Free Printable Alg2 S1 Final Review

1.

Simplify the expression: 2x + 1 + 7x

a)

10x

b)

10

c)

9x + 1

d)

9 + 1x

2.

Simplify the following expression:
-6x + 4(-x - 3)

a)

-2x - 12

b)

10x + 12

c)

-10x - 12

d)

-2x + 12

3.

Which expression is equivalent to -5(x + 10)?

a)

5x + 50

b)

-5x + 10

c)

-5x - 50

d)

5x - 50

4.

Expand and simplify $3\left(2a+5\right)+5\left(a-2\right)$

a)

$11a+5$

b)

$6a+15$

c)

$11a-5$

d)

$6a+15+5a-10$

5.

Students brought in 300 canned goods for the food drive on Monday. On Tuesday students brought in x more than the day before. Write an expression for how many canned goods students brought on Tuesday.

a)

300 + x

b)

300 - x

c)

300x

d)

x - 300

6.

Given: $\frac{13y-zx}{4}$

Evaluate the expression for: $x=7,\ y=15,\ and\ z=8$

(a)

7.

Evaluate the expression when m = 5

m² + 4

a)

9

b)

14

c)

21

d)

29

8.

2x + 3(5x - 7) = 47

a)

x = 1

b)

x = 2

c)

x = 3

d)

x = 4

9.

Solve:
^{-3x + 6(1 + 2x) = 2x + 27}

a)

x = 3

b)

Many Solutions

c)

No Solutions

d)

x = (-11)

10.

Solve:
3x + 15 = 3(x + 5)

a)

No Solution

b)

x = 15

c)

Infinitely Many Solutions

11.

$x+9\ =\ x-9$

a)

one solution

b)

no solution

c)

infinite solutions

12.

John's mother age is 5 years more than the three times of John's present age. Find John's present age , if his mother is 44 years old.

a)

$13$

b)

$15$

c)

$29$

d)

$39$

13.

Barry’s age is twice Alex age now. Five times Alex’s age 2 years ago is equal to Barry’s age in 5 years. How old is Alex now?

a)

$5$

b)

$8$

c)

$10$

d)

$15$

14.

Sean is 3 times as old as Jean. 8 years from now, Sean will be twice as old as Jean. How old is Jean?

a)

$16$

b)

$14$

c)

$8$

d)

$12$

15.

(a)

16.

Solve for x
l 4x−3 l = 17

a)

x = 5 and x =-3.5

b)

x = 0 and x = -5

c)

x = 10 and x = -10

d)

No Solution

17.

Solve for x
l x−6 l + 4= 10

a)

x = 12 and x = 0

b)

x = 3 and x = -3

c)

x = -12 and x = 0

d)

No Solution

18.

−2|−2r − 4| = -12

a)

{3,1}

b)

{-5,1}

c)

{-3}

d)

No Solution

19.

Evaluate each expression.
| x + 9 | = -5

a)

-14

b)

-4

c)

{-14, -4}

d)

no solution

20.

When do you "flip the inequalities sign"?

a)

When you add or subtract a negative

b)

When it's a 1-step problem

c)

When you multiply or divide a negative

d)

When it's a 2-step problem

21.

-3x ≤ 18

a)

x ≤ -6

b)

x ≤ 6

c)

x ≥ 6

d)

x ≥ -6

22.

Solve 3x + 7 < 22

a)

x < -29/3

b)

x < -5

c)

x < 29/3

d)

x < 5

23.

What inequality is graphed?

a)

x > 2 and x ≤ -3

b)

x > 2 and x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

24.

Write an inequality for Graph 4.

a)

-2 < x < 5

b)

x < -2 or x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x ≤ 5

25.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-2 ≤ x ≤ 6

c)

-3 ≤ x ≤ 3

d)

1 ≤ x ≤ 3

26.

x + 8 < 3 or - 8x < -40

a)

x > -5 or x < 5

b)

x < -5 and x > 5

c)

x < -5 or x > 5

d)

x > -5 and x < 5

27.

Which of the following would result in NO SOLUTION?

a)

x < 1 or x > 5

b)

x > 1 or x < 5

c)

x < 1 and x > 5

d)

x > 1 and x < 5

28.

