Free Printable A1 Semester 2 Review

1.

Simplify by combining like terms:
5a + 2b - 3a + 4

a)

8a + 2b + 4

b)

2a + 2b + 4

c)

8ab

d)

4ab + 4

2.

5x + 3y + 5 + 4x + 3y + y + 8

a)

9x + 7y + 13

b)

6x + 2y + 2

c)

25x + 2y + 3

d)

x + 7y + 12

3.

Simplify by combining like terms:

7v + 2 + 2v = -12

a)

23

b)

23v

c)

9 + 14v

d)

9v + 14

4.

Solve for x

a)

x = 1/10

b)

x = 10

c)

x = 4

d)

x = 5

5.

Solve for x

a)

x = 16

b)

x = 28

c)

x = 1/26

d)

x = 26

6.

Solve the proportion:

a)

15

b)

5

c)

10

d)

12

7.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

8.

What inequality does the number line graph represent?

a)

$x>-1$

b)

$x<-1$

c)

$x\ge-1$

d)

$x\le-1$

9.

What inequality does the number line graph represent?

a)

$x>5$

b)

$x<5$

c)

$x\ge5$

d)

$x\le5$

10.

What inequality does the number line graph represent?

a)

$x>-6$

b)

$x<-6$

c)

$x\ge-6$

d)

$x\le-6$

11.

Find the slope of the line that passes through:
(6,7) and (4,2)

a)

2/5

b)

-5/2

c)

5/2

d)

-1/2

12.

Find the slope of the line that passes through:
(2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

13.

Find the slope of the line that passes through:
(10, 1) and (5, 2)

a)

1/5

b)

-1/5

c)

5

d)

-5

14.

-2 < x - 9 < 3

a)

x < 12

b)

7 < x

c)

7 < x < 12

d)

x > 7 or x < 12

15.

−6 < 2t − 5 < 3

a)

−0.5 < t < 1

b)

0.5 < t < −1

c)

−11/2 < t < 2

d)

11/2 < t < −2

16.

$-20<-10+x\le0$

a)

$x\le10$

b)

$-10<x\le10$

c)

$x>-10$

d)

$All\ Solutions$

17.

Evaluate the given function below for x = -1

f(x)=6x²-4,

a)

-2

b)

13

c)

2

d)

0

18.

Evaluate the given function below for x = 10

f(x)=-2x+13

a)

-7

b)

1

c)

-8

d)

7

19.

Evaluate the given function below for x = -1

f(x) = 2x² + 5x - 3

a)

f(-1) = -6

b)

f(-1) = 1

c)

f(-1) = -10

d)

f(-1) = -1

20.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

21.

Graph

a)

b)

c)

d)

22.

Which graph represents 2x + 4y = 12?

a)

b)

c)

d)

23.

3⁻⁴

a)

1 ⁄ 81

b)

-81

c)

81

d)

1 ⁄ 12

24.

Simplify.
s^-5⋅ s^-2

a)

s^-3

b)

¹/_s⁷

c)

s^-7

d)

¹/_s³

25.

Simplify.

a)

y⁶⁰

b)

¹/_y¹⁶

c)

y^-16

d)

y⁴

26.

Simplify

a)

42x⁵

b)

-42/x⁵

c)

42/x^-⁵

d)

42/x⁵

27.

Simplify the expression so that it contains only positive exponents.

a)

b)

c)

d)

28.

Write in simplified exponent form with no negative exponents.
$\frac{a^{-2}b^3}{a}$

a)

$\frac{b^3}{a^3}$

b)

$a^{-3}b^{-3}$

c)

$-\frac{b^3}{a^1}$

d)

$\frac{b^3}{a^1}$

29.

Simplify: $\frac{12x^5y^4}{2x^9y}$

a)

$6x^{-4}y^3$

b)

$\frac{6y^3}{x^4}$

c)

$\frac{12y^3}{2x^4}$

d)

$\frac{6x^{-4}}{y^3}$

30.

Simplify: $\frac{-15x^9}{10x^{17}}$

a)

$\frac{5}{x^8}$

b)

$\frac{-3x^8}{2}$

c)

$\frac{-3x^{-8}}{2}$

d)

$\frac{-3}{2x^8}$

31.

Simplify: $\frac{50r^6n^{-7}}{2n^2r^4}$

a)

$25r^4n^5$

b)

$\frac{25r^4}{n^5}$

c)

$\frac{25r^2}{n^9}$

d)

$25r^2n^{-9}$

32.

$\left(\frac{3x}{5m}\right)^{-2}$

a)

$\frac{3x^{-2}}{5m^{-2}}$

b)

$\frac{3x^2}{5m^2}$

c)

$\frac{-3x^2}{-5m^2}$

d)

$225x^2m^2$

33.

Simplify $\sqrt[]{40}$

a)

4√10

b)

10√4

c)

2√10

d)

10√2

34.

