pic] B. [pic] C. [pic] D. [pic]

_______ 4. Find the slope of the line 2x + 5y = 8

A. [pic] B. [pic] C. [pic] D. [pic]

_______ 5. The degree of the monomial 8x y 2 z 2 is:

A. 3 B. 4 C. 5 D. 6

_______ 6. The degree of the polynomial – 3x 4 + 2x 3 y 2 + 3x 2y 2 + 2x y 3 + y 4 is:

A. 4 B. 5 C. 18 D. 21

_______ 7. Simplify. ( x 3 – 3x 2 – 2x + 5 ) – ( x 2 – 2x + 2 )

A. – x 2 + 7 B. x 3 – 4x 2 – 4x + 3

C. x 3 – 2x 2 – 4x + 3 D. x 3 – 4x 2 + 3

_______ 8. Simplify. x y 2 ( x + y ) – x 2 y ( y – x )

A. x y 3 + x 3 y B. x y 3 – x 3 y C. 2 x 2 y 2 D. 0

_______ 9. Express ( 2x – 3a ) ( x + 2a ) as a simplified polynomial.

A. 2 x 2 – 6a 2 B. 2 x 2 + ax – 6 a 2 C. – 4 a 2 x 2 D. 2 x 2 – 7ax – 6a2

_______ 10. The slope of the line perpendicular to the line described by the equation [pic] is

A. [pic] B [pic] C. [pic] D. [pic]

_______11. Simplify: [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

_______12. Simplify: [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

_______13. Simplify: [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

_______14. Express 0.00345 in scientific notation

A. [pic] B. [pic] C. [pic] D. [pic]

_______15. Which of the following is a rational algebraic expression ?

A. [pic] B. [pic] C. [pic] D. both A and B

_______16. Simplify: [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

_______17. Simplify: [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

_______18. Simplify: [pic]

A. [pic] B. [pic] C. [pic] D. [pic]

_______19. Find a one-significant-digit estimate for: [pic]

A. 4000 B. 400 C. 40 D. 4

_______20. Which of the following is a complex fraction ?

A. [pic] B. [pic] C. [pic] D. both A and C

_______21. In the expression [pic] the number 4 is called the ? .

A. index B. root C. radical D. radicand

_______22. Find the real roots of the equation y 2 – 7 = 0.

A. [pic] B. [pic] C. [pic] D. no real root

_______23. Simplify: [pic]

A. [pic] B. 225 C. 45 D. 75

_______24. Simplify: [pic]

A. ± 2 B. 2 C. – 2 D. 512

_______25. Use synthetic division to find the remainder when [pic] is divided by x – 1

A. – 2 B. 0 C. 2 D. 6

_______26. Find an x 3 equation that has roots of 2 , 2 , and – 3.

A. [pic] B. [pic] C. [pic] D. [pic]

_______27. What number must be added to the expression x2 + 3x to complete the square?

A. [pic] B. [pic] C. 9 D. 3

_______28. Describe the nature of the roots of the equation [pic]

A. two imaginary roots B. one imaginary root C. two real roots D. one real double root

_______29. Find the roots of [pic].

A. [pic] B. [pic] C. [pic] D. [pic]

_______30. If the solution set for z = { 4 , 9 } and z = x2 , what is the solution set for x ?

A. [pic] B. [pic] C. [pic] D. [pic]

_______31. Find the vertex of the parabola y – 4 = 2 ( x + 7 ) 2.

A. ( – 7 , 4 ) B. ( 4 , – 7 ) C. ( 7 , – 4 ) D. ( – 4 , 7 )

_______32. The quadratic function identified by [pic]opens in which direction?

A. Down B. Left C. Up D. Right

_______33. In the quadratic function identified by [pic]

A. the vertex is (4, -3) and it is a minimum

B. the vertex is (-3, 4) and it is a minimum

C. the vertex is (-3, 4) and it is a maximum

D. the vertex is (4, -3) and it is a maximum

PART 3 – Show All necessary equations and work. Put answers in space provided here.

1. Simplify. 5 ( 3x – 2y ) – 4 ( 6y – x ) + 10

1 __________________________________

2. Solve for x. 3x + 10 – 7x = 9x + 15

2. x = _____________

3. Solve and graph the solution set of this inequality.

– 7 < 4y + 1 < 15

4. Graph the equation (on the grid here). Give the coordinates of the x-intercept and the y-intercept

3x – 2 y = 12 x-int ( , 0 ) y-int ( 0 , )

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

5. Solve the system of equations by linear combinations method or by the substitution method.

[pic]

5. x = ____________ y = ______________

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |6. Graph the system of inequalities on the grid provided here

[pic]

7. Sam asked a bank teller for $710 worth of Travelers Checks in $20 and $50 amounts. If the teller handed her 22 Travelers checks, how many of each denomination did she receive?

$20 Travelers Checks ________ $50 Travelers Checks ________

8. The perimeter of a basketball court is 266 feet and its length is 35 feet more than its width. What are the dimensions of the court?

Simplify and write without zero or negative exponents

9. [pic] 10. [pic]

9. _______________________ 10. ________________________

11. [pic] 12. [pic]

11. _________________________ 12. ________________________

Solve the equation for m.

13. [pic]

13. m =

Simplify each radical expression

14. [pic] 15. [pic]

14. _________________________ 15. _________________________

Find the real roots of the equation. If there is an extraneous root, say so.

16. [pic]

16. x =

17. Solve the equation by Completing the Square or by using the Quadratic Formula

[pic]

{ }

18. For the function defined by this formula, [pic], find the following:

a. Vertex _____________

b. Axis of Symetry ___________

c. Graph opens in which direction? ___________

d. Vertex is a __________ (min/max)

e. Coordinates of the y-intercept ___________

f. Coordinates of the x-intercept(s), if it/they exist_________; ________

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19. For the function defined by this formula, [pic], find the following:

a. The function in the [pic]format is ___________________________

b. Vertex _____________

c. Axis of Symetry ___________

d. Graph opens in which direction? ___________

e. Vertex is a __________ (min/max)

f. Coordinates of the y-intercept ___________

g. Coordinates of the x-intercept(s), if it/they exist_________; ________

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Some Helpful Information

Exponent Rules Quadratic Formula

[pic] [pic]

Perfect Square Trinomial[pic]Square of a Binomial

[pic] [pic][pic]

[pic] [pic][pic]

Difference of Two Squares[pic] Sum [pic] Difference

[pic] [pic][pic]

Equations of Lines Exponent Rules

slope (m) = [pic] [pic]

slope / y-intercept form

y = m x + b

point / slope form

[pic]

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