Give the final solution set for:

2x + 1 > 9 or x - 4 < 6

a)

No solution

b)

4 < x < 10

c)

x > 4 or x < 10

d)

All real numbers

29.

Solve.
|y - 4| ≥ 8

a)

y ≤ -4 or y ≥ 12

b)

-4 ≤ y ≤ -12

c)

y ≤ 4 or y ≥ -12

d)

-12 ≤ x ≤ 4

30.

Solve.

3|d - 4| ≥ 12

a)

d = -8 or d = 0

b)

no solution

c)

d ≥ 8 or d ≤ 0

d)

d = 40 or d = 32

31.

| x - 6 | < 4
Is this an "and" or an "or" problem?

a)

and

b)

or

32.

Write the equation in point-slope form for the line that contains the points
(-2, -3), (4, 3)

a)

y - 3 = 1(x - 2)

b)

y + 3 = 1(x + 2)

c)

y -3 = -1(x + 2)

d)

y + 3 = -1(x - 2)

33.

Write the equation in slope-intercept form for the line that contains the points
(3, -5) and (5, - 1)

a)

y = 2x + 11

b)

y = 2x + 1

c)

y = 2x - 1

d)

y = 2x - 11

34.

What is the equation of the line that goes through the points ( 3, - 1 ) and ( 2, - 4 )?

a)

y = 3x - 4

b)

y = - 3x + 8

c)

y = 3x - 1

d)

y = 3x - 10

35.

The graph of a linear function is shown on the grid. Which equation is best represented by this graph?

a)

$y+7=-3\left(x-4\right)$

b)

$y+1=-3\left(x+2\right)$

c)

$y-4=3\left(x+7\right)$

d)

$y-2=3\left(x-1\right)$

36.

The graph of a linear function is shown on the grid. Which equation is best represented by this graph?

a)

$g\left(x\right)=6x+4$

b)

$g\left(x\right)=4x-\frac{2}{3}$

c)

$g\left(x\right)=-\frac{3}{2}x+6$

d)

$g\left(x\right)=-\frac{2}{3}x+4$

37.

What are the equation and slope of the line shown on the grid?

a)

$y=6,\ slope\ is\ -\frac{1}{6}$

b)

$x=6,\ slope\ is\ zero$

c)

$y=6,\ slope\ is\ 6$

d)

$x=6\ slope\ is\ undefined$

38.

Which of the following is the graph of $5x\ +\ 2y\ =\ 10$ ?

a)

b)

c)

d)

39.

Which of the following is the graph of $x\ -\ 2y\ =\ -8$ ?

a)

b)

c)

d)

40.

What is the equation of a line that is parallel to y = 3x - 7 and goes through (2, 1) ?

a)

$y=3\left(2\right)-7$

b)

$y=3x-7$

c)

$y=3x+1$

d)

$y=3x-5$

41.

What is the equation of a line that is parallel to $y=\frac{2}{3}x+5$ and goes through $\left(6,-7\right)$ ?

a)

$y=\frac{2}{3}x-7$

b)

$y=\frac{2}{3}x-11$

c)

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

d)

$y=\frac{2}{3}x-9$

42.

Write the equation of a line that is PARALLEL to $x-3y=12$ going through the point (6,1)

a)

$y-1=\frac{1}{3}\left(x-6\right)$

b)

$y-6=\frac{1}{3}\left(x-1\right)$

c)

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

d)

$y=\frac{1}{3}x-6$

43.

Write the equation of a line that is PERPENDICULAR to $y=-2x-8$ going through the point (2,5)

a)

$y-5=\frac{1}{2}\left(x-2\right)$

b)

$y=\frac{1}{2}x+4$

c)

$y-2=\frac{1}{2}\left(x-5\right)$

d)

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

44.

Write the equation of a line that is PERPENDICULAR TO $y=-4x+1$ going through (12,3)

a)

$y-3=\frac{1}{4}\left(x-12\right)$

b)

$y=\frac{1}{4}x$

c)

$y-12=\frac{1}{4}\left(x-3\right)$

d)

$y-3=-4\left(x-12\right)$

45.

