Free Printable Algebra exam review first semester

1.

What is the domain of the graph?

a)

y ≥ 1

b)

x ≥ 1

c)

All real numbers

d)

none of these

2.

What is the range of the graph?

a)

y ≥ 1

b)

x ≥ 1

c)

All real numbers

d)

none of these

3.

What is the domain of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

4.

What is the range of the graph?

a)

-7 ≤ x < 5

b)

-3 ≤ x < 1

c)

-3 ≤ y < 1

d)

-7 ≤ y < 5

5.

What is the domain?

a)

-3 < y ≤ 3

b)

-4 ≤ y ≤ 5

c)

-4 ≤ x ≤ 5

d)

-3 < x ≤ 3

6.

What is the range?

a)

-3 < y ≤ 3

b)

-4 ≤ y < 5

c)

-4 ≤ y ≤ 5

d)

-3 < y ≤ 3

7.

Find the common difference: 29, 21, 13, 5, ...

a)

d = -10

b)

d = -9

c)

d = -8

d)

d = -7

8.

What is a₁ in the following sequence?

-6, -14, -22, -30, ...

a)

-6

b)

-14

c)

-22

d)

-30

9.

Is the sequence arithmetic?

17, 9, 1, -7, ...

a)

Yes

b)

No

10.

A sequence is shown below.

32, 26, 20, 14, ...

Which explicit formula can be used to determine the nth term of the sequence?

a)

a_n = -6n + 38

b)

a_n = 6n + 32

c)

a_n = 6n + 38

d)

a_n = -6n + 32

11.

An arithmetic sequence has these properties:

a₁ = 2

a_n = a_(n-1) + 5

What are the first four terms of the sequence?

a)

2, 5, 10, 15

b)

2, 5, 7, 12

c)

2, 7, 9, 14

d)

2, 7, 12, 17

12.

Find the first term of the given sequence:
a₁₄=68
d=3

a)

14

b)

20

c)

26

d)

29

13.

Find the 22nd term of the following sequence:
5, 8, 11, ...

a)

14

b)

68

c)

63

d)

71

14.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

15.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

16.

What is the system of inequalities represented?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

17.

This system has an infinite number of solutions, TRUE or FALSE?

a)

TRUE

b)

FALSE

18.

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing

a)

x + y ≤ 300
7.5x + 5.5y ≥ 2000

b)

x + y < 300
7.5x + 5.5y ≥ 2000

c)

x + y ≤ 300
7.5x + 5.5y ≤ 2000

d)

x + y > 2000
7.5x + 5.5y ≤ 300

19.

a)

A

b)

B

c)

C

d)

D

20.

a)

A

b)

B

c)

C

d)

D

21.

Simplify:

$\sqrt[]{200x^2}$

a)

$5x\ \sqrt[]{2}$

b)

$100x\ \sqrt[]{2}$

c)

$10x\ \sqrt[]{2}$

d)

$10\ \sqrt[]{2x}$

22.

Simplify.

a)

$5x^8y^{10}\ \sqrt[]{10x}$

b)

$5x^4y^5\ \sqrt[]{10x}$

c)

$5x^4y^5\ \sqrt[]{2x}$

d)

$5\ \sqrt[]{2x^9y^{10}}$

23.

Which of the following is irrational?

a)

$\sqrt{49}$

b)

$\sqrt{50}$

c)

$\sqrt{81}$

d)

$\sqrt{121}$

24.

Which is equivalent to $\sqrt[3]{54}$ in simplest form?

a)

$3\sqrt[3]{6}$

b)

$9\sqrt[3]{2}$

c)

$3\sqrt[3]{2}$

d)

$3\sqrt[3]{3}$

25.

Simplify
$\sqrt{6}\left(\sqrt{6}+\sqrt{10}\right)$

a)

$6+2\sqrt{15}$

b)

$8\sqrt{15}$

c)

$\sqrt{96}$

d)

$6\sqrt{6}+2\sqrt{15}$

26.

Simplify
$\left(2+\sqrt{3}\right)\left(8-\sqrt{3}\right)$

a)

$13+6\sqrt{3}$

b)

$13-6\sqrt{3}$

c)

$19+10\sqrt{3}$

d)

$19-10\sqrt{3}$

27.

Simplify the radical.

