Free Printable Math 2 Final Review (Semester 2)

1.

Determine the values of a, b, and c for the quadratic equation: $4x^2-8x=3$

$a=$ (a)

$b=$ (b)

$c=$ (c)

Choose from the below words

$4$

$-8$

$-3$

-4

8

-4x^2

4x^2

-8x

3

8x

2.

Identify the coefficients a, b, and c from the quadratic equation: $3x^2+6x=-9$

$a=$ (a)

$b=$ (b)

$c=$ (c)

Choose from the below words

$3$

$6$

$9$

-3

-6

-9

3x^2

6x

-3x^2

-6x

3.

Identify the coefficients a, b, and c from the quadratic equation: $5x^2+2x-4=0$

$a=$ (a)

$b=$ (b)

$c=$ (c)

Choose from the below words

-5

-2x

4

2x

2

-2

5x^2

$5$

$-4$

7x^2

4.

Identify the coefficients a, b, and c from the quadratic equation: $8x^2+1=5x$

$a=$ (a)

$b=$ (b)

$c=$ (c)

Choose from the below words

$1$

-8

-1

$-5$

5

$8$

8x^2

3x^2

5x

-5x

5.

This one needs to change!! Identify the coefficients a, b, and c from the quadratic equation: $8x^2+1=5x$

$a=$ (a)

$b=$ (b)

$c=$ (c) !!

Choose from the below words

$1$

-8

-1

$-5$

5

$8$

8x^2

3x^2

5x

-5x

6.

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

$x^2\ -\ 6\ =\ 3x$

a)

$A\ =\ x^2,\ B\ =\ 3x,\ C\ =\ -6$

b)

$A=1,\ B=-3,\ C=-6$

c)

$A=1,\ B=-6,\ C=3$

d)

$A=x^2,\ B=-6,\ C=3x$

7.

Which of the following represents the correct application of the quadratic formula to solve the equation $2x^2-6=-4x$ ?

a)

$\frac{-4 \pm \sqrt[]{4^2 - 4 \cdot 2 \cdot (-6)}}{2 \cdot 2}$

b)

$\frac{-4 \pm \sqrt[]{4^2 + 4 \cdot 2 \cdot 6}}{2 \cdot 2}$

c)

$\frac{-4 \pm \sqrt[]{(-4)^2 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}$

d)

$\frac{-4 \pm \sqrt[]{4^2 - 4 \cdot 2 \cdot 6}}{2 \cdot 2}$

8.

Which of the following shows the quadratic formula correctly used to solve the polynomial equation $9x^2+5=-2x$

a)

$\frac{-\left(5\right)\pm\sqrt[]{\left(5\right)^2-4\left(9\right)\left(-2\right)}}{2\left(9\right)}$

b)

$\frac{-\left(5\right)\pm\sqrt[]{\left(5\right)^2-4\left(9\right)\left(2\right)}}{2\left(9\right)}$

c)

$\frac{-\left(-2\right)\pm\sqrt[]{\left(-2\right)^2-4\left(9\right)\left(5\right)}}{2\left(9\right)}$

d)

$\frac{-\left(2\right)\pm\sqrt[]{\left(2\right)^2-4\left(9\right)\left(5\right)}}{2\left(9\right)}$

9.

Which of the following represents the correct application of the quadratic formula to solve the equation $3x^2 + 7 = 4x$ ?

a)

$\frac{-\left(4\right)\pm\sqrt[]{\left(4\right)^2-4\left(3\right)\left(7\right)}}{2\left(3\right)}$

b)

$\frac{-\left(-4\right)\pm\sqrt[]{\left(-4\right)^2-4\left(3\right)\left(7\right)}}{2\left(3\right)}$

c)

$\frac{-\left(-7\right)\pm\sqrt[]{\left(-7\right)^2-4\left(3\right)\left(4\right)}}{2\left(3\right)}$

d)

$\frac{-\left(-4\right)\pm\sqrt[]{\left(-4\right)^2-4\left(3\right)\left(-7\right)}}{2\left(3\right)}$

10.