Write the equation of a line PERPENDICULAR to $y=\frac{2}{5}x+\frac{3}{5}$ and passes through the point (2, -3).

a)

$=-\frac{5}{2}x-\frac{11}{2}$

b)

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

c)

$y=-\frac{5}{2}x+8$

d)

$y=\frac{2}{5}x+\frac{19}{5}$

46.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

47.

This is a graph of which inequality?

a)

y > 4x - 2

b)

y > -2x + 4

c)

y < -2x

d)

y < 4X - 2

48.

Choose the correct inequality for this graph.

a)

b)

c)

d)

49.

Which inequality describes this graph...

a)

y < 3x - 2

b)

y > 3x + 2

c)

y < 3x + 2

d)

y > 3x -2

50.

What is the solution?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(0, 1)

51.

Give the solution to the system.

a)

(3,1)

b)

(1,3)

c)

(-1,3)

d)

(1, -3)

52.

What is the solution to the system of equations?

a)

No Solution

b)

(2, 0)

c)

Infinitely Many Solutions

d)

(0, 2)

53.

How many solutions?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

54.

How many solutions does this system have?

y = 2x + 1

y = 4x - 1

a)

One Solution

b)

No Solution

c)

Infinite Solutions

55.

How many solutions does this system have?

3x-4=-4+3x

a)

One Solution

b)

No Solution

c)

Infinite Solutions

56.

How many solutions does this system have?

y=2x + 4

y=2x -4

a)

One Solution

b)

No Solution

c)

Infinite Solutions

57.

Solve using Elimination Method:

x - y = 11

2x + y = 19

a)

(10,-1)

b)

(-1,10)

c)

(3,-4)

d)

(6,7)

58.

Solve using Elimination Method:

4x+ 9y = 28

-4x -y = -28

a)

(-7,0)

b)

(6,0)

c)

(-6,0)

d)

(7,0)

e)

(6,7)

59.

a)

b)

c)

d)

60.

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same.

Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

a)

4y = 3x + 64

8y = x + 68

b)

4y = 3x + 64

8y = x + 60

c)

3x + 4y = 64

x + 8y = 68

d)

3x + 4y = 64

x + 8y = 60

61.

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

a)

x + y = 33
y = 2x - 3

b)

x + y = 33
x = 2y - 3

c)

x + y = 33
x = 3 - 2y

d)

x + y = 3
x = 33 - 2y

62.

Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation?

a)

x - y = -10
x + y = -2

b)

x = -2
y = 5

c)

x + y = -2
x - y = -10

d)

x + y = -10
x - y = -2

63.

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?

a)

x + y = 15
4x + 2y = 44

b)

4x + 2y = 15
x + y = 44

c)

x = 2y + 44
4x = y + 15

d)

2x - 4y = 44
x - y = 15

64.

Describe the transformation of the equation below from the absolute value parent function.

$y=\left|x-4\right|$

a)

Left 4

b)

Right 4

c)

Up 4

d)

Down 4

65.

Choose the equation that best matches the graphed function.

a)

$f(x)=|x|+2$

b)

$f(x)=|x|-2$

c)

$f(x)=-|x|$

d)

$f(x)=-|x|+2$

66.

What is the vertex of the following function? $y=|x-3|+1$

a)

$(2,3)$

b)

$(-3,1)$

c)

$(2,-3)$

d)

$(3,1)$

67.

Describe the transformation of the equation below from the absolute value parent function.

$y=|x|+10$

a)

Shifted left 10

b)

Shifted right 10

c)

Shifted up 10

d)

Shifted down 10

68.

What is the y-intercept of the function

$f\left(x\right)=\left|x+3\right|-7$

a)

-4

b)

0

c)

3

d)

7

69.

What is the domain of the function

$g\left(x\right)=\left|x-2\right|+3$

a)

All Real Numbers

b)

$x\ge-2$

c)

$x<2$

d)

$\left[0,\infty\right)$

70.

What is the range of the function

$y=\left|x\right|+2$

a)

$y\ge2$

b)

All Real Numbers

c)

$y>0$

d)

$y\le-2$

71.

