Free Printable Evaluation 1

1.

Simplify (3a³b³)(4ab²)²

a)

48a⁵b⁷

b)

144a⁴b⁵

c)

144a⁶b¹²

d)

48a⁸b¹⁰

2.

Expand and simplify (x + 2)³

a)

x³+ 8

b)

x³+ 6x²+ 12x+ 8

c)

x³+ 6x²+ 8

d)

x³+ 4x²+ 8x+ 8

3.

Factor x³y - 4xy

a)

x(x²y - 4y)

b)

x²(xy - 4y)

c)

xy(x² - 4)

d)

xy(x - 2)(x + 2)

4.

Solve the equation x²- x - 12 = 0

a)

-3, 4

b)

12

c)

1, 12

d)

3, -4

5.

When solved, which equation gives 1 as a result?

a)

none

b)

x + 5 = 14 - x/2

c)

2x/(x + 1) = (2x - 1)/x

d)

x²+ 4x + 3 = 0

6.

Solve the following equation for w

5w + 5 = -90

a)

19

b)

-19

c)

17

d)

-17

7.

Solve for k

-20 = k - 2 + 8k

a)

-2

b)

2

c)

-3

d)

3

8.

Solve for p

4(p - 2) = 2(p + 5)

a)

1

b)

6

c)

8

d)

9

9.

Solve the equation for x:

a)

x = -1/4

b)

x = 1/3

c)

x = -3/4

d)

x = 3/4

10.

Factor the Trinomial:
x² - 8x + 15

a)

(x + 5) ( x + 3)

b)

(x - 5) (x - 3)

c)

(x + 15) (x - 1)

d)

(x - 7) (x - 8)

11.

Factor
x²+ 12x + 36

a)

(x + 6)(x +6)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 6)(x - 6)

12.

Factor:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

13.

The area of a rectangle is
(x² + 17x+42) ft².
If its width is (x + 3) ft.
What is its length?

a)

(x + 17) ft

b)

(x + 14) ft

c)

(x - 14) ft

d)

(x - 17) ft

14.

Factor completely:

3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

15.

Factor Completely.
$4x^2+24x-64$

a)

$4\left(x+8\right)\left(x-2\right)$

b)

$4(x^2+6x-16)$

c)

$4\left(x^2+24x-16\right)$

d)

$4\left(x-8\right)\left(x+2\right)$

16.

Determine the values of
a, b, and c for
the quadratic equation:
4x² – 8x = 3

a)

a = 4, b = -8, c = 3

b)

a = 4, b =-8, c =-3

c)

a = 4, b = 8, c = 3

d)

a = 4, b = 8, c = -3

17.

Solve using the quadratic formula.
2x² - 9x - 35 = 0

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

18.

Solve using the Quadratic Formula:
x² + 4x + 3 = 0

a)

x = 1 and x = 3

b)

x = 6 and x = -2

c)

x = -1 and x = -3

19.

Solve:
2x² - 9x = 35

a)

x = 7/2, x = -6

b)

x = -5/2, x =5

c)

x = -3/7, x =6

d)

x = -5/2, x = 7

20.

What method would you use to solve $x^2-16=0$

a)

Factoring Method

b)

Completing the Square Method

c)

Quadratic Formula

d)

Square Root Method

21.

Solve the following system of equations using the elimination method:

a)

(-2, 1)

b)

no solutions

c)

(-2, 0)

d)

(-1, -3)

22.

Solve the following system of equations using the elimination method.

a)

infinite solutions

b)

(0, -2)

c)

no solutions

d)

(0, 2)

23.

Solve for x and y
3x + 2y = 16
7x + y = 19

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

24.

Solve the system of equations by substitution.
y = -4x + 5
y = 3x - 16

a)

(-3, -25)

b)

(3,-7)

c)

(11, 17)

d)

(21, 47)

25.

Solve the system using any method.
−4x − 4y = 0
4x + 4y = 0

a)

(−6, −4)

b)

Infinite number of solutions

c)

No solutions

d)

(6, 4)

26.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. Which system of equations represents the situation?

a)

3x + 2y = 315
2x + 4y = 450

b)

3x + 2y = 450
2x + 4y = 315

c)

2x + 2y = 315
3x + 4y = 450

27.

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes. How long does it take her to do a haircut?
3x + 2y = 315
2x + 4y = 450

a)

45 minutes

b)

90 minutes
2x + 4y = 315

c)

60 minutes
3x + 4y = 450

d)

30 minutes

28.