Which of the following is the correct application of the quadratic formula to solve the equation $3x^2-7x+2=0$ ?

a)

$\frac{-\left(-7\right)\pm\sqrt[]{7^2-4\cdot3\cdot2}}{2\cdot3}$

b)

$\frac{-7\pm\sqrt[]{7^2-4\cdot3\cdot(-2)}}{2\cdot3}$

c)

$\frac{-\left(-7\right)\pm\sqrt[]{\left(-7\right)^2-4\cdot3\cdot2}}{2\cdot3}$

d)

$\frac{-7\pm\sqrt[]{7^2-4\cdot3\cdot2}}{2\cdot3}$

11.

Which of the following is the correct application of the quadratic formula to solve the equation $2x^2+5x=3$ ?

a)

$\frac{-5\pm\sqrt{5^2-4\cdot2\cdot(-3)}}{2\cdot2}$

b)

$\frac{-5\pm\sqrt{5^2-4\cdot2\cdot3}}{2\cdot2}$

c)

$\frac{5\pm\sqrt{5^2-4\cdot2\cdot3}}{2\cdot2}$

d)

$\frac{5\pm\sqrt{5^2-4\cdot2\cdot(-3)}}{2\cdot2}$

12.

Which of the following represents the correct application of the quadratic formula to solve the equation $3x^2-6x=9$ ?

a)

$\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot3\cdot9}}{2\cdot3}$

b)

$\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot3\cdot(-9)}}{2\cdot3}$

c)

$\frac{6\pm\sqrt[]{6^2-4\cdot3\cdot9}}{2\cdot3}$

d)

$\frac{6\pm\sqrt[]{6^2-4\cdot3\cdot(-9)}}{2\cdot3}$

13.

Solve the equation using the quadratic formula: $7x^2-11x=16$

a)

$\frac{11+\sqrt{569}}{14}\ ,\ \ \frac{11-\sqrt{569}}{14}$

b)

$\frac{11+\sqrt{185}}{14}\ ,\ \ \frac{11-\sqrt{185}}{14}$

c)

$\frac{11+\sqrt{233}}{14}\ ,\ \ \frac{11-\sqrt{233}}{14}$

d)

$\frac{-11+\sqrt{569}}{14}\ ,\ \ \frac{-11-\sqrt{569}}{14}$

14.

Solve the equation using the quadratic formula: $3x^2-19=11x$

a)

$\frac{1+\ \sqrt[]{37}}{12},\ \frac{1-\ \sqrt[]{37}}{12}$

b)

$\frac{-7+\ \sqrt[]{449}}{20},\ \frac{-7-\ \sqrt[]{449}}{20}$

c)

$\frac{-2+\ \sqrt[]{43}}{6},\ \frac{-2-\ \sqrt[]{43}}{6}$

d)

$\frac{11+\ \sqrt[]{349}}{6},\ \frac{11-\ \sqrt[]{349}}{6}$

15.

Solve the equation using the quadratic formula: $a^2+17=11a$

a)

$\frac{9+\ \sqrt[]{101}}{2},\ \frac{9-\ \sqrt[]{101}}{2}$

b)

$\frac{11+\ \sqrt[]{53}}{2},\ \frac{11-\ \sqrt[]{53}}{2}$

c)

$\frac{9+\ \sqrt[]{61}}{2},\ \frac{9-\ \sqrt[]{61}}{2}$

d)

$\frac{11+2\ \sqrt[]{26}}{2},\ \frac{11-2\ \sqrt[]{26}}{2}$

16.

