Free Printable Algebra 1 Semester 2 Study Guide

1.

Evaluate using the quotient rule:

a)

a⁸b¹³

b)

a²b⁷

c)

a¹⁵b³⁰

2.

Evaluate the expression using the quotient rule.

a)

2¹⁴ z¹³

b)

2²/z⁷

c)

2¹⁴/ z⁷

d)

2²z⁷

3.

Simplify

(2a²b⁴z)(6a³b²z⁵)

a)

8a⁵b⁶z⁶

b)

12a⁶b⁸z⁵

c)

12a⁵b⁶z⁶

d)

8a⁶b⁸z⁵

4.

a)

b)

c)

d)

5.

Simplify:

a)

2

b)

8

c)

16

d)

32

6.

Write the expression in radical form.
$x^{\frac{7}{2}}$

a)

$\sqrt{x^7}$

b)

$7\sqrt{x^2}$

c)

7x²

d)

∛x⁷

7.

a)

4^4/3

b)

4^3/4

c)

2^4/3

d)

2^3/4

8.

Simplify the following expression:

a)

2

b)

4

c)

16

d)

64

9.

Classify the model as Exponential GROWTH or DECAY.
A=1200(0.85)⁶

a)

Growth

b)

Decay

10.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

11.

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

12.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42

b)

$33,672.68

c)

$34,157.04

d)

$34,710.88

13.

Find the common ratio for the geometric sequence:

10,\ 20,\ 40,\ 80

a)

10

b)

1/2

c)

2

d)

4

14.

$3,\ 24,\ 192,\ 1536$

Write the explicit formula for the following geometric sequence

a)

$a_n=8\cdot3^{n-1}$

b)

$a_n=3\cdot8^{n-1}$

c)

$a_n=3+8\left(n-1\right)$

15.

Find the 9th term in the following geometric sequence:

4, 8, 16, 32, ...

a)

384

b)

512

c)

768

d)

1,024

16.

Simplify (-4m³-m+9)-(4m²+m-12)

a)

-4m³-4m²-2m-21

b)

-4m³-4m²-2m+21

c)

-8m³-2m+21

d)

-4m³+4m²+2m+21

17.

Simplify (8xy²+6xy) + (-12x²y+13xy²)

a)

21xy² +12x²y+6xy

b)

21xy² -12x²y-6xy

c)

21xy² +12x²y-6xy

d)

21xy² -12x²y+6xy

18.

(x + 7)(x + 9)

a)

x² + 63x + 16

b)

x² + 16x + 63

c)

x² + 79

d)

x² + 16x + 2

19.

Multiply 7x²y³ (2x⁴y⁵+6xy³)

a)

14x⁸y¹⁵+42x²y⁹

b)

9x⁶y⁸+13x³y⁶

c)

14x⁶y⁸+42x³y⁶

d)

14x⁶y⁸+42x²y⁶

20.

(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

21.

Find the product:

\left(5s+2\right)^2

a)

$25s^2+4$

b)

$25s^2+10s+4$

c)

$25s^2+20s+4$

d)

$5s^2+20s+4$

22.

(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

23.

(7r-6)(7r+6)

a)

49r²+36

b)

49r²-36

c)

49r²+84r+36

d)

49r²+42r+36

24.

(x - 9)² is the same as...

a)

(x - 9)(x + 9)

b)

(x - 9)

c)

(x - 9) (x - 9)

25.

Factor
k²+7k+10

a)

(k+2)(k+5)

b)

(k-2)(k-5)

c)

(k+10)(k+4)

d)

(k+2)(k-5)

26.

factor:x²- 25

a)

( x + 5 ) ( x - 5 )

b)

( x - 5 ) ( x - 5 )

c)

( x + 5 ) ( x + 5 )

d)

Prime

27.

Factor Completely:
3x² + 18x +15

a)

3(x² + 6x + 5)

b)

(x + 5)(x + 1)

c)

3(x + 5)(x + 1)

d)

Prime

28.

Solve
a² + 10a + 21 = 0

a)

± √21

b)

-3 , -7

c)

3 , 7

d)

28 , -7

29.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

30.

Factor
3a² + 4a + 1

a)

(7a-10)(a-8)

b)

Not factorable

c)

(3a+1)(a+1)

d)

(3a-1)(a-1)

31.

Which of the following is a factor of
4n²-17n-15?

a)

n+5

b)

4n-5

c)

4n-3

d)

4n+3

32.

