Free Printable Spring Final Review

1.

If a system of equations has no solution, what does the graph look like?

a)

intersecting lines

b)

parallel lines

c)

same lines

2.

How Many Solutions

$y=-\frac{1}{2}x+1\ and\ \ y=\frac{1}{2}x-5$

a)

None

b)

1

c)

2

d)

Infinite

3.

How many solutions

y=5x + 7 and y=5x + 7

a)

None

b)

1

c)

2

d)

Infinite

4.

Use substitution to find the solution for the system:

x=6y-11

3x-2y=-1

a)

(1, 2)

b)

(8, 7)

c)

(3, -1)

d)

(3, 0)

5.

Use elimination to find the solution for the system:

2x+y=25

-2x+3y=-13

a)

(11, 3)

b)

(5, 7)

c)

(3, 2)

d)

(0, 13)

6.

What is the solution to the system?

a)

(0, 3)

b)

(1, -1)

c)

(-3, 1)

d)

(1, 3)

7.

Find the solution of the system given:

5x + 4y= −14

y = −7x − 15

a)

(-2, -1)

b)

(1, -2)

c)

(-2, 1)

d)

(-1, -2)

8.

You have a total of 17 coins. All of your coins are nickels and dimes. The total value of the coins is $1.35. Which system of equations represents this situation?

a)

n+d=17
.05n+.10d=1.35

b)

.05n+.10d=17
n+d=1.35

c)

.25n+.10d=1.35
n+d=17

9.

How many solutions does this system of equations have?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

d)

Two Solutions

10.

John was 20 feet away and was running 5 feet per minute. Alex was 50 feet away and was 3 feet per minute. Write a system of two equations for this situation?

a)

y = 5x + 20

y = 3x + 50

b)

y = 20x + 5

y = 50x + 3

c)

y = 5x + 50

y = 2x + 20

d)

y = 50x + 5

y = 20x + 3

11.

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

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

12.

Select the graph for y ≥ -3.

a)

A

b)

B

c)

C

d)

D

13.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, -10)

c)

(-1, 5)

d)

(5, 20)

14.

Which of the following equations match the given graph?

a)

y < 2/5x + 1

b)

y ≥ -2/5x + 1

c)

y ≤ 2/5x + 1

d)

y ≥ -2/5x - 1

15.

a)

y < 5x + 1

b)

y > 5x + 1

c)

y ≤ 5x + 1

d)

y ≥ 5x + 1

16.

Simplify.
5⁰

a)

5

b)

1

c)

0

d)

5⁰

17.

Simplify

(2m⁴)(5m²)

a)

10m⁶

b)

10m⁸

c)

7m⁶

d)

7m⁸

18.

Evaluate

a)

b)

c)

d)

19.

Simplify.

a)

b)

c)

d)

20.

Simplify

a)

b)

c)

d)

21.

Simplify.

a)

b)

c)

d)

22.

For the quotient rule, you need to ____________ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

23.

a)

2 / x²

b)

-2x²

c)

2x²

d)

2x¹⁴

24.

(x⁸)(x^-5)

a)

x^-40

b)

x^-13

c)

x¹³

d)

x³

25.

a)

A

b)

B

c)

C

d)

D

26.

$\sqrt{\frac{15}{16}}$

a)

$\frac{15}{4}$

b)

$\frac{\sqrt{15}}{4}$

c)

$\sqrt{\frac{240}{4}}$

d)

$\frac{5}{2}$

27.

Simplify:

√72

a)

√72

b)

2√2

c)

6√2

d)

4√18

28.

Which of the following in NOT a perfect square?

a)

49

b)

81

c)

111

d)

144

29.

Simplify:
√96

a)

16√6

b)

6√16

c)

9√6

d)

4√6

30.

Express this cube root in simplest form:

$\sqrt[3]{500}$

a)

$5\sqrt[3]{4}$

b)

$4\sqrt[3]{5}$

c)

$10\sqrt[3]{5}$

d)

$5\sqrt[3]{10}$

31.

Express this cube root in simplest form:

$\sqrt[3]{-648}$

a)

$3\sqrt[3]{6}$

b)

$-6\sqrt[3]{3}$

c)

$-3\sqrt[3]{6}$

d)

$6\sqrt[3]{3}$

32.

$\sqrt{98a^{20}c^{15}}$

a)

$7c\sqrt{a^{10}c^7}$

b)

$7a^{10}c^7\sqrt{2}$

c)

$49a^{10}c^7\sqrt{2c}$

d)

$7a^{10}c^7\sqrt{2c}$

33.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

34.

(2x + 3)(x² + 4x + 1)

a)

2x³ + 10x² + 14x + 4

b)

2x³ + 11x² + 14x + 3

c)

-2x³ - 11x² + 14x + 5

d)

x³ - 11x² + 14x + 3

35.

Simplify:

(x-7)²

a)

x²-49

b)

x²+49

c)

x²-14x+49

d)

x²-14x-49

36.

Find the sum.
(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x -4

c)

2x² + 5x -7

d)

-2x² + 11x -4

37.

Find the difference.
(3- 2x + 2x²) - (4x -5 +3x²)

a)

x_² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

38.

Name the polynomial by its term.

a)

quadratic polynomial with four terms

b)

quartic trinomial

c)

9th degree polynomial with four terms

d)

quartic polynomial with four terms

39.

Name the polynomial by its degree.

a)

quadratic trinomial

b)

quartic trinomial

c)

quadratic binomial

d)

quintic trinomial

40.

Name the polynomial by its degree.

a)

quintic binomial

b)

quadratic binomial

c)

cubic binomial

d)

quartic binomial

41.