Solve the equation using the quadratic formula: $4b^2-9b=14$

a)

$\frac{-9+\ \sqrt[]{305}}{8},\ \frac{-9-\ \sqrt[]{305}}{8}$

b)

$\frac{9+\ \sqrt[]{305}}{8},\ \frac{9-\ \sqrt[]{305}}{8}$

c)

$\frac{5+\ \sqrt[]{85}}{12},\ \frac{5-\ \sqrt[]{85}}{12}$

d)

$\frac{-9+\ \sqrt[]{137}}{8},\ \frac{-9-\ \sqrt[]{137}}{8}$

17.

Solve the quadratic equation: $9n^2-15=-n$ .

a)

$\frac{-1+2\ \sqrt[]{34}}{18},\ \frac{-1-2\ \sqrt[]{34}}{18}$

b)

$\frac{-1+\ \sqrt[]{541}}{18},\ \frac{-1-\ \sqrt[]{541}}{18}$

c)

$\frac{-1+2\ \sqrt[]{14}}{11},\ \frac{-1-2\ \sqrt[]{14}}{11}$

d)

$\frac{-11+\ \sqrt[]{561}}{10},\ \frac{-11-\ \sqrt[]{561}}{10}$

18.

Solve the quadratic equation: $5k^2=24-3k$ .

a)

$\frac{-3+\ \sqrt[]{129}}{10},\ \frac{-3-\ \sqrt[]{129}}{10}$

b)

$\frac{11+\ \sqrt[]{41}}{10},\ \frac{11-\ \sqrt[]{41}}{10}$

c)

No solution.

d)

$\frac{-3+\ \sqrt[]{489}}{10},\ \frac{-3-\ \sqrt[]{489}}{10}$

19.

Solve the quadratic equation: $11a^2=-7a+2$ .

a)

$\frac{-7+\ \sqrt[]{137}}{22},\ \frac{-7-\ \sqrt[]{137}}{22}$

b)

No solution.

c)

$\frac{-7+\ \sqrt[]{71}}{22},\ \frac{-7-\ \sqrt[]{71}}{22}$

d)

$\frac{7+\ \sqrt[]{137}}{22},\ \frac{7-\ \sqrt[]{137}}{22}$

20.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$ for the equation $x^2-16x+53=0$ ?

a)

$(x-16)^2=53$

b)

$(x+1)^2=37$

c)

$(x-8)^2=-3$

d)

$(x-8)^2=11$

21.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$ for the equation $x^2+20x+89=0$ ?

a)

$(x+10)^2=11$

b)

$(x+10)^2=-8$

c)

$(x+20)^2=89$

d)

$(x)^2=26$

22.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$ for the equation $x^2+14x+38=0$ ?

a)

$(x+7)^2=-7$

b)

$(x+14)^2=38$

c)

$(x+7)^2=11$

d)

$(x-9)^2=2$

23.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$ for the equation $x^2+16x+47=0$ ?

a)

$(x+16)^2=47$

b)

$(x-2)^2=47$

c)

$(x+8)^2=-8$

d)

$(x+8)^2=17$

24.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$ for the equation $x^2+6x-4=0$ ?

a)

$(x+3)^2=-1$

b)

$(x+3)^2=13$

c)

$(x-5)^2=18$

d)

$(x+6)^2=-4$

25.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$ for the equation $x^2+8x-1=0$ ?

a)

$(x+8)^2=-1$

b)

$(x-7)^2=24$

c)

$(x+4)^2=9$

d)

$(x+4)^2=17$

26.

Which equation completes the square to create an equivalent equation in the form of $(x-p)^2=q$

for the equation $x^2+2x-16=0$

a)

$(x+1)^2=17$

b)

$(x+2)^2=-16$

c)

$(x+1)^2=3$

d)

$(x+5)^2=5$

27.

Match the following equations to their corresponding graphs.

a)

1.

$y=\left|x-4\right|-1$

b)

2.

$y=\left|x+4\right|-1$

c)

3.

$y=\left|x+4\right|+1$

d)

4.

