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Name__________________________ Period_____ Date______________________

Pre-AP Algebra I Spring 2017 Final Exam Review 1. Solve the following systems by graphing. Write the solution(s).

a. 432 -= xy b. y – 1 = 2x c. y = 4x21

- d. x = 4

y = 4 y = 2x – 4 2y = x- y – x = 1 2. Solve each of the following systems of equations by using elimination or substitution. Show your work and write as ordered pairs. a. 3x – y = 8 b. x + 2y = 49 a. –2x + y = 3 b. x + 3y = 11 y = 4 x = 5y 2x + 3y = 13 4x + 3y = 8 3. Write two equations to represent the problem and then solve the system.

a. The band sold a total of 184 turkeys and hams at Christmas to raise money for their trip to Carnegie Hall. They collected $2738 for the $18 turkeys and the $11 hams. How many hams did they sell?

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b. The math club and science club had fundraisers to buy supplies for a hospice. The math club spent $135 buying six cases of juice and one case of bottled water. The science club spent $110 buying four cases of juice and two cases of bottled water. How much did each case of juice cost?

c. Christy has a coin collection consisting of nickels and dimes. She has 28 coins worth $2.25. How many of each coin does Christy have?

4. Graph each of the following inequalities.

a. y > 2x - 5 b. x < -1 c. y x£ - -32

3 d. –2y > -3x + 6

5. Graph each system of inequalities. Write 1 solution to each system.

a. 5x3y1x4y

-£

+-³ b. 4y

3xy<

+> c. 42

£+

->

xyxy

d. 4£>

yxy

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6. For each of the following: i) Write the polynomial in standard form. ii) Name the polynomial by its degree. iii) Name the polynomial by the number of terms.

a. -5x2 + 2x3 + 3x b. 3 – 9x c. 9x2 d. 9 e. 9x2 – 3x4 + 2

7. Simplify the expressions. a. (3x2 + 5x – 6) + (2x2 – 4x + 2) b. (4x3 – 3x2 + 2) – (2x3 + 5x + 2) c. (4x3 – 2x) – 5(3x3 – 5x) d. 4(2x + 7) e. t(5t2 + 6t) f. 6x2(9x3 + 6x – 8) g. 2g2(g2 + 6g + 5) h. (3x + 4)(x – 7) i. (x + 5)(x – 2) j. (x2 + 5x – 7)(3x – 2) k. (3x + 2)(3x - 2) l. (2x + 5)2

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8. Factor out the GCF. a. 6x2 + 9 b. 4w4 + 8w3 – 12w2 c. b2 – b d. 8p3 – 24p2 + 16p 9. Completely factor the polynomials.

a. x2 + 13x + 42 b. x2 - x + 6 c. x2 – 9x + 20 d. x2 – 17x + 70

e. 3x2 + 2x – 5 f. x2 – 36 g. 25x2 – 49 h. 6x2 + x – 2

10. Solve each of the following by factoring.

a. y2 – 7y – 18 = 0 b. x2 + 8x – 48 = 0 c. x2 –10x + 24 = 0

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d. 3x2 = 5x e. 25m2 – 36 = 0 f. x2 – 8x = -12

11. Solve each of the following by quadratic formula.

a. y = 6x2 – 5x + 10 b. y = 7x2 – 15 c. y = 3x - x2

12. Solve each of the following by the method of your choice (factor, quadratic formula, complete the square).

a. x2 – x – 12 = 0 b. 2x2 – 11x = 6 c. x2 = -12x – 36 d. x2 + 4x + 13 = 0

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13. Order the following quadratic functions from narrowest (1) to widest (5).

y = 31

x2 ; y = -12x2 ; y = 5x2 ; y = -8x2 ; y = 21

x2

14. Graph and analyze the quadratic functions.

a. y = -x2 b. y = x2 + 1 c. y = -2x2 + 4 d. y = 21 x2 – 1

Vertex:_____ Vertex:_____ Vertex:_____ Vertex:_____ max/min max/min max/min max/min Axis of Symmetry: ____ Axis of Symmetry: ____ Axis of Symmetry: ____ Axis of Symmetry: ____ y-intercept_____ y-intercept_____ y-intercept_____ y-intercept_____

e. y = 3x2 f. y = 31

(x + 1)2 – 2 g. y = 4(x – 2)2 h. y = 21

- x2 + 1

Vertex:_____ Vertex:_____ Vertex:_____ Vertex:_____ max/min max/min max/min max/min Axis of Symmetry: ____ Axis of Symmetry: ____ Axis of Symmetry: ____ Axis of Symmetry: ____ y-intercept_____ y-intercept_____ y-intercept_____ y-intercept_____

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15. Create a quadratic function to match each situation.

a. Wider than y = 12

2x with a vertex at (0,-2)

b. The same size as y = 3x2 + 5 translated 8 units down c. Narrower than y = x2 with a vertex at (0,8) and opening downward d. A quadratic with an a = 4 , b = 0 and c = 5 e. The equation of the function y = (x + 2)2 – 2 translated to the right 3 units and down 5 units.