Last season two running backs on the Steelers football team rushed a combined total of 1550 yards. One rushed 4 times as many yards as the other. Let x and y represent the number of yards each individual player rushed. Which system of equations could be used?

a)

x + y = 1550
y = 4x

b)

x + y = 1550
y = x + 4

c)

y - x = 1550
y = 4x

d)

y = 1550 + x
y = x + 4

29.

On Monday Joe bought 10 cups of coffee and 5 doughnuts for his office at the cost of $16.50. It turns out that the doughnuts were more popular than the coffee. On Tuesday he bought 5 cups of coffee and 10 doughnuts for a total of $14.25. Which equations could be used to determine the cost of the coffee?

a)

10c + 5d = 14.25
5c + 10d = 16.50

b)

10c + 5d = 16.50
5c + 10d = 14.25

c)

c + d = 10
5c + 10d = 16.50

d)

c + d = 5
5c + 10d = 16.50

30.

Factor
3v² - 4v - 7

a)

(3v-7)(v+1)

b)

3(v-7)(v-1)

c)

(3v+1)(v-9)

d)

(3v+1)(v-10)

31.

Solve: b² = -35 + 12b RE-ARRANGE AND FACTOR

a)

b = 5 and 7

b)

b = -5 and -7

c)

b = -5 and 7

d)

b = 5 and -7

32.

What is standard form of a quadratic Equation?

a)

Ax²+ Bx + C = 0

b)

Ax²+ B + Cx = 0

33.

A rectangle has an area of 2x² – 19x +45 ft². What are the dimensions of the rectangle?

a)

(2x - 9)(x - 5)

b)

(2x + 9)(x + 5)

c)

(2x - 5)(x - 9)

d)

(2x - 5)(x + 9)

34.

$2a\times2b$ =

a)

2ab

b)

4ab

35.

$9k-\left(-2k\right)=$

a)

9k+2k

b)

9k-2k

36.

Simplify: (2w⁻²)⁴

a)

2w⁶

b)

2/w^-8

c)

16/w⁸

d)

2w²

37.

$64^{\frac{1}{3}}$ Simplify

a)

262144

b)

8

c)

4

d)

105

38.

Rewrite the following as a sum:

(x+3)²

a)

x²+ 9

b)

x²-6x -9

c)

x²+ 6

d)

x²+ 6x + 9

39.

$\frac{14x^3y^2}{2x^4y}$ Simplify:

a)

$\frac{x^2y^2}{14y}$

b)

$14x^7y^9$

c)

$\frac{7y}{x}$

d)

Cannot be simplified

40.

Shirley starts with $85 in the bank and saves $15 every 2 months. What is the equation for the balance of the account?

a)

$y=85x+15$

b)

$y=15x+7.5$

c)

$y=15x-85$

d)

$y=7.5x+85$

41.

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

42.

Solve by completing the square:
k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

43.

solve:
4x²+16x+15=0

a)

-5/2,-3/2

b)

(2x+5)(2x+3)

c)

-10,-6

d)

5/2, 3/2

44.

Miked solved the equation x² + 8x = 14 by completing the square. Which of the following equations is part of the correct solution.

a)

(x + 4)² = 14

b)

(x + 4)² = 18

c)

(x + 4)² = 30

d)

(x+ 4)² = 30

45.

A ball is thrown into the air with an upward velocity of 100 ft/s. Its height, h, after t seconds is given by the function
h = -16t² + 64t + 960.
When did the ball hit the ground?

a)

10 seconds

b)

2 seconds

c)

5 seconds

d)

7 seconds

46.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

47.

Solve by factoring: 4x² + 11x - 3 = 0

a)

x = -3/4 and x = -1

b)

x = 4 and x = 3

c)

x = 1/4 and x = -3

d)

x = -1/4 and x = 3

48.

If a ball if thrown into the air is represented by the function
h(t) = -16t²+80t, where t represents the time in seconds and h(t) is the height of the ball in feet. Find the time it will take to reach its maximum height.

a)

8 mins

b)

2.5 seconds

c)

5 seconds

d)

604 seconds

49.

Which of the following situations could be descried by the equation y=120-25x?

a)

There are 120 people in the football stadium, and 25 more are entering each hour.

b)

A plumber charges $25 for a house call and $120 per hour.

c)

A teacher has 120 students. Her third period has 25 students

d)

There are 120 gallons of water in a tank. It releases water at a rate of 25 gallons per minute

50.

4x²- 64y²

a)

Prime

b)

( 2x - 32y) (2 x + 32y)

c)

( 2x - 8y) (2 x - 8y)

d)

( 2x - 8y) (2 x + 8y)

Evaluation 1

Total questions: 50

Worksheet time: 3hrs 49mins

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