Is this a perfect square trinomial?
x² + 16x + 64

a)

Yes

b)

No

33.

Which is the vertex of y = x²+ 16x + 71 ?

a)

V(-8, 7)

b)

V(-8, 3)

c)

V(8, 10)

d)

V(16, -2)

34.

Find the y-intercept y = x² - 6x + 5

a)

(0, 8)

b)

(0, - 6)

c)

(5, 0)

d)

(0, 5)

35.

Does the equation open up or down?
Y = -3x² +7x - 2

a)

up

b)

down

c)

Neither; it opens to the right.

d)

Neither; it opens to the left.

36.

Determine the solutions of the graph:

a)

No Solutions

b)

(-3, 0) and (-1, 0)

c)

Infinity Many Solutions

d)

(-1, 0)

37.

If the blue is f(x)=x^2,then the red must be

a)

g(x) = x²- 5

b)

g(x) = x²+ 5

c)

g(x) = (x - 5)²

d)

g(x) = (x + 5)²

38.

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

a)

g(x) = x² - 3

b)

g(x) = x² + 3

c)

g(x) = (x - 3)²

d)

g(x) = (x + 3)²

39.

Compare the function y = 0.3x² to the parent function y = x²

a)

Wider

(Compressed Vertically)

b)

Narrower

(Stretched Vertically)

40.

Match the equation to its description.

a)

Reflected over the x-axis and stretched vertically

b)

Stretched vertically

c)

Reflected over the x-axis

d)

Reflected over the x-axis and translated down 3 units

41.

Match the equation to its description.

a)

Reflected over x-axis, translated right 2 units and up 1 unit

b)

Reflected over x-axis, translated left 2 units and up 1 unit

c)

Reflected over x-axis, translated right 2 units and down 1 unit

d)

Reflected over x-axis, translated left 2 units and down 1 unit

42.

Find the last term:

x^2+22x+c

a)

22

b)

11

c)

121

d)

44

43.

Given the perfect square trinomial, identify the equivalent expression

x²-18x+81

a)

(x-18)²

b)

(x-9)²

c)

(x+81)²

d)

(x+9)²

44.

Use the graph to determine the solutions.

a)

-1 and -3

b)

1 and -3

c)

1 and 3

d)

-1 and 3

45.

Identify a, b, and c in: x²−6x+14

a)

a=3, b=5, c=9

b)

a=1, b=-6, c=14

c)

a=1, b=-6, c=-14

d)

a=1, b=6, c=14

46.

What are the zeros of

$f\left(x\right)=x^2+7x-18$ ?

a)

$x=-2,\ -9$

b)

$x=2,\ -9$

c)

$x=-2,\ 9$

d)

$x=2,\ 9$

47.

Solve using the quadratic formula:

4x²+ 4x + 1 = 0

a)

x = -½

b)

x = -2

c)

x = 0

d)

x = ½

48.

Which piecewise function corresponds to this graph? (Take your time)

a)

f(x) = { x if x < 4; -x+1 if x ≥ 4

b)

f(x) = { x if x ≤ 4; -x+1 if x > 4

c)

f(x) = { -x+1 if x < 4; x if x ≥ 4

d)

f(x) = { -x+1 if x ≤ 4; x if x > 4

49.

Simplify.

a)

b)

c)

d)

50.

Simplify.

a)

b)

c)

d)

51.

Simplify.

a)

b)

c)

d)

52.

Which is equivalent to √121p⁵r⁷s⁴?

a)

11prs √pr

b)

11p^2.5r^3.5s²√pr

c)

11p²r³s²√pr

d)

11p²r³s²

53.

Simplify

a)

9

b)

5√2 + 2

c)

10√2

d)

2√2 + 3√30

54.

Add: 4√7 - 10 √7 + 7√7

a)

-6√7

b)

14√7

c)

-3√14

d)

√7

55.

Simplify
-3√24 - √18 - 2√54

a)

-12√5 - 3√2

b)

-12√6 - 3√2

c)

-3√2+ 12√3

d)

3√2

56.

a)

A

b)

B

c)

C

d)

D

57.

Divide and simplify.

a)

4x√x

b)

3x²/x³√36

c)

2x

d)

4x²

58.

$5\sqrt{2xy^6}\cdot2\sqrt{2x^3y}$

a)

40x⁴y⁷

b)

40x²y³

c)

20x²y³√y

d)

20x√2y⁷

59.