$y=\left|x-4\right|+1$

28.

Choose the graph that matched the equation.
y = |x - 1|

a)

b)

c)

d)

29.

Choose the equation that best matches the graphed function.

a)

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

b)

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

c)

$f(x)=-|x|$

d)

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

30.

What is the equation of the graph below?

a)

f(x ) = I x + 4 I + 2

b)

f(x ) = -I x - 4 I + 2

c)

f(x ) = I x - 4 I + 2

d)

f(x ) = -I x + 4 I + 2

31.

Identify the equation of the graph.

a)

y = |x-3|-2

b)

y = -|x-3|-2

c)

y = |x+3|-2

d)

y = |x+3|+2

32.

Which function defines the graph?

a)

f(x) = |x - 4| + 3

b)

f(x) = |x - 3| + 4

c)

f(x) = |-x + 4| + 3

d)

f(x) = |x + 4| + 3

33.

If the parent graph is y = x²

what would the equation be if the new graph

was shifted right 5 and shifted up 8

a)

$y=\left(x-5\right)^2-8$

b)

$y=\left(x-5\right)^2+8$

c)

$y=\left(x+5\right)^2+8$

d)

$y=\left(x+5\right)^2-8$

34.

The equation of red graph is y = x². What is the equation of the blue graph?

a)

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

b)

$y=-3x^2$

c)

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

d)

$y=-x^2-3$

35.

Jose drew the graph of $y=3\left(x+2\right)^2-4$ . How should he transform the graph to produce the graph of $y=3\left(x+2\right)^2+1$ ?

a)

He should shift right 5 units.

b)

He should shift left 5 units.

c)

He should shift up 5 units.

d)

He should shift down 5 units.

36.

Isaac drew the graph of $y=2\left(x-3\right)^2+6$ . How should he transform the graph to produce the graph of $y=2\left(x-3\right)^2+1$ ?

a)

He should shift right 5 units.

b)

He should shift left 5 units.

c)

He should shift up 5 units.

d)

He should shift down 5 units.

37.

Jack drew the graph of $y=-\left(x+3\right)^2+4$ . How should he transform the graph to produce the graph of $y=-\left(x-2\right)^2+4$ ?

a)

He should shift right 5 units.

b)

He should shift left 5 units.

c)

He should shift up 5 units.

d)

He should shift down 5 units.

38.

The graph of $y=-7\left(x-9\right)^2-4$ is drawn. How should it be translated to produce the graph of $y=-7\left(x-3\right)^2-4$

a)

It should shift 6 units right.

b)

It should shift 6 units left.

c)

It should shift 6 units down.

d)

It should shift 6 units up.

39.

Which function below represents the function $f\left(x\right)=\left(x+4\right)^2+3$ after a vertical shift 4 units up and a horizontal shift 2 units to the left?

a)

$f\left(x\right)=\left(x+6\right)^2+7$

b)

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

c)

$f\left(x\right)=\left(x+6\right)^2-1$

d)

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

40.

Which function below represents the function $g\left(x\right)=\left(x-3\right)^2-2$ after a vertical shift 3 units up and a horizontal shift 1 unit to the right?

a)

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

b)

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

c)

$g\left(x\right)=\left(x-4\right)^2-5$

d)

$g\left(x\right)=\left(x-2\right)^2-5$

41.

What is the new function of $f\left(x\right)=\left(x+2\right)^2+3$ after a vertical shift 2 units down and a horizontal shift 3 units to the left?

a)

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

b)

$f\left(x\right)=\left(x+5\right)^2+1$

c)

$f\left(x\right)=\left(x-1\right)^2+5$

d)

$f\left(x\right)=\left(x+5\right)^2+5$

42.