What is the transformation of $y=-\left|x\right|$

a)

Reflected across the x-axis

b)

Shifted down 1

c)

Shifted left 1

d)

Reflected across the y-axis

72.

Which function is graphed?

a)

f(x) = -|2x - 5| + 5

b)

f(x) = -|x - 3| - 3

c)

f(x) = -|2x + 3| + 5

d)

f(x) = -2|x + 5| - 3

73.

Which function is graphed?

a)

$f\left(x\right)=2\left|x+2\right|-3$

b)

$f\left(x\right)=\frac{1}{2}\left|x+4\right|-3$

c)

$f\left(x\right)=\frac{1}{2}\left|x+2\right|-3$

d)

$f\left(x\right)=2\left|x+4\right|-3$

74.

Choose the correct translated function.

a)

f(x)= |x|+2

b)

f(x)= |x|-2

c)

f(x)= -|x|

d)

f(x)= -|x|+2

75.

$y=\left|3x\right|+2$

a)

Vertical Stretch

b)

Vertical Compression

c)

Horizontal Stretch

d)

Horizontal Compression

76.

What is/are the x-intercept(s) of the absolute value function?

a)

(0, 4)

b)

none

c)

(4, 0)

d)

(-4, 0)

77.

Given the following function, on which interval is the function increasing?

a)

$\left(-\infty,\ \ 4\right]$

b)

$\left[4,\ \infty\right)$

c)

$\left(-\infty,\ 3\right]$

d)

$\left[3,\ \infty\right)$

78.

Given the following function, on which interval is the function decreasing?

a)

$\left(-\infty,\ 4\right]$

b)

$\left[4,\ \infty\right)$

c)

$\left[-\infty,\ 3\right]$

d)

$\left[3,\ \infty\right)$

79.

Given the following function, on which interval is the function decreasing?

a)

$\left(-\infty,\ -4\right]$

b)

$\left[4,\ \infty\right)$

c)

$\left(-\infty,-3\right]$

d)

$\left[-3,\ \infty\right)$

80.

Write an absolute value function given the following transformations from the parent function:

Reflection across the x-axis

Vertical shift right 2 units

Horizontal shift down 7 units

a)

$y=-|x+2|-7$

b)

$y=|x-2|-7$

c)

$y=-|x-2|-7$

d)

$y=-|x-2|+7$

81.

What is the minimum value of the function over the interval [-4, 0]?

a)

0

b)

2

c)

-2

d)

-1

e)

-3

82.

Describe the transformations

$-\frac{1}{3}|x-5|+7$

Multiple answers.

a)

Reflection on x-axis

b)

Reflection on y - axis

V.S.

c)

left 5

up 7

d)

right 5

up 7

e)

V.C.

83.

Describe the transformation of the equation below from the parent function of y = I x I
y = -2 I x - 3 I + 3

a)

reflected over x axis, stretched by 2, right 3, up 3

b)

reflected over x axis, stretched by 2, left 3 up 3.

c)

reflected over x axis, shrunk by 2, right 3, up 3

d)

reflected over the x axis, shrunk by 2, left 3, up 3

84.

Describe the end behavior of the graph.

a)

x →∞, y→⁻∞ and x →⁻∞,y→⁻∞

b)

x →∞, y→∞ and x→⁻∞, y→∞

c)

x →∞, y→∞ and x→⁻∞, y→0

d)

x →∞,y→∞ and x→⁻∞, y→⁻∞

85.

Describe the end behavior of the graph.

a)

x → ∞, y→ ∞ and x→ ∞, y→⁻∞

b)

x → ∞, y→ ∞ and x→⁻∞, y→∞

c)

None of these

d)

x →∞,y→⁻∞ and x→∞, y→⁻∞

86.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

87.

What is f(-2)?

a)

4

b)

1

c)

1

d)

DNE

88.

Match the graph with the correct equation.

a)

b)

c)

d)

89.

Graph

a)

b)

c)

d)

90.

What is the domain restriction of the blue piece of this function?

a)

x > 0

b)

x ≥ 0

c)

x > 2

d)

x ≥ 2

91.