Simplify $\sqrt[]{24}$

a)

4√6

b)

3√8

c)

2√6

d)

6√2

35.

Simplify completely.

a)

8√3xy

b)

y√24xy

c)

8y√3xy

d)

8√24x

36.

$\sqrt[]{98}+5\sqrt[]{2}$

a)

8√3

b)

12√2

c)

7√2

d)

7√3

37.

Simplify:

a)

2√3√14

b)

4√42

c)

2√42

d)

4√3√14

38.

Simplify the expression:

a)

8√6

b)

6√6

c)

8√5

d)

64√6

39.

Simplify:

a)

240

b)

300

c)

340

d)

360

40.

Simplify completely.

a)

3v√2v

b)

3v√2v³

c)

v√18v

d)

9v√v

41.

$\frac{\sqrt{16x^5}}{\sqrt{2x}}$

a)

$\sqrt{8x^4}$

b)

$2x\sqrt{2}$

c)

$2x^2\sqrt{2}$

42.

$\frac{\sqrt{9xy}}{\sqrt{2x}}$

a)

$\frac{x\sqrt{18y}}{2x}$

b)

$\frac{\sqrt{18x^2y}}{2x}$

c)

$\frac{3\sqrt{2y}}{2}$

43.

Simplify each expression.

$\left(\frac{2a^4c^3}{5b^2d^2}\right)^2=$

a)

$\frac{4a^4c}{20b^4d^4}$

b)

$\frac{3a^8c^3}{24b^4d^4}$

c)

$\frac{4a^8c^6}{25b^4d^4}$

d)

$\frac{8a^3c^6}{18b^4d^4}$

44.

a)

A

b)

B

c)

C

d)

D

45.

a)

A

b)

B

c)

C

d)

D

46.

a)

3x³+8x

b)

x³+3x²+8x

c)

2x²+8x

d)

x³-3x³+8x²

47.

a)

4g²-2g

b)

4g²+4g-6

c)

6g²+2g+6

d)

4g²+2g

48.

a)

3y⁴+3y³+7y²+4y

b)

3y⁴+3y³+7y²+4y+6

c)

3y⁴+3y³+7y²+6

d)

3y⁴+3y³+7y²+4y-6

49.

a)

3n²+4n

b)

-3n²+4n

c)

3n²+20n

d)

3n²-4n

50.

a)

23x^5_11x

b)

-5x⁵-x

c)

23x⁵+11x

d)

5x⁵+x

51.

a)

2x²-13x-7

b)

2x²+13x+7

c)

-2x²-13x-7

d)

-2x²+13x-7

52.

a)

3x³+5x²+3x+15

b)

3x³+6x²+3x+16

c)

3x³+6x²+3x+15

d)

2x³+5x²+2x+16

53.

Simplify:
2x ( -2x -3)

a)

-4x - 3

b)

x² - 3

c)

-4x² - 6x

d)

-4x - 6

54.

(x +2)(x + 3)

a)

x² + 5x + 6

b)

x² + x + 6

c)

x² + 5x + 5

d)

x² + 6x + 6

55.

(x + 5)(x + 4)

a)

x² + x + 20

b)

x² + 20x + 9

c)

x² + 9x + 20

d)

x² - 9x + 54

56.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

57.

Multiply 7x²y³ (2x⁴y⁵+6xy³)

a)

14x⁸y¹⁵+42x²y⁹

b)

9x⁶y⁸+13x³y⁶

c)

14x⁶y⁸+42x³y⁶

d)

14x⁶y⁸+42x²y⁶

58.

(5c-2)(3c²-5c+4)

a)

15c³-31c⁴+30c²-8

b)

15c³-19c²+10c-8

c)

15c³-31c²+30c-8

d)

15c³-31c²+30c+8

59.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

60.

a)

5p²- 16p

b)

5p + 4

c)

5p - 4

d)

5p + 4p

61.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

62.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

63.

Divide the polynomial by the monomial.

a)

15x⁹ - 8x³

b)

3x⁶ - 8x³

c)

-5x¹²

d)

3x⁶ - 40x³

64.

Factor by using GCF:
8n³ + 2n²

a)

2n²(4n-1)

b)

2n²(4n + 1)

c)

n²(8n+2)

d)

3n(4n+1)

65.

Factor:
18a²-15a

a)

15a(3a-1)

b)

3a(6a-1)

c)

3(6a-5)

d)

3a(6a-5)

66.

Factor Completely: x²-17x+72

a)

(x-9)(x+8)

b)

(x-9)(x-8)

c)

x(x-3)

d)

(x+9)(x+8)

67.

Find the factors of

3b² + 17b + 20

a)

(2b - 5)(b - 7)

b)

(5b - 7)(b - 2)

c)

(b + 5)(3b + 4)

d)

(3b + 5)(b + 4)

68.