$2\ \sqrt[3]{-72x^9y^6}$

a)

$12xy\ \sqrt[3]{-2x^6y^3}$

b)

$-6\ x^4y^2\sqrt[3]{2x}$

c)

$-4x^3y^2\ \sqrt[3]{9}$

d)

$-2x^4y^3\ \sqrt[3]{9x}$

28.

Rewrite in radical form: $\left(5v\right)^{\frac{2}{3}}$

a)

$\sqrt{5^3v^3}$

b)

$^3\sqrt{5v^2}$

c)

$\sqrt{\left(5v\right)^3}$

d)

$^3\sqrt{\left(5v\right)^2}$

29.

Rewrite in exponential form: $\sqrt{\left(5b\right)^3}$

a)

$\left(5b\right)^{\frac{2}{3}}$

b)

$\left(5b\right)^{\frac{3}{2}}$

c)

$5b^{\frac{3}{2}}$

d)

$5b^{\frac{2}{3}}$

30.

Factor
k²+ 7x + 10

a)

(k + 2)(k + 5)

b)

(k - 2)(k - 5)

c)

(k + 10)(k + 4)

d)

(k + 2)(k - 5)

31.

Factor:
v² + 3v - 88

a)

(v + 11)(v - 8)

b)

(v + 22)(v - 4)

c)

(v + 8)(v - 11)

d)

(v - 22)(v + 4)

32.

Factor the difference of squares:
x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

33.

3x²- 75

a)

3( x + 5 ) ( x - 5 )

b)

Prime

c)

( x + 5 ) ( x - 5 )

d)

3( x - 5 ) ( x - 5 )

34.

Factor: x² + 24x + 144

a)

(x + 12)²

b)

(x + 9)²

c)

(x + 15)²

d)

(x + 13)²

35.

Factor
3a² + 4a + 1

a)

(7a - 10)(a - 8)

b)

Prime

c)

(3a + 1)(a + 1)

d)

(3a - 1)(a - 1)

36.

Factor:
6x² – 19x – 7

a)

(2x + 7)(3x – 1)

b)

(x – 1)(6x + 7)

c)

(2x – 7)(3x + 1)

d)

(6x – 7)(x + 1)

37.

Factor the Polynomial

12x³- 9x² + 4x - 3

a)

(3x² + 1) (4x - 3)

b)

(3x² - 1) (4x + 3)

c)

(4x² + 1) (3x - 3)

d)

(4x² - 1) (3x + 3)

38.

Solve the quadratic equation using the quadratic formula.

a)

n = -4, 2

b)

n = -2, 4

c)

n = -16

d)

n = -4

39.

Solve using factoring OR the quadratic formula.

a)

b = -2, 4

b)

b = -8

c)

b = ±8

d)

b = 2, -4

40.

If the discriminant equals 0, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

Half a Solution

d)

No Real Solution

41.

If the discriminant is negative, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

No Real Solutions

42.

If the discriminant is positive, then the quadratic has:

a)

1 Real Solution

b)

2 Real Solutions

c)

No Real Solution

43.

Solve for x by taking the Square Root:

(x + 6)²= 49

a)

x = 7 and 12

b)

x = ±7

c)

x = 1 and -13

d)

x = 43 and -55

44.

Solve by completing the square:

x² + 10x = -9

a)

x = 1 and -12

b)

x = -1 and -9

c)

x = 1 and -9

d)

x = 1 and -1

45.

Solve using the Quadratic Formula:
(Hint: Set the equation = to 0)

$15x^2+22x=-8$

a)

$x=-\frac{2}{3},\ \frac{4}{5}$

b)

$x=\frac{2}{3},\ -\frac{4}{5}$

c)

$x=\frac{2}{3},\ \frac{4}{5}$

d)

$x=-\frac{2}{3},\ -\frac{4}{5}$

46.

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

47.

What is the vertex of y = x²+ 4x + 3?

a)

(2, 1)

b)

(-2, 1)

c)

(0, 0)

d)

(-2, -1)

48.

What are the x-intercepts of the function
f(x) = (x - 2)(x + 3)?

a)

(-2, 0) and (3, 0)

b)

(2, 0) and (-3, 0)

c)

The are no real roots

d)

(2, 0) and (3, 0)

49.

Which equation best represents the graph?

a)

y = 2(x - 4)² + 5

b)

y = 2(x + 4)² + 5

c)

y = -2(x - 4)² + 5

d)

y = -2(x + 4)² + 5

50.