Name the polynomial by its term.

a)

constant monomial

b)

linear monomial

c)

quartic monomial

d)

4th degree monomial

42.

Name the polynomial by its term.

a)

quartic trinomial

b)

quadratic trinomial

c)

4th degree trinomial

d)

6th degree trinomial

43.

Factor
n²-13n+40

a)

(n-5)(n-8)

b)

(n+5)(n-8)

c)

(n-5)(n+8)

d)

(n+6)(n+1)

44.

Identify all the factors of the expression 18x²-9x-5.

Select all that apply.

a)

2x+5

b)

6x-5

c)

18x-5

d)

3x+5

e)

3x+1

45.

Find the factors of

5m² - 45m + 90

a)

3(m + 1)(m + 8)

b)

5(m - 3)(m - 6)

c)

2(m - 7)(m + 3)

d)

5(m - 5)(m + 3)

46.

What is the GCF of the polynomial
24x⁹ - 36x⁶ + 60x³?

a)

6x

b)

6x³

c)

24x⁹

d)

24x

47.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

48.

Factor completely:

5n³-10n²+3n-6

a)

(5n²+3)(n-2)

b)

(5n²-3)(n-2)

c)

(5n³+3)(n-2)

d)

10n(n²-6)

49.

Factor completely:

81m² - 1

a)

not factorable

b)

(m-9)(m+9)

c)

9m(9m-1)

d)

(9m-1)(9m+1)

50.

Factor completely:

3x² - 7x + 2

a)

(x - 1) (3x + 2)

b)

(x - 2) (3x -1)

c)

(x - 1) (3x - 2)

d)

(x + 2) (3x + 1)

51.

Factor completely:

4h² - 12h + 9

a)

(2h - 3)²

b)

4(h + 9)(h + 1)

c)

(2h - 3)(2h + 3)

d)

(h - 9)(4h - 1)

52.

Solve by finding square roots and simplify completely:
$x^2+20=0$

a)

$x=-20$

b)

$x=\pm2\sqrt{5}$

c)

$x=-2\sqrt{5}$

d)

No real solutions

53.

Solve by factoring:
$x^2+2x-15=0$

a)

$x=3\ or\ x=-5$

b)

$x=\pm\sqrt{13}$

c)

$x=-3\ or\ x=5$

d)

No real solutions

54.

Solve the equation:

$x^2\ =\ 1\ -\ x$

a)

$x\ =\ \frac{1\ \pm\ \sqrt[]{5}}{2}$

b)

$No\ Solution$

c)

$x\ =\ \pm1$

d)

$x\ =\ \frac{-1\ \pm\ \sqrt[]{5}}{2}$

55.

Solve the equation:

$x^2\ -\ 8x\ -\ 5\ =\ 0$

a)

$x\ =\ -4\ +\ \sqrt[]{21}$

b)

$x\ =\ -4\ -\ \sqrt[]{21}$

c)

$x\ =\ 4\ +\ \sqrt[]{21}$

d)

$x\ =\ 4\ -\ \sqrt[]{21}$

56.

How many solutions does this graph have?

a)

one

b)

two

c)

no real solutions

d)

cannot be determined

57.

How many solutions does this graph have?

a)

one

b)

two

c)

no solutions

d)

cannot be determined

58.

Solve: $20x=5x^2+20$ by factoring

a)

$x=0$ and $x=2$

b)

$x=-2$

c)

$x=2$

d)

$x=2$ and $x=-2$

59.

Solve by factoring.

n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

60.

Solve by using a method of your choice:

k² − 12k + 23 = 0

a)

{6 + √13, 6 - √13}

b)

{-6 + √13, -6 - √13}

c)

{6 + √59, 6 - √59}

d)

{-6 + √59, -6 - √59}

61.

Solve the equation:
5x² - 35x + 60 = 0

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

62.

Solve the equation:
4x²+2x - 6 = 0

a)

x = 1 & -1.5

b)

x = -1 & 1.5

c)

x = (-2 ±√92)/8

d)

x = (-2 ± √100)/8

63.

A parabola has a vertex at (-3,2). Where is the axis of symmetry?

a)

y = -2

b)

x = 3

c)

x = -3

d)

y = 2

64.

Which answer choice describes y = -3x² +7x - 2 accurately?

a)

opens up with a maximum

b)

opens up with a minimum

c)

opens down with a maximum

d)

opens down with a minimum

65.

Find the y-intercept of f(x) = 2x²-2x + 1

a)

2

b)

-2

c)

1

d)

-1

66.

What is the vertex of this parabola?

a)

(−1, 3)

b)

(−3, 11)

c)

(−2, 5)

d)

(0, 5)

67.

Given the equation above, find h(-3).

a)

-13

b)

5

c)

-23

d)

23

68.

Solve by factoring
3m² - 2m = 1

a)

{4/5, 3}

b)

{1/5, 5/2}

c)

{3/2, 1}

d)

{-1/3, 1}

69.

Select the TRUE statements.

a)

Range: All Real Numbers

b)

minimum: (3,-4)

c)

zero (1,0) and (5,0)

d)

Domain: (-4, infinity)

70.

What is the domain and the range for the graph?

a)

Domain : -2 ≤ x ≤ 2
Range : 0 ≤ y ≤ 4

b)

Domain : 0 ≤ x ≤ 4
Range : -2 ≤ y ≤ 2

c)

Domain : All real #s
Range : y ≤ 4

d)

Domain : -2 ≤ x ≤ 2
Range : y ≤ 4

71.

Determine the vertex of the parabola:
y = 5x²- 20x + 13

a)

(5, -7)

b)

(-2, -7)

c)

(2, -7)

d)

(-7, -2)

Spring Final Review

Total questions: 71

Worksheet time: 4hrs 50mins

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