Factor
n² + 16n + 63

a)

(n-7)(n+4)

b)

(n+7)(n-9)

c)

(n-3)(n-10)

d)

(n+7)(n+9)

69.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

70.

x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

71.

Factor Completely: 5x²-11x+6

a)

(5x+6)(x-1)

b)

(5x-6)(x-1)

c)

(2x-7)(x-3)

d)

(5x-6)(x+1)

72.

Solve
a² + 2a - 24 = 0

a)

a = -6, 4

b)

a = 6, -4

c)

a = 12, -2

d)

a = 8, -3

73.

Solve 3x² - 192 = 0

a)

-32 or 32

b)

No Solution

c)

-8 or 8

d)

-64 or 64

74.

Find the zeros of the equation:
(x+10)(x-2) = 0

a)

10 and 2

b)

-2 and 10

c)

-10 and 2

d)

-2 and -10

75.

Factor and Solve

2x² - 3x - 2 = 0

a)

x = 1, x = -1

b)

x = -1/2, x = 2

c)

x = 1/2, x = 2

d)

x = 1/2, x = 1

76.

Solve

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

77.

True or false:
The solutions, roots, x-intercepts, and zeros of a quadratic equation are all the same thing.

a)

True

b)

False, because the solution and root are the same but the x-intercept and zero are different

c)

False, because the x-intercept and root are the same but the zero and solution are different

d)

False, they are all different

78.

What do we call the highest or lowest point of a quadratic?

a)

parabola

b)

vertex

c)

graph

d)

point

79.

The standard form of a quadratic function is

a)

y = ax² + bx + c

b)

a(x - h)² + k

c)

y - y₁= m(x - x₁)

d)

Ax + By = C

80.

Identify a, b, and c if y = +3x²+5x - 8

a)

a=3, b=5, c= - 8

b)

A=3, B=-8, C=5

c)

A=3x², B=5x, C=-8

d)

A=3x² , B=-8, C=5x

81.

Which equation is Vertex Form?

a)

y=ax²+bx+c

b)

y=a(x-h)²+k

82.

What is the vertex of this quadratic equation?

y = 2(x + 2)² + 5

a)

(-2,5)

b)

(2,5)

c)

(5,-2)

d)

(-5,-2)

83.

What are the x- intercepts?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

84.

What is the vertex?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

85.

What are the x-intercepts (solutions)?

a)

(-2,0) and (2,0)

b)

(0,-4)

c)

(-2,-4) and (2,-4)

86.

Which equations matches the graph above?

a)

$h\left(x\right)=\ \left(x+1\right)^2-4$

b)

$h\left(x\right)=-\left(x+1\right)^2-4$

c)

$h\left(x\right)=\left(x+4\right)^2-1$

d)

$h\left(x\right)=-\left(x+4\right)^2+1$

87.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

88.

What is the equation of this graph?

a)

f(x) = (x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) = (x + 1)² - 5

d)

f(x) = (x + 5)² +1

89.

Which expression below would you use to solve the equation $-3x^2+11x+21=0$ using the quadratic formula?

a)

$\frac{3\pm\sqrt{\left(-3\right)^2-4\left(11\right)\left(21\right)}}{2\left(-3\right)}$

b)

$\frac{11\pm\sqrt{11^2-4\left(-3\right)\left(21\right)}}{2\left(-3\right)}$

c)

$\frac{-3\pm\sqrt{\left(-3\right)^2-4\left(11\right)\left(21\right)}}{2\left(-3\right)}$

d)

$\frac{-11\pm\sqrt{11^2-4\left(-3\right)\left(21\right)}}{2\left(-3\right)}$

90.

Use the quadratic formula to solve $4x^2+10x+3=0$

a)

$\frac{-10\pm\sqrt{10^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}$

b)

$\frac{-4\pm\sqrt{4^2-4\left(10\right)\left(3\right)}}{2\left(4\right)}$

c)

$\frac{10\pm\sqrt{10^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}$

d)

$\frac{4\pm\sqrt{4^2-4\left(10\right)\left(3\right)}}{2\left(4\right)}$

91.

Solve the system:

4x+9y=28

-4x-y=-28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

92.

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

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

93.

Solve for x and y
y = 2x + 1
y = 4x - 1

a)

(1,3)

b)

(-1,-3)

c)

(-1,3)

d)

(3,1)

94.

Describe the transformations of f(x) when compared to the parent function.
f(x)=x²+5

a)

horizontal shift right 5 units

b)

horizontal shift left 5 units

c)

vertical shift up 5 units

d)

vertical shift down 5 units

95.

Match the equation to its description.

a)

Right 2 and up 2

b)

Left 2 and up 2

c)

Right 2 and down 2

d)

Left 2 and down 2

96.