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

92.

What are the domain restrictions for the middle piece of this function?

a)

x ≥ 1

b)

x ≥ 2

c)

2 ≤ x < 6

d)

1 ≤ x < 3

93.

Identify the domain.

a)

$x\in R$

b)

$-4\le x\le4$

c)

$-4<x<4$

d)

$-3\le x\le2$

94.

Identify the range.

a)

$y\in R$

b)

$y\le2$

c)

$-3\le y<2$

d)

$-3\le y\le2$

95.

Identify where the graph is increasing.

a)

none

b)

$-4<x<-1$

c)

$-4\le x\le-1$

d)

$-4\le x<3$

96.

Identify where the graph is decreasing.

a)

none

b)

$-4<x<-1$

c)

$-1<x<3$

d)

$x>3$

97.

Identify where the graph is constant.

a)

none

b)

$-4<x<-1$

c)

$x>-1$

d)

$-1<x<4$

98.

Identify the domain.

a)

$x\in R$

b)

$x<-2\ \ or\ \ x>3$

c)

$x<-2\ \ \ or\ \ -2\le x<3$

d)

$x<1\ \ or\ \ 2<x<5$

99.

Identify the range.

a)

$y\in R$

b)

$y\le5$

c)

$y<1\ \ or\ \ y\ge-1$

d)

$2<y\le5\ \ or\ \ y\ge-1$

100.

Identify where the graph is decreasing.

a)

$x\in R$

b)

$x<-2$

c)

$0<x<3$

d)

$x>3$

101.

How many jump discontinuities does the function have?

(a)

102.

The function is:

a)

Continuous

b)

Discontinuous

c)

Neither continuous nor discontinuous

d)

Both continuous and discontinuous

103.

This piecewise function is:

a)

Continuous

b)

Discontinuous

c)

Neither continuous nor discontinuous

d)

Both continuous and discontinuous

104.

Describe the transformation of y = f(x) for the new function
y = - f(x)

a)

The graph of y = f(x) was flipped vertically across the x axis.

b)

The graph of y = f(x) was flipped horizontally across the y axis.

c)

The graph of y = f(x) was shifted down.

d)

The graph of y = f(x) was shifted up

105.

Describe the transformation of y = g(x) for the function
y = 3g(x - 3) + 5

a)

Shifted up 5 units
Shifted right 3 units
Stretched vertically by a factor of 3

b)

Shifted up 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

c)

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 3

d)

Shifted down 5 units
Shifted left 3 units
Stretched vertically by a factor of 1/3

106.

What is one of the solutions to this equation?
(2x - 1)² = 49

a)

7

b)

-7

c)

-4

d)

-3

107.

Solve the equation using square roots:

x² = 121

a)

x = 60.5

b)

x = ± 11

c)

x = ± 12

d)

x= 11

108.

Simplify $\frac{4}{\sqrt{5}}$

a)

$\frac{\sqrt{5}}{2}$

b)

$\frac{\sqrt{6}}{2}$

c)

$\frac{5\sqrt{10}}{5}$

d)

$\frac{4\sqrt{5}}{5}$

109.

Simplify $\frac{2}{\sqrt{2}}$

a)

$\sqrt{2}$

b)

$\frac{\sqrt{6}}{3}$

c)

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

d)

$\frac{\sqrt{2}}{2}$

110.

What is the conjugate of:
$5+\sqrt{7}$

a)

18

b)

$5+\sqrt{7}$

c)

$5-\sqrt{7}$

d)

32

111.

For direct variation, you ______.

a)

Add

b)

Subtract

c)

Multiply

d)

Divide

112.

What is the constant (k) in this inverse variation?
y = 400/x

a)

x

b)

y

c)

400

d)

Not enough information given

113.

The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?

a)

$2

b)

$308

c)

$1.57

d)

$265

114.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

115.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

116.

State what type of variation the equation represents.

a)

Direct

b)

Inverse

c)

Joint

d)

None

117.

What kind of variation does the two quantities shown in the given situation?

