Free Printable Semester 2 ('24) Final Review

1.

Use substitution to solve the system.

$6x-2y\ =\ 20$

$4x-y\ =\ 4$

a)

(2,4)

b)

(-6, -28)

c)

(2, -4)

d)

(1, -6)

2.

Use elimination to solve the system.

$3x-4y\ =\ -24$

$x\ +\ y\ =\ -1$

a)

(-4,3)

b)

(0,6)

c)

(3,4)

d)

(4,3)

3.

Billy has some one-dollar bills and some five-dollar bills. He has 14 bills. The value of the bill is $30. Solve a system of equations using elimination to find how many of each kind of bill he has.

a)

4 five-dollar bills,

10 one-dollar bills

b)

3 five-dollar bills,

15 one-dollar bills

c)

5 five-dollar bills,

5 one-dollar bills

d)

5 five-dollar bills,

9 one-dollar bills

4.

The school cafeteria sells two kinds of wraps: vegetarian and chicken. The vegetarian wrap cost $1 and the chicken wrap costs $2.90. Today they made $294.10 from the 144 wraps sold. How many of the wraps sold were vegetarian?

a)

79 wraps

b)

89 wraps

c)

64 wraps

d)

65 wraps

5.

You decide to market your own custom computer software. You must invest $3255 for computer hardware, and spend $2.90 to buy and package each disk. If each program sells for $13.75, how many copies must you sell to break even?

a)

196 copies

b)

301 copies

c)

300 copies

d)

195 copies

6.

Which ordered pair is a solution of the inequality?

$y\ge\ 4x\ -5\$

a)

(3,4)

b)

(2,1)

c)

(3,0)

d)

(1,1)

7.

Which ordered pair is a solution of the inequality?

$y\ +1\ <3x$

a)

(5, 14)

b)

(-1, 3)

c)

(5, -4)

d)

(-5, 11)

8.

What is the solution of the system? Pick the correct graph.

$y=x+1$

$y\ =4x-2$

a)

b)

c)

d)

9.

Graph the inequality.

$y<4x-2$

a)

b)

c)

d)

10.

Which inequality represents the graph?

a)

$y\le-3x-4$

b)

$y\le-3x\ +4$

c)

$y\ge-3x+4$

d)

$y\ge-3x-4$

11.

What system of inequalities is represented by the graph?

a)

$y\ge x-2$ $y\ge-3x-6$

b)

$y\le x-2$ $y\le-3x-6$

c)

$y\le x+3$

$y\ge2x-6$

d)

$y\ge x+3$

$y\le2x-6$

12.

$\left(-8.9\right)^0$

a)

-1

b)

-8.9

c)

1

d)

0

13.

$8k^{-6}d^4$

a)

b)

c)

d)

14.

$\frac{4}{x^{-9}y^5}$

a)

b)

c)

d)

15.

Simplify:

$7x^{-8}\cdot6x^3$

a)

b)

c)

d)

16.

Simplify:

$\left(-3c^8\right)\cdot2d^6\cdot5c^5$

a)

b)

c)

d)

17.

Simplify:

$16^{\frac{5}{4}}$

a)

16

b)

64

c)

80

d)

32

18.

Simplify:

$27^{\frac{1}{3}}$

a)

81

b)

3

c)

27

d)

9

19.

$\left(2\ \cdot\ 10^{-3}\right)\left(5\cdot10^{-4}\right)$

a)

$10\cdot10^{-6}$

b)

$1\cdot10^{-9}$

c)

$1\cdot10^{-8}$

d)

$1\cdot10^{-6}$

20.

$k^3\left(k^{\frac{8}{5}}\right)^{-5}$

a)

b)

c)

d)

21.

$\left(8h^{10}\right)^{-5}$

a)

$8h^{100000}$

b)

$\frac{1}{32768}h^{-50}$

c)

$8h^{-50}$

d)

$32768h^5$

22.

Simplify:

$\left(-4m^3n^5\right)^2\left(m^7n^8\right)^3$

a)

$\frac{m^{27}n^{34}}{16}$

b)

$16m^{27}n^{34}$

c)

$16m^{15}n^{18}$

d)

$-16m^{27}n^{34}$

23.

