Free Printable Algebra 2 S2 Final Review

1.

Which of the following is a factor of x²-10x+24?

a)

x-4

b)

x+4

c)

x+6

d)

x-2

2.

Factor:
x²+ 7x - 30

a)

(x + 10)(x - 7)

b)

(x - 10)(x + 3)

c)

(x + 10)(x + 3)

d)

(x + 10)(x - 3)

3.

Factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

4.

Factor
v² - 6v + 9

a)

(v-3)²

b)

(v-6)²

c)

(v-9)(v+6)

d)

not factorable

5.

Factor completely.
3x² + 10x - 8

a)

(3x + 2)(x + 4)

b)

(7x + 5)(x + 2)

c)

(3x - 2)(x + 4)

d)

(7x - 3)(x - 4)

6.

Factor completely.
5x² - 7x + 2

a)

5(x - 2)(x + 1)

b)

(5x - 2)(x + 1)

c)

(7x - 1)(x - 4)

d)

(5x - 2)(x - 1)

7.

Factor:
x² - 9

a)

(x + 3)(x - 3)

b)

(x + 3)²

c)

(x - 3)²

d)

(x+3)(x+3)

8.

Which of the following is a factor of 3x² - 7x + 2?

a)

x - 1

b)

x - 2

c)

3x - 2

d)

3x + 1

9.

What do you call a polynomial that cannot be factored?

a)

FOIL

b)

Simplified

c)

Prime

d)

Proper

10.

6m² + 16m

a)

2(3m² + 8m)

b)

2m(3m + 8)

c)

2m(3m - 8m)

d)

not factorable

11.

Factor the following
12x³y⁴z²+14x⁴yz-6x⁵y⁴z²

a)

2x³yz(6xy³z+7x-3x²y³z)

b)

6x³yz(2y³z+2x-1x²y³z)

c)

2x²y²z(6y³z+7x-3x²y³z)

d)

2xyz(6x²y³z+7xyz-3x²y³z)

12.

Which of the following binomials is not a difference of squares?

a)

x² - 64

b)

x² - 16

c)

x²+ 400

d)

x² - 100

13.

Factor by grouping:
$x^3-4x^2-4x+16$

a)

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

b)

$\left(x-4\right)\left(x^2-4\right)$

c)

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

d)

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

14.

Factor by grouping:

4p^3+8p^2+3p+6

a)

$\left(2p^2+3\right)\left(p+2\right)$

b)

$\left(2p^2+6\right)\left(p+4\right)$

c)

$\left(4p^2+3\right)\left(p+2\right)$

d)

$\left(4p^2+8p\right)\left(3p+6\right)$

15.

Factor by grouping:

x^3+7x^2-2x-14

a)

$\left(x^2-2\right)\left(x-7\right)$

b)

$\left(x^2+2\right)\left(x+7\right)$

c)

$\left(x^2+2\right)\left(x-7\right)$

d)

$\left(x^2-2\right)\left(x+7\right)$

16.

Solve by factoring: x² - 9x + 20 = 0

a)

x = -4 and x = -5

b)

x = 20 and x = -9

c)

x = 4 and x = 5

d)

x = -4 and x = 5

17.

Solve by factoring: x² + 3x - 18 = 0

a)

x = -3 and x = 6

b)

x = 3 and x = -6

c)

x = -9 and x = 2

d)

x = 9 and x = -2

18.

Solve for n by factoring.

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

19.

What is the first step in solving
(x + 2)(x - 3) = 0 ?

a)

Plug in zero for x

b)

Solve for x

c)

FOIL

d)

Set each binomial factor equal to zero

20.

Solve by taking the square root:

x² = 49

a)

-7

b)

7

c)

49

d)

±7

21.

x² -4 = 77

a)

9

b)

-9

c)

No Real Solutions

d)

±9

22.

Solve by taking the Square Root:

16a² - 9 = 0

a)

a = ± ³/₄

b)

a = ± ⁴/₃

c)

a = ± ⁹/₁₆

d)

a = ± ¹⁶/₉

23.

$4r^2-10=-26$

a)

$2$

b)

$-4$

c)

$\pm2i$

d)

$\pm i\sqrt{2}$

24.

Solve by taking square roots:

k² - 6 = -50

a)

k = ±4i√11

b)

k = ±4√11

c)

k = ±2i√11

d)

k = ±2√11

25.

Simplify:
(10+ 15i)-(48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

26.

Simplify:
(7 + 2i)(9 - 6i)

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

27.

a)

10

b)

-10

c)

10i

d)

-10i

28.

What does i² = ?

a)

-1

b)

√-1

c)

1

d)

-√1

29.

Simplify:
3√-81

a)

-27

b)

3i√3

c)

27i

d)

9i

30.

Simplify
2i - 7i + 10

a)

-5i+10

b)

5i

c)

9i+10

d)

5i+10

31.

What do you do to the b value to correctly complete the square?

a)

square it

b)

divide it by 2 and square the result

c)

divide it by 2 and take the square root of the result

d)

divide it by 2 only

32.