Simplify completely $\frac{\sqrt{256x^{11}}}{\sqrt{8x^3}}$

a)

$4x\sqrt{x}$

b)

$\frac{4x^2}{\sqrt{8}}$

c)

$4x^4\sqrt{2}$

d)

$4x^2\sqrt{2}$

60.

Solve for x.

$\sqrt[]{x-4}=9$

a)

77

b)

85

c)

81

d)

9

61.

Solve for x.

$2\ \sqrt[]{x+3}-5=3$

a)

4

b)

13

c)

9

d)

16

62.

Solve for x.

$-3\ \sqrt[]{x-2}+1=-11$

a)

144

b)

16

c)

121

d)

18

63.

Do three squares with side lengths of 6, 12, and 13 form a right triangle?

a)

Yes

b)

No

64.

_{^{Find the missing side}}

a)

9

b)

41

c)

6.4

d)

6.2

65.

Find the length of the missing side.

a)

25 cm

b)

42 cm

c)

52 cm

d)

48 cm

66.

a)

27/36

b)

27/45

c)

45/36

d)

45/27

67.

a)

18/30

b)

24/30

c)

18/24

d)

24/18

68.

Choose the correct ratio.

a)

cos(33)=x/14

b)

sin(33)=x/14

c)

cos(33)=14/x

d)

sin(33)=14/x

69.

Solve for the missing angle.

a)

32°

b)

44°

c)

61°

d)

50°

70.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

71.

What are the asymptotes for the following rational function?

$f\left(x\right)\ =\ \frac{6x}{2x+1}$ ?

a)

$y\ =3,\ x\ =\ \frac{1}{2}$

b)

$y=-\frac{1}{2},\ x\ =\ 3$

c)

$y\ =3,\ x\ =-\frac{1}{2}$

d)

$y=\frac{1}{2},\ x\ =\ 3$ y=1/2

72.

Find the Vertical Asymptotes for the following function

g\left(x\right)\ =\frac{2x^2+x-9}{x^2-2x-8}

a)

$x=-4,\ x=2$

b)

$x=-2,\ x=4$

c)

$x=-6,\ x\ =\ -2$

d)

$x=\ 2,\ x=6$

73.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

74.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

75.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

76.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

77.

Find the excluded value(s). $\frac{x-5}{x^2-10x+25}$

a)

x does not equal 5

b)

x does not equal 10

c)

x does not equal -25

d)

x does not equal -5

78.

Find the excluded value(s).

a)

n does not equal 0

b)

n does not equal 24

c)

n does not equal -24

d)

n can be any real number

79.

Simplify

a)

A

b)

B

c)

C

d)

D

80.

a)

A

b)

B

c)

C

d)

D

81.

Multiply the following expressions.

a)

$\frac{8x^2y^7}{3x^3y^3}$

b)

$\frac{8y^4}{3x}$

c)

$\frac{40x^2y^7}{30x^3y^3}$

d)

$\frac{12y^{10}}{50x^5}$

82.

Divide the following expressions.

a)

$\frac{4\left(x-4\right)}{\left(x+5\right)}$

b)

$\frac{\left(x+4\right)^2\left(x-4\right)}{16\left(x+5\right)}$

c)

Can't be simplified

d)

$\frac{\left(x+5\right)}{4\left(x-4\right)\ }$

83.

Multiply the Rational Expression

a)

A

b)

B

c)

C

d)

D

84.

Divide the polynomial by the monomial.

a)

2x⁸-8x²-28x

b)

2x⁸-2x²-7x

c)

8x⁷-8x-28x

d)

2x⁷-2x -7

85.

$\frac{x^2+12x+27}{x+9}$

a)

x+3

b)

x+9

c)

x-3

d)

x-9

86.

$\frac{2x^2-15x+7}{x-7}$

a)

x-7

b)

2x-1

c)

2x+7

d)

x-1

87.

$\frac{2x^2+7x-15}{2x-3}$

a)

x+5

b)

2x-3

c)

x-5

d)

2x+15

88.

$\frac{6x^2+17x+5}{2x+5}$

a)

2x-5

b)

6x+1

c)

3x-1

d)

3x+1

89.

a)

A

b)

B

c)

C

d)

D

90.

$\frac{\frac{2x-1}{x}}{\frac{2}{x}+3}$

a)

$\frac{7}{2\left(x+2\right)}$

b)

$\frac{2x-1}{2+3x}$

c)

$\frac{x}{x-1}$

d)

$\frac{y}{2-y}$

Algebra 1 Semester 2 Study Guide

Total questions: 90

Worksheet time: 5hrs 30mins

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