The time the painter paints a wall is related to the area of the wall painted?

a)

Direct Variation

b)

Inverse variation

118.

y varies inversely as x. When x=2, y= 1/2, find y when x=1/8.

a)

1

b)

1/8

c)

8

d)

4

119.

The length of time a bag of cat food lasts varies inversely with the number of cats. If the bag of cat food will feed 5 cats for 10 days, how long will it feed 10 cats?

a)

50 days

b)

5 days

c)

1/2 day

d)

1

120.

What kind of variation does the two quantities show?

The age of used car is related to the price the owner can get for it.

a)

Direct variation

b)

Inverse Variation

121.

The width of a rectangle varies inversely with its length. If the width is 6 when the length is 24, give an equation that shows the relationship.

a)

y = 4x

b)

y = 144x

c)

y = 4/x

d)

y = 144/x

122.

Y varies directly with x, and y is 84 when x is 16. Which equation represents this situation?

a)

y=1344x

b)

y=100x

c)

y=5.25x

d)

y=4/21x

123.

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

124.

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

125.

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

126.

The equation
xy = 25 represents:

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

127.

Choose all information that is given in the word problem.

The driving range charges $2.75 for each bucket of golf balls plus an fixed amount to rent a golf club. For 5 hours, it would cost $17.75.

a)

Slope

b)

Y-intercept

c)

Point

128.

y = -2/3x + 2

y = 3/2x + 9

These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

129.

A farmer wants to construct a rectangular pigpen using 400m of fencing. The pen will be built next to an existing stone wall, so only three sides of fencing need to be constructed to enclose the pen. What dimensions should the farmer use to construct the pen with the largest possible area?

a)

100m x 200m

b)

102m x 196m

c)

50m x 300m

d)

50m x 175m

130.

We need to enclose a field with a fence. We have 500 meters of fencing material and a building is on one side of the field so we won't need any fencing on that side. Determine the dimensions of the field that will enclose the largest area.

a)

x=250m, y=125m

b)

x=150m, y=200m

c)

x=125m, y=100m

d)

x=200m, y=150m

131.

Write the explicit formula for the sequence.

9, 5, 1, -3, ...

a)

$a_n=9+5\left(n-1\right)$

b)

$a_n=9-4\left(n-1\right)$

c)

$a_n=4+9\left(n-1\right)$

d)

$a_n=9\cdot4^{\left(n-1\right)}$

132.

Write the explicit formula for the sequence.

216, 72, 24, 8, ...

a)

$a_n=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$

b)

$a_n=8\cdot3^{\left(n-1\right)}$

c)

$a_n=216-144\left(n-1\right)$

d)

$a_n=216\cdot3^{\left(n-1\right)}$

133.

Write the explicit formula for the sequence.

15, 22, 29, 36, 43, ...

a)

$a_n=15+22\left(n-1\right)$

b)

$a_n=15\cdot7^{\left(n-1\right)}$

c)

$a_n=15+7\left(n-1\right)$

d)

$a_n=29-14^{\left(n-1\right)}$

134.

Write the explicit formula for the sequence.

7, 28, 112, 448, ...

a)

$a_n=7+4\left(n-1\right)$

b)

$a_n=7\cdot4^{\left(n-1\right)}$

c)

$a_n=\frac{448}{4n}$

d)

$a_n=28+84\left(n-1\right)$

135.

Determine the values of A, B, and C for the quadratic equation:

4x^2\ -\ 8x\ =\ 3

a)

$A\ =\ 4,\ B\ =\ -8,\ C\ =\ 3$

b)

$A=4,\ B=-8,\ C=-3$

c)

$A=4,\ B=8,\ C=3$

d)

$A=4,\ B=8,\ C=-3$

136.

What is this formula?

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.

137.

What number should be added to complete the square?

x^2+6x

4 lines

138.

Now you: What number should be added to complete the square?

x^2+14x

4 lines

139.

Find the roots of the quadratic equation $x^2+6x+8=0$ by completing the square.

a)

-4 and 2

b)

4 and -2

c)

4 and 2

d)

-4 and -2

140.

The value of $\frac{1}{2\ }b$ and $\left(\frac{1}{2}b\right)^2$ in the equation $x^2+6x-8=0$ are ________________.

a)

8 and 9

b)

8 and -9

c)

3 and 9

d)

-3 and 9

141.