To solve by completing the square, what needs to be moved in this equation?
x² = 9 - 4x

a)

the -4x

b)

the 9

c)

the x²

33.

What is the first step to solving THIS equation by completing the square?
a² + 10a + 21 = 0

a)

Set the equation equal to zero

b)

Divide 10 by 2 and add the result to both sides

c)

Add a² and 10a together

d)

Subtract the 21

34.

When factoring
x² - 4x + 4 = 20,
what goes in the blank?
(x - __ )² = 20

a)

4

b)

2

c)

8

d)

20

35.

Complete the Square
x² + 6x = 5

a)

(x + 3)² = 5

b)

(x + 6)² = 9

c)

(x + 3)² = 14

d)

(x + 6)² = 14

36.

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}

37.

What is this?

a)

This is the speed of light formula.

b)

This is the quadratic formula.

c)

This is the zero product property.

d)

This is scary.

38.

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

39.

Identify the 'a' value: y = 16x² -8x -24

a)

16

b)

8

c)

-8

d)

-24

40.

Solve 8x² - 6x + 1 = 0

a)

No Solution

b)

0 or 1

c)

-0.5 or -0.25

d)

0.25 or 0.5

41.

Solve 2x² + 7x - 15 = 0

a)

-1.5 or 5

b)

No Solution

c)

-5 or 1.5

d)

0.7 or 5

42.

Use the quadratic formula to find the solutions for

y = 2x² - 9x + 5

a)

-8.14 and 6.14

b)

-4.07 and 3.07

c)

3.9 and 0.6

d)

ZERO solutions

43.

If path of a projectile is modeled by:
h(t) = -16t² + 20t +6, what is the height after 1 second?

a)

6 feet

b)

20 feet

c)

10 feet

d)

4 feet

44.

To calculate the TIME that a maximum height occurs, you should use:

a)

-b/(2a)

b)

Quadratic formula

c)

the c value

d)

0

45.

For that same projectile, at what TIME does the maximum height occur?
h(t) = -16t² + 20t + 6

a)

0 seconds

b)

.625 seconds

c)

160 seconds

d)

2 seconds

46.

To calculate the maximum height, you should:

a)

Use the time you got from -b/(2a) and plug it in for each "t"

b)

-b/(2a)

c)

use the c value

d)

use the b value

47.

If we are trying to find out when an object hits the GROUND, what should we put in for "h"?

a)

0

b)

1

c)

2

d)

3

48.

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation
s(t) = –16t² + 64t + 80.
What will be the object's maximum height?

a)

2 ft

b)

80 ft

c)

144 ft

d)

64 ft

49.

Classify by the DEGREE:
3x - 2

a)

1

b)

2

c)

3

d)

4

50.

Classify the expression with its most specific name.

a)

Monomial

b)

Binomial

c)

Trinomial

d)

Polynomial

51.

Put the polynomial in standard form.

7xy - 12y² + 8xz + 5x²

a)

5x²+7xy + 8xz - 12y²

b)

- 12y²+ 5x²+ 7xy + 8xz

c)

5x² - 12y² +7xy + 8xz

d)

- 12y²+ 7xy + 8xz + 5x²

52.

Simplify: (m⁹)²

a)

m¹¹

b)

2m⁹

c)

m¹⁸

d)

m^4.5

53.

Simplify: (-5p)²

a)

-25p²

b)

25p²

c)

-5p²

d)

5p²

54.

Simplify: (5p⁹q³)(2pq⁷)

a)

7p¹⁰q¹⁰

b)

10p⁹q²¹

c)

10p¹⁰q¹⁰

d)

10p⁸q^-4

55.

Simplify: 7p⁰

a)

7

b)

1

c)

simplified

d)

7p

56.

a)

y¹⁶⁰

b)

y¹

c)

1

d)

y⁴

57.

a)

b)

16c³d³

c)

d)

58.

Divide:

(4x² - 24x + 35) / (2x - 5)

a)

2x - 7

b)

2x - 12

c)

2x + 12

d)

2x + 7

59.

$\frac{6x^2+19x+3}{x+3}$

(a)

60.

$\frac{15x^2+19x+6}{5x+3}$

(a)

61.

(f + g) (x)

a)

5x² + 3x

b)

4x² + 3x

c)

5x² - 3x

d)

4x² - 40x

62.

(f - g)(x)

a)

5x² + 3x

b)

-3x² - 13x

c)

3x² + 3x

d)

-3x² + 3x

63.

Find $\left(f\cdot g\right)\left(-2\right)$

a)

3375

b)

-432

c)

-205

d)

450

64.

f(x) = 3x + 10
g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

65.

If f(x) = 3x-1 and g(x) = x²+2,

what is (f ° g)(x) ?

a)

3x² +5

b)

x² +1

c)

3x² +1

d)

3x² +6

Algebra 2 S2 Final Review

Total questions: 65

Worksheet time: 5hrs 48mins

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