Which of these shows a parent function of a quadratic equation moved 5 units to the right?

a)

f(x) = (x - 5)²

b)

f(x) = (x + 5)²

c)

f(x) = 5x²

d)

f(x) = x²+ 5

51.

Which of these shows a parent function of a quadratic equation moved 1 unit down?

a)

f(x) = (x - 1)²

b)

f(x) = (x + 1)²

c)

f(x) = x²

d)

f(x) = x²- 1

52.

Find the y-intercept y = (x - 3)² - 4.

a)

(0, 8)

b)

(0, - 6)

c)

(5, 0)

d)

(0, 5)

53.

Which of these shows a parent function of a quadratic equation vertically stretched by 2?

a)

f(x) = (x + 2)²

b)

f(x) = x²+ 2

c)

f(x) = 2x²

d)

f(x) = (x - 2)²

54.

Where is the function decreasing?

a)

(-∞, -1)

b)

(-1, ∞)

c)

(-∞, 3)

d)

(-∞, ∞)

55.

Determine the interval in which this function is increasing.

a)

(-4, ∞)

b)

(-3, ∞)

c)

(-∞, -3)

d)

(-∞, -4)

56.

What is the negative interval of the function?

a)

$\left(-2,1\right)$

b)

$\left(0,-4\right)$

c)

$\left(-1,0\right)$

d)

$\left(-2,0\right)$

57.

Identify the intervals where the function is positive and where it is negative.

a)

positive (-1, ∞) and negative (-∞, -1)

b)

positive none and negative (-1, -4)

c)

positive (-∞,-3) $\cup$ (1,∞) and negative (-3,1)

d)

positive (-∞,∞) and negative (-4,∞)

58.

Given the function $g\left(x\right)\ =\ x^2-5x$ determine the average rate of change of the function over the interval
1 < x < 8.

a)

8

b)

-4

c)

2.5

d)

4

59.

Solve the system of equations:

y = -4

y = 2x - 2

a)

(1, 4)

b)

(-4, -1)

c)

(-1, -4)

d)

(1, -4)

60.

Solve the following system:

$3x+2x=16$
$7x+y=19$

a)

(-2, 5)

b)

(-2, -5)

c)

(2, -5)

d)

(2, 5)

61.

Solve the following system:

-12x - 4y = -8

-6x - 2y = -4

a)

no solution

b)

(0, 0)

c)

infinitely many solutions

d)

(4, 0)

62.

Trevor and Kylie are selling fruit for a school fundraiser. Customers can buy small boxes of oranges (x) and large boxes of oranges (y). Trevor sold 3 boxes of small oranges and 14 boxes of large oranges for a total of $203. Kylie sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220.

a)

$14x\ +\ 3y\ =\ 203$
$11x\ +\ 11y\ =\ 220$

b)

$3x\ +\ 14y\ =\ 203$
$11x\ +\ 11y\ =\ 220$

c)

$3x\ +\ 14y\ =\ 220$
$11x\ +\ 11y\ =\ 203$

d)

$14x\ +\ 3y\ =\ 220$
$11x\ +\ 11y\ =\ 203$

63.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

a)

Sugar Cookies $5
Oatmeal Cookies $3

b)

Sugar Cookies $4
Oatmeal Cookies $8

c)

Sugar Cookies $2
Oatmeal Cookies $6

d)

Sugar Cookies $3
Oatmeal Cookies $6

64.

Find the slope given the points (3, 2) and (4, 7).

a)

$m=\frac{1}{5}$

b)

$m=5$

c)

$m=-5$

d)

$m=-\frac{1}{5}$

65.

Which of the following is the equation of the line that has a slope of 3 and passes through the point (-1, 9)?

a)

y = - 3x + 12

b)

y = 3x + 3

c)

y = 3x + 12

d)

y = 3x - 3

66.

Factor:
8x² – 10x – 3

a)

(4x – 3)(2x + 1)

b)

(8x + 3)(x – 1)

c)

(2x + 1)(4x – 3)

d)

(4x + 1)(2x – 3)

67.

Rewrite in radical form: $(3y)^{\frac{5}{2}}$

a)

$\sqrt{(3y)^5}$

b)

$^2\sqrt{3y^5}$

c)

$^5\sqrt{3y^2}$

d)

$\sqrt{3y^5}$

68.