What is the new function of $g\left(x\right)=\left(x-3\right)^2-4$ after a vertical shift 3 units up and a horizontal shift 2 units to the right?

a)

$g\left(x\right)=\left(x-5\right)^2-1$

b)

$g\left(x\right)=\left(x-1\right)^2-1$

c)

$g\left(x\right)=\left(x-5\right)^2+1$

d)

$g\left(x\right)=\left(x-1\right)^2-7$

43.

What is the new function of $f\left(x\right)=\left(x+2\right)^2+5$ after a vertical shift 2 units down and a horizontal shift 3 units to the left?

a)

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

b)

$f\left(x\right)=\left(x+5\right)^2+3$

c)

$f\left(x\right)=\left(x-1\right)^2+7$

d)

$f\left(x\right)=\left(x+5\right)^2-3$

44.

Lilian has decided to open up a hotdog stand to raise money for charity. The amount of money Lilian makes from their hotdog stand is modeled by the function f(x) where x is the number of hours after the hotdog stand opens. Find the average rate of change of the linear function f(x) in the table from x = 1 to x = 7.

a)

12 $ / hour

b)

84 $ / hour

c)

-13 $ / hour

d)

13 $ / hour

45.

Scientist Kirsti is studying the growth of a colony of algae. The colony's population is modeled by the function f(x), where x is the number of hours after Kirsti begins studying the colony. Find the average rate of change of the linear function f(x) in the table from x = 6 to x = 10.

a)

-50 algae / hr

b)

171 algae / hr

c)

57 algae / hr

d)

50 algae / hr

46.

Scientist Melinda is studying the growth of a colony of bacteria. The colony's population is modeled by the function f(x), where x is the number of hours after Melinda begins studying the colony. Find the average rate of change of the linear function f(x) in the table from x = 1 to x = 6.

a)

12 bacteria / hr

b)

84 bacteria / hr

c)

36 bacteria / hr

d)

108 bacteria / hr

47.

Sebastian has decided to open up a candy stand to raise money for charity. The amount of money Sebastian makes from their candy stand is modeled by the function f(x) where x is the number of hours after the candy stand opens. Find the average rate of change of the linear function f(x) in the table from x = 3 to x = 8.

a)

34 $ / hour

b)

289 $ / hour

c)

17 $ / hour

d)

290 $ / hour

48.

What is Mrs. Gordon's rate from 0 to 2 seconds?

a)

2.5 feet per second

b)

.4 feet per second

c)

5 feet per second

d)

.2 feet per second

49.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

50.

Find the measure of each side indicated. Round to the nearest tenth.

a)

11.8

b)

11.3

c)

12.5

d)

13.5

51.

What is the length of y in this 45-45-90 triangle?

a)

8√2

b)

4√2

c)

4

d)

8

52.

Find x.

a)

10

b)

√3

c)

5

d)

10√3

53.

Find x.

a)

4

b)

2

c)

√3

d)

2√2

54.

Find x.

a)

10

b)

20

c)

10√3

d)

√3

55.

Choose the correct values for x and y in the right triangle.

a)

$x=\frac{5\sqrt{6}}{2}$

b)

$x=5$

c)

$y\ =\ 10$

d)

$y=10\sqrt{3}$

56.

What is the value of x?

a)

$7$

b)

$14\sqrt[]{3}$

c)

$14$

d)

$\frac{7\sqrt[]{3}}{2}$ $.$

e)

$None\ of\ these$

57.

Simplify: $15x^{-3}$

a)

$\frac{15}{x^3}$

b)

$\frac{1}{15x^3}$

c)

$12x$

d)

$\frac{-3}{15x}$

e)

$\frac{15}{3x}$

58.

Simplify: $8y^{-2}$

a)

$\frac{1}{8y^2}$

b)

$\frac{8}{y^2}$

c)

$8y^2$

d)

$\frac{-2}{8y}$

e)

$\frac{y^2}{8}$

59.

Simplify: $12x^{-3}$

a)

$\frac{1}{12x^3}$

b)

$\frac{12}{x^3}$

c)

$12x^3$

d)

$\frac{-3}{12x}$

e)

$\frac{x^3}{12}$

60.