Simplify:

$\frac{x^{-5}y^{-12}}{x^{-11}y^{-7}}$

a)

$\frac{y^{-17}}{x^{-18}}$

b)

$x^6y^5$

c)

$\frac{x^6}{y^5}$

d)

$x^{-7}y^4$

24.

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

a)

b)

c)

d)

25.

What is the value of $\frac{y^{-5}}{x^{-3}}$ for x = 2 and y= -4?

a)

$\frac{10}{3}$

b)

$128$

c)

$-\frac{1}{128}$

d)

$-128$

26.

What is the simplified form of the expression:

$\sqrt[5]{243}$

a)

$243$

b)

$243^5$

c)

$\sqrt[]{243^5}$

d)

$3$

27.

Write the exponential expression $3x^{\frac{3}{10}}$ in radical form.

a)

b)

c)

d)

28.

What is the degree of the monomial?

$7m^6n^5$

a)

5

b)

11

c)

6

d)

7

29.

What is the degree of the monomial?

-5

a)

0

b)

-6

c)

1

d)

5

30.

Standard form of the polynomial and name based on degree and number of terms.

$6g-8g^3+3g^2-9$

a)

$-9+6g+3g^2-8g^3$

cubic binomial

b)

$-8g^3+3g^2+6g-9$

cubic polynomial

c)

$3g^3-8g^2+6g-9$

quadratic binomial

d)

$8g^3-3g^2+6g-9$

cubic polynomial

31.

Simplify.

a)

b)

c)

d)

32.

Simplify.

a)

b)

c)

d)

33.

Simplify.

a)

b)

c)

d)

34.

Find the GCF.

$8x^6+36x^2$

a)

$4x^2$

b)

$4x^6$

c)

$x^2$

d)

$8x^6$

35.

Factor.

$2x^3+4x^2+8x$

a)

$2x\left(x^2+2x+4\right)$

b)

$2x\left(x^2+2x+8\right)$

c)

$2x\left(x+2\right)\left(x+4\right)$

d)

$2x\left(x+2\right)\left(x+2\right)$

36.

Factor.

$24w^9+64w^4$

a)

$8w^3\left(3w^6+8w\right)$

b)

$8\left(3w^9+8w^4\right)$

c)

$w^4\left(24w^5+64\right)$

d)

$8w^4\left(3w^5+8\right)$

37.

F.O.I.L.

$\left(4h+7\right)\left(4h-3\right)$

a)

$16h^2-40h+21$

b)

$16h^2+40h+21$

c)

$16h^2-16h-21$

d)

$16h^2+16h-21$

38.

F.O.I.L.

$\left(-5h-4\right)\left(5h+7\right)$

a)

$-25h^2+55h-28$

b)

$-25h^2-55h-28$

c)

$-25h^2+15h+28$

d)

$-25h^2-15h+28$

39.

Write in simpler form.

$\left(2n^2+5n+4\right)\left(3n-5\right)$

a)

$6n^3+25n^2-37n-20$

b)

$6n^3-5n^2+37n-20$

c)

$6n^3+13n^2-5n-20$

d)

$6n^3+5n^2-13n-20$

40.

Write in simpler form.

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

a)

$4x^2-24x+36$

b)

$4x^2+36$

c)

$4x^2-8x+36$

d)

$4x^2-12x+36$

41.

Write in simpler form.

$\left(2n+2\right)\left(2n-2\right)$

a)

$4n^2-4$

b)

$4n^2+2n-4$

c)

$4n^2-4n-4$

d)

$4n^2+4n-4$

42.

Factor

$d^2-8d+12$

a)

(d-6)(d-2)

b)

(d+6)(d-2)

c)

(d-6)(d+2)

d)

(d+6)(d+2)

43.

Factor.

$x^2-x-42$

a)

(x-7)(x+6)

b)

(x+7)(x-6)

c)

(x+7)(x+6)

d)

(x-7)(x-6)

44.

Factor.

$d^2+d-6$

a)

(d+3)(d-2)

b)

(d+3)(d+2)

c)

(d-3)(d-2)

d)

(d-3)(d+2)

45.

Factor.

$6x^2+5x+1$

a)

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

b)

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

c)

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

d)

$\left(3x+1\right)\left(2x+1\right)$

46.