Rewrite in exponential form: $\sqrt[3]{(2a)^4}$

a)

$(2a)^{\frac{4}{3}}$

b)

$2a^{\frac{3}{4}}$

c)

$(2a)^{\frac{3}{4}}$

d)

$2a^{\frac{4}{3}}$

69.

Which of the following describes the direction of the parabola y = 2x² - 5x + 1?

a)

Opens up with a maximum

b)

Opens down with a minimum

c)

Opens up with a minimum

d)

Opens down with a maximum

70.

Find the explicit formula for the arithmetic sequence:

12, 7, 2, -3, ...

a)

a_n = -5n + 17

b)

a_n = 5n + 12

c)

a_n = -5n + 12

d)

a_n = 5n + 17

71.

Which of these shows a parent function of a quadratic equation moved 3 units up?

a)

f(x) = x² + 3

b)

f(x) = (x + 3)²

c)

f(x) = (x - 3)²

d)

f(x) = x² - 3

72.

Solve using the Quadratic Formula:
$4y^2 - 12y + 5 = 0$

a)

$y=\frac{3 \pm \sqrt{9}}{2}$

b)

$y=\frac{3 \pm \sqrt{16}}{4}$

c)

$y=\frac{3 \pm \sqrt{11}}{4}$

d)

$y=\frac{3 \pm \sqrt{4}}{2}$

73.

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

a)

(-2,5)

b)

(-2,-5)

c)

(2,-5)

d)

(2,5)

74.

5x + 16y = -16
-9x - 8y = 8

a)

(3, 1)

b)

(3, -1)

c)

(-3, -1)

d)

(0, -1)

75.

A boy has seven more nickels than quarters. The total value of the coins is $4.90. Which system could be used to find out how many nickels and quarters he has?

a)

b)

c)

d)

76.

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

77.

Expand the squared binomial.
(x - 5)²?

a)

x² + 25

b)

x² - 25

c)

x² - 10x - 25

d)

x² - 10x + 25

78.

Classify by number of terms:

$3x^3-6x$

a)

Monomial

b)

Binomial

c)

Trinomial

79.

What is the value of the constant? $2x^2\ +\ 4x\ -\ 5\$

a)

2

b)

4

c)

5

d)

−5

80.

Classify: $9x^{ }$

a)

Quadratic polynomial

b)

Linear monomial

c)

Quadratic monomial

d)

Exponential monomial

81.

Classify this polynomial by its degree and number of terms: $x^2\ +\ 2x\ +\ 6\$

a)

Linear polynomial

b)

Quadratic trinomial

c)

Quadratic binomial

d)

Cubic trinomial

82.

Multiply
(x²- 2x + 1)(x + 1)

a)

x³- x²- x + 1

b)

x³- 2x + 2

c)

x³+ x²+ x + 1

d)

x³- 3x²- 3x + 1

83.

Find the difference.

(7p + 4p³ - 8) - (-3p²+ 2 - 9p)

a)

-3p²+ 4p³ - 15 + 9

b)

3p³ + 4p² - p + 3

c)

4p³ + 3p² + 16p - 10

d)

4p³ + 3p² + 16p + 10

84.

4k²(6k² + 9kq - 5q²)

a)

24k² + 36k³q - 20k²q²

b)

24k⁴ + 36kq - 20k²q²

c)

24k⁴ + 36k³q - 20k²q²

d)

24k + 36 kq - 20 k²q

85.

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h(t) = -16t²+ 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

a)

126.56 ft

b)

5.625 sec

c)

2.81 sec

d)

0 ft

86.

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h(t) = -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

87.

If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation
h(t) = -16t² + 128t
When will the object reach its maximum height?

a)

4 ft

b)

0 seconds

c)

0 ft

d)

4 seconds

88.

Jason launched a rocket for a physics experiment. This equation can be used to find the height (h), in feet, of the rocket after t seconds.
h(t) = -16t² + 288t + 8
How many seconds will it take for the rocket to reach a height of 1,304 feet?

a)

9.0 seconds

b)

9.6 seconds

c)

81.0 seconds

d)

82.0 seconds

89.

Alain throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Alain threw it, is modeled by:
h(x)= -5x² + 10x + 15
How many seconds after being thrown will the stone hit the water?

a)

-1 seconds

b)

1 second

c)

2 seconds

d)

3 seconds

Algebra exam review first semester

Total questions: 89

Worksheet time: 8hrs 37mins

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