16. A skyrocket is shot into the air. It height h in feet t seconds is given by the function

h = -16t2 + 128t. In how many seconds will the rocket reach its maximum height and what is its maximum height? 17. Solve for x by using square root properties.

a. x2 = 81 b. 2x2 + 5 = 7 c. 3x2 – 4 = -16 d. 3x2 – 8 + 2x2 = -8

e. 13

2 102x - = f. 2(x – 1)2 + 4 = 6 g. 3(x + 2)2 = 27

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18. For each exponential function, find

i) the initial amount ii) the growth/decay factor iii) the percent of growth/decay

a. y = 5(0.03)x b. y = 1.5x c. y = 10,000(2.20)x d. y = 80(1.01)x

19. Determine the exponential function to represent each of the following. Then find the amount after 10 years.

a. Attendance at minor league baseball teams’ games has been declining by 3.5%. At the beginning of the study it was determined that 5750 people on average were attending.

b. A population of 18 kangaroos increases at a rate of 12% per year.

20. Identify each function as modeling exponential growth or decay, and then find the percent of increase or decrease.

a. y = 2(4)x b. y =x

56

21

÷øö

çèæ c. y = 3(0.68)x d. f(x) = 5(1.025)x

Growth / Decay Growth / Decay Growth / Decay Growth / Decay Percent: _____ Percent: _____ Percent: _____ Percent: _____ 21. Write the following numbers in scientific notation.

a. 141,600,000 b. 383,000 c. 0.000000678 d. 0.0047 22. Write the following numbers in standard notation.

a. 49.2 10• b. 70.05 10• c. 71.25 10-• d. 50.42 10-•

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23. Simplify the following expressions.

a. x2•x-5 b. 30 c. 9x4•4x2•3y-2 d. –2x5•3y3•(-4x3) •5y e. x6 f. 12x12 g. 2x4•3x2 h. –12x5•3y x4 24x9 7x-3•3w 3x3•4y2 i. (x3)10 j. ((x4)5)-2 k. ((x4)3(y2)3)2 l. (2x)3(y4)3

m. (3x2y3)3 n. (-7x2)2 o. (3x2y4)2•(2x3y3)2 p. (5x2y)2•(4x3)2

24. Completely simplify each of the following.

a. 20 b. ( )332 c. 353 cba d. 82 125 xx e. 2

5

996aa

f. 12 3 2• g. 2739 ba h. 4924 i. 4204 x j. 3205

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25. Add/Subtract each of the following. Write answers in simplest radical form.

a. 5520 + b. 27 4 3+ c. 4 6 3 6- d. 362412 -+

26. Solve each of the following equations.

a. 64x =+ b. 3x55x3 -=- c. 4x231x52 +=- d. x34x +=

e. 25x2 =- f. 12x3x -= g. 1x2x -= h. x39x2 -=+

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27. A right triangle has legs with lengths a and b and hypotenuse with length c. Find the missing value. Leave answers in simplest radical form. (Use 𝒂𝟐 + 𝒃𝟐 = 𝒄𝟐)

a. a = _____ b = 8, c = 10 b. a = 4, b = ______, c = 8 c. a = 10, b = 10, c = _______

28. Simplify the following rational functions.

a. x2 − 36x2 +12x + 36

b. 8x2y2zxz3

÷ 10xyx4z

c. x2 −16x − 4

• x +1x2 −1

d.

'()*'+,

+ -'+*

e. ''.+/'+*

− /'+*

29. A baseball diamond is a square. The distance between consecutive bases is 90 feet. a. How far does a catcher have to throw the ball

from home plate to second base? b. How far does a third baseman throw the ball to the

first baseman from a point in the baseline 15 feet from third to second base?

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30. Given the following triangles, find the missing side lengths.

a.

b.

c.

d.