Factor.

$20x^2+22x-12$

a)

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

b)

$\left(10x-2\right)\left(4x+3\right)$

c)

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

d)

$2\left(5x\ +4\right)\left(2x-3\right)$

47.

Area of a square lawn is $16x^2+24x+9$ . What is the length of one side of the lawn?

a)

-4x+3

b)

4x+3

c)

3x+4

d)

4x-3

48.

Factor.

$32x^2-50$

a)

$2\left(5x+4\right)\left(5x-4\right)$

b)

$2\left(4x+5\right)^2$

c)

$2\left(4x+5\right)\left(4x-5\right)$

d)

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

49.

Identify the vertex. Is it a maximum or minimum?

a)

(-1, 1) minimum

b)

(-1, 1) maximum

c)

(1, -1) minimum

d)

(1, -1) maximum

50.

Order the quadratic functions from widest to narrowest graphs

a)

b)

c)

d)

51.

A ball is thrown into the air with an upward velocity of 40ft/s. Its height h in feet after t seconds is given by the function h = -16t² + 40t + 10. How long does it take the ball to reach its maximum height? What is the ball's maximum height? Round to the nearest hundredth, if necessary.

a)

1.25 sec

35 feet

b)

1.25 sec

40 feet

c)

2.5 sec

10 feet

d)

1.25 sec

85 feet

52.

Graph the function. Identify the vertex and axis of symmetry

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

a)

b)

c)

d)

53.

Solve using square roots.

$3x^2-243\ =0$

a)

$-81,\ 81$

b)

$-9,\ 9$

c)

$-\sqrt[]{9},\ \sqrt[]{9}$

d)

No real number solutions

54.

Solve the equation using the Zero-Product Property.

$\left(4x\ +4\right)\left(7x-3\right)\ =\ 0$

a)

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

b)

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

c)

$-4,\ 7$

d)

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

55.

Solve the equation using the Zero-Product Property

$9n\left(10n-3\right)\ =0$

a)

$\frac{1}{9},\frac{3}{10}$

b)

$\frac{1}{9},\ -\frac{3}{10}$

c)

$0,\ \frac{3}{10}$

d)

$0,\ -\frac{3}{10}$

56.

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

$z^2-11z+24=0$

a)

-8, 3

b)

8, 3

c)

8, -3

d)

-8, -3

57.

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

$2z^2-2z-4=0$

a)

-2, -2

b)

-2, 2

c)

-1, 2

d)

-1, -2

58.

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

$6x^2-17x+13=20x^2-32$

a)

$\frac{5}{3},\ \frac{9}{2}$

b)

$-\frac{5}{2},\frac{9}{7}$

c)

$-\frac{5}{2},-\frac{9}{7}$

d)

$-\frac{5}{3},\frac{9}{2}$

59.

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

$x^2-3x=4$

a)

-4, 1

b)

4, -1

c)

1.58, -1.58

d)

7.75, -4.75

60.

Using the Quadratic Formula to solve the equation.

$x^2-4=5x$

a)

-.7, -5.7

b)

.7, -5.7

c)

.7, 5.7

d)

-.7, 5.7

61.

What is the value of c such that $x^2-14x+c$ is a perfect square trinomial?

a)

196

b)

-7

c)

98

d)

49

62.

Use Completing the Square to solve equation.

$x^2+7x=11$

a)

8.32, -1.32

b)

-8.32, -1.32

c)

8.32, 1.32

d)

-8.32, 1.32

63.

Simplify: $\sqrt[]{98}$

a)

$5$

b)

$14$

c)

$7\sqrt[]{2}$

d)

$7\sqrt[]{5}$

64.

Simplify: $\sqrt[]{40c^4d^2}$

a)

$2c^2d\ \sqrt[]{10}$

b)

$2\ \sqrt[]{10c^4d^2}$

c)

$4\ \sqrt[]{10c^4d^2}$

d)

$cd\ \sqrt[]{20}$

65.

Simplify: $\sqrt[]{2\ }\cdot\ 2\ \sqrt[]{6}$

a)

$4\ \sqrt[]{6}$

b)

$3\ \sqrt[]{12}$

c