Simplify: $5z^{-4}$

a)

$\frac{1}{5z^4}$

b)

$5z^4$

c)

$\frac{5}{z^4}$

d)

$\frac{-4}{5z}$

e)

$\frac{z^4}{5}$

61.

x^-3

a)

-x³

b)

1 / x³

c)

1 / x^-3

d)

-x^-3

62.

Simplify the following expression:
xy^-7

a)

xy⁷

b)

x/y⁷

c)

x⁷/y

d)

x⁷y

63.

Write in radical form: $3^{\frac{1}{2}}$

a)

$\left(\sqrt[4]{5}\right)^5$

b)

$\sqrt[4]{3}$

c)

$\sqrt{3}$

d)

$\sqrt[3]{4}$

64.

Write in radical form: $5^{\frac{1}{2}}$

a)

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

b)

$\left(\sqrt[3]{4}\right)^4$

c)

$\left(\sqrt[]{6}\right)^3$

d)

$\sqrt[]{5}$

65.

Write in radical form: $6^{\frac{1}{3}}$

a)

$\sqrt[3]{6}$

b)

$\sqrt[]{6}$

c)

$\sqrt[]{5}$

d)

$\left(\sqrt[3]{4}\right)^2$

66.

Write the expression in radical form: $7^{\frac{1}{3}}$

a)

$\sqrt[]{5}$

b)

$\sqrt[3]{7}$

c)

$\left(\sqrt[5]{2}\right)^8$

d)

$\sqrt[4]{5}$

67.

Write the expression in exponential form: $\sqrt[]{5}$

a)

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

b)

$6^{\frac{5}{2}}$

c)

$5^{\frac{1}{2}}$

d)

$2^{\frac{5}{6}}$

68.

Write the expression in exponential form: $\left(\sqrt[3]{7}\right)^4$

a)

$7^{\frac{2}{3}}$

b)

$7^{\frac{4}{3}}$

c)

$6^{\frac{3}{2}}$

d)

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

69.

Write the expression in exponential form: $\left(\sqrt[]{2}\right)^3$

a)

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

b)

$7^{\frac{4}{3}}$

c)

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

d)

$6^{\frac{1}{2}}$

70.

Write the expression in exponential form: $\sqrt[]{6}$

a)

$5^{\frac{1}{3}}$

b)

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

c)

$6^{\frac{1}{3}}$

d)

$6^{\frac{1}{2}}$

71.

Find the volume of the Cylinder

a)

7230 cubic meters

b)

6621 cubic meters

c)

1130 cubic meters

d)

907 cubic meters

72.

V = ?

a)

14.13 in³

b)

56.52 in³

c)

169.56 in³

73.

What is the volume of the cone? Round to the nearest whole number.

a)

400 $ft^3$

b)

1200 $ft^3$

c)

3600 $ft^3$

d)

324 $ft^3$

74.

find the volume. Round to the nearest hundredth.

a)

1526.81 $mi^3$

b)

1326 cm³

c)

6104.16 mi³

d)

1026.04 mi³

75.

v = ?

a)

2,144.66 m³

b)

1,608.49 m³

c)

536.17 m³

d)

498.62 m³

76.

Find the Volume.

a)

$150.8\ km^3$

b)

$176.4\ km^3$

c)

$603.2\ km^3$

d)

$103.6\ km^3$

77.

Calculate the volume of the pyramid in the picture. Round to the nearest whole number if necessary.

a)

216 yd³

b)

108 yd³

c)

72 yd³

d)

36 yd³

78.

What is the volume of the following rectangular pyramid?

a)

990 cubic inches

b)

495 cubic inches

c)

660 cubic inches

d)

330 cubic inches

Math 2 Final Review (Semester 2)

Total questions: 78

Worksheet time: 3hrs 42mins

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