If we move the constant term of the equation $8x^2+8x+8=0$ to the right side, the resulting equation is ___________.

a)

$8𝑥^2+8𝑥=8$

b)

$8𝑥^2+8𝑥=−8$

c)

$8𝑥^2+8=8𝑥$

d)

$8𝑥^2+8=−8𝑥$

142.

What is the first step to solving THIS equation by completing the square?

2a² + 10a = -12

a)

Set the equation equal to zero

b)

Divide 10 by 2, square it, and add the result to both sides

c)

Add a² and 10a together

d)

Divide both sides by 2

143.

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

144.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

145.

Solve by completing the square.
y² + 10y = -9

a)

1 and -12

b)

-1 and -9

c)

1 and -9

d)

1 and -1

146.

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

a)

x = -2 ± √3

b)

x = -3 ± √2

c)

x = 2 ± √3

d)

x = 2 ± √2

147.

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

a)

x = 3, -4

b)

x = -3, 4

c)

x = 3, 4

d)

x = -3, -4

148.

Solve by completing the square.
x² − 10x - 11= 0

a)

x = −1 and 11

b)

x = 1 and −11

c)

x = −10 and 11

d)

x = −5 and 25

149.

Solve by completing the square.
x² − 10x - 11= 0

a)

x = −1 and 11

b)

x = 1 and −11

c)

x = −10 and 11

d)

x = −5 and 25

150.

Solve by completing the square.
x² + 4x= 12

a)

x = 2 and -2

b)

x = -6 and 2

c)

x = 6 and -2

d)

x = 1 and -1

151.

What is the correct factored form of this equation?

x² + 2x = 8

a)

(x-1)²= 9

b)

(x+1)²= 9

c)

(x+4)² = 9

d)

(x-4)² = 9

152.

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

153.

Solve $\left(x+5\right)^2-20=0$ , and leave your answer in the form $p\pm\sqrt[]{q}$

a)

$x=-5\pm\sqrt[]{20}$

b)

$x=5\pm\sqrt[]{20}$

c)

$x=5+\sqrt[]{20}$

d)

$x=-5-\sqrt[]{20}$

154.

Solve $\left(x+5\right)^2-20=0$ , and leave your answer in the form $p\pm\sqrt[]{q}$

a)

$x=-5\pm\sqrt[]{20}$

b)

$x=5\pm\sqrt[]{20}$

c)

$x=5+\sqrt[]{20}$

d)

$x=-5-\sqrt[]{20}$

155.

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

156.

$7p^2-38p-24=0$

a)

$-\frac{7}{2},\ 2$

b)

$-\frac{4}{7},\ 6$

c)

$\frac{3}{5},\ 2$

157.

$x^2+17x+49=3x$

a)

$-7$

b)

$-8,\ -7$

c)

$3,\ 6$

158.

$3m^2=-16m-21$

a)

$7,\ 4$

b)

$-\frac{5}{8},\ 6$

c)

$-\frac{7}{3},\ -3$

159.

$10x^2-26x=-12$

a)

$\frac{7}{3},\ -7$

b)

$\frac{3}{5},\ 2$

c)

$-\frac{2}{3},\ \frac{2}{5}$

160.

$10x^2-26x=-12$

a)

$\frac{7}{3},\ -7$

b)

$\frac{3}{5},\ 2$

c)

$-\frac{2}{3},\ \frac{2}{5}$

161.

$15b^2+4b-4=0$

a)

$-\frac{3}{7},-\frac{1}{5}$

b)

$-\frac{4}{7},\ 6$

c)

$-\frac{2}{3},\ \frac{2}{5}$

162.

$35n^2+22n+3=0$

a)

$-\frac{3}{7},-\frac{1}{5}$

b)

$-\frac{4}{7},\ 6$

c)

$-\frac{2}{3},\ \frac{2}{5}$

163.

Solve the following quadratic equation:
$x^2=49$

a)

$x=0$

b)

$x=7$

c)

$x=-7$

d)

$x=7\ \ \ \&\ \ \ x=-7$

164.