Match the equation to its description.

a)

Reflected over x, right 2 and up 1

b)

Reflected over x, left 2 and up 1

c)

Reflected over x, right 2 and down 1

d)

Reflected over x, left 2 and down 1

97.

Describe the transformations of f(x) when compared to the parent function.
f(x)=(x+7)²

a)

horizontal shift left 7 units

b)

horizontal shift right 7 units

c)

vertical shift up 7 units

d)

vertical shift down 7 units

98.

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

a)

Vertical stretch by a factor of 5

b)

Vertical compress by a factor of 5

c)

Reflect over x-axis

d)

Vertical shift up 5 units

99.

What is the axis of symmetry and vertex for the following equation?

y = 4x²- 8x + 9

a)

x = -8

(-8, 329)

b)

x = 1

(1, 5)

c)

x = -1

(-1, 21)

d)

x = 2

(2, 9)

100.

Find the AOS and vertex of

f(x) = -x²- 4x + 12

a)

x = -2

(-2, 16)

b)

x =2

(2, 0)

c)

x = 2

(2, 4)

d)

x = -2

(-2, 4)

101.

What is the AOS and vertex of the quadratic function: y = x² - 6x + 11?

a)

x = 3

(3,2)

b)

x = -3

(-3,-2)

c)

x = -3

(-3,2)

d)

x = 3

(3,-2)

102.

Where is the AOS and vertex for

y = -2x²+4x+2

a)

x = 2

(2, 18)

b)

x = 1

(1, 8)

c)

x = -1

(-1, 0)

d)

x = 4

(4, 50)

103.

Find the AOS and vertex of the quadratic: y = -2x² + 4x + 3

a)

x = 0

(0, 3)

b)

x = -1

(-1, 5)

c)

x = 1

(1, 5)

d)

x = 1

(1, -5)

104.

A dolphin jumps from the water. The equation $h\left(t\right)=-8t^2+16t$ models the dolphin's height at any given time, t. You want to know the maximum height the dolphin jumps -- what do you need to find on the parabola?

a)

y-intercept

b)

x-coordinate of the vertex

c)

y-coordinate of the vertex

d)

x-intercept

105.

Your friend passes you the ball during a soccer game. The height off the ground is modeled by the equation $h\left(t\right)=-4t^2+12t$ . You want to know when the soccer ball will hit the ground -- what part of the parabola do you need to find?

a)

y-intercept

b)

x-coordinate of the vertex

c)

y-coordinate of the vertex

d)

x-intercept

106.

A frog is sitting on the ground when he is scared by a big dog. The movement of the frog is modeled by the equation

h = -6t² + 6t where h is the frog's height at any given time, t. How high does the frog jump?

a)

0.5

b)

1

c)

1.5

d)

2

e)

5

107.

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t²+ 90t gives the height h of the ball after t seconds.
What is the maximum height of the ball?

a)

126.56 ft

b)

5.625 sec

c)

2.81 sec

d)

90 ft

108.

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

109.

Find the dimensions of the rectangle shown.

a)

$x=\left\{-13\ ,6\right\}$

b)

$x=\left\{13,-6\right\}$

c)

$x=\pm\sqrt[]{71}$

d)

$x=\pm6$

110.

Find the dimensions of the rectangle shown.

a)

$x=\left\{-12,\ 9\right\}$

b)

$x=\left\{-9,\ 12\right\}$

c)

$x=\pm\sqrt[]{111}$

d)

$x=\pm11$

111.

The polynomial $12x^2-24x+36$ would be called a:

a)

Quadratic Binomial

b)

Quadratic Trinomial

c)

Cubic Trinomial

d)

Quintic Trinomial

112.

The polynomial $4x^2-15$ would be called a:

a)

Quadratic Binomial

b)

Quadratic Trinomial

c)

Cubic Trinomial

d)

Quintic Trinomial

113.

The polynomial $16x^2-81$ would be called a:

a)

Quadratic Binomial

b)

Quadratic Trinomial

c)

Cubic Trinomial

d)

Quintic Trinomial

114.

The polynomial $2x^2+x-21$ would be called a:

a)

Quadratic Binomial

b)

Quadratic Trinomial

c)

Cubic Trinomial

d)

Quintic Trinomial

115.

The product of two consecutive negative even integers is 24. Find the integers.

a)

6, 8

b)

6, 4

c)

-6, -8

d)

-6, -4

116.

Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. Find the integers.

a)

16, 18, 20

b)

18, 20, 22

c)

20, 22, 24

d)

22, 24, 26

117.

Find three consecutive even integers such that 27 more than 3 times the second is 7 less than 8 times the first.

a)

8, 10, 12

b)

-4, -2, 0

c)

6, 8, 10

d)

2, 4, 6

A1 Semester 2 Review

Total questions: 117

Worksheet time: 29hrs 15mins

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