Solve. x² - 81 = 0

a)

x = 3, x = -3

b)

x = 0

c)

x = 9, x = -9

d)

x = 81

165.

Solve. 7m² - 12m + 5 = 0

a)

x = 5/7 and x = 1

b)

x = 8/3 and x = 2

c)

x = 8/3 and x = -1/2

d)

x = -2/3 and x = -5

166.

Solve by factoring

a)

-4, 2

b)

-2, 4

c)

-16

d)

-4

167.

Solve

x² + 2x - 20 = 4

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

168.

Solve this quadratic equation?

x² + 6x - 13 = 3

a)

x= -8 or -2

b)

x = 8 or -2

c)

x = -8 or 2

d)

x = 4 or 2

e)

x = -4 or -6

169.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

170.

Solve by factoring

a)

-2, 4

b)

-8

c)

±8

d)

No real solution

171.

Solve by factoring: x²- 9x + 20 =0

a)

x = -2, 10

b)

x = -5, -4

c)

x = 4, 5

d)

Not factorable

172.

The solutions of the quadratic equation
x²+12x+35=0 are

a)

x = -5 or x = -7

b)

x = 5 or x = 7

c)

x = -35 or x = -1

d)

x = -9 or x = -4

173.

The solutions of the quadratic equation
x²+12x+35=0 are

a)

x = -5 or x = -7

b)

x = 5 or x = 7

c)

x = -35 or x = -1

d)

x = -9 or x = -4

174.

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

a)

$x=0$ and $x=2$

b)

$x=-2$

c)

$x=2$

d)

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

175.

Solve by factoring.

n² - 2n = 0

a)

n = 2 and 0

b)

n = -2 and 0

c)

n = 2

d)

n = 0

176.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

177.

What should you do first in solving this equation?
x² + 6x - 13 = 3

a)

Get factored form

b)

Find two numbers which add to make 6 and multiply to make -13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

178.

What are the factors AND solutions of x² + 2x – 3 = 0

a)

(x - 2)(x + 1); x=2, x=-1

b)

(x + 1)(x - 3); x=-1, x=3

c)

(x + 2)(x - 1); x=-2, x=1

d)

(x - 1)(x + 3); x=1, x=-3

179.

Solve by factoring: x² = 7x + 18

a)

-7 and -18

b)

9 and 2

c)

9 and -2

d)

2 and 7

180.

Solve:

0=x(x - 6)

a)

x=0 and x=-6

b)

x=1 and x=-6

c)

x=0 and x=6

d)

x=6

181.

Solve for the values of x:

(x + 2)(x - 3) = 0

a)

{ 2, 3 }

b)

{ -2, -3 }

c)

{ 2, 3 }

d)

{ -2, 3 }

182.

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

183.

$k^2-2=43$

a)

$\pm\sqrt{34}$

b)

$\pm\sqrt{30}$

c)

$\pm45$

d)

$\pm3\sqrt{5}$

184.

Solve By Square Roots:

$5m^2-3=127$

a)

$\sqrt{26}$

b)

26

c)

$\pm\sqrt{26}$

d)

$\pm26$

185.

√108

a)

3√12

b)

4√27

c)

8√2

d)

6√3

186.

$Solve\ for\ a:\ \ \ \ v=\frac{1}{3}a^2h$

a)

$a=\sqrt{\frac{v}{3h}}$

b)

$a=\sqrt{\frac{3v}{h}}$

c)

$a=\sqrt{3vh}$

d)

no real solution

187.

Solve: (2x - 1)² = 49

a)

7 and - 7

b)

3 and -4

c)

4 and -3

d)

no real solutions

188.

$Solve\ 2\left(x-2\right)^2=6$

a)

$\pm\sqrt{10}$

b)

$2\pm\sqrt{3}$

c)

5, -1

d)

$4\pm\sqrt{3}$

189.

Solve by taking square roots.

2x² - 8 =100

a)

x = ±√54

b)

x = ±3√6

c)

x = ± 9√6

d)

x = ±2√27

Alg2 S1 Final Review

Total questions: 189

Worksheet time: 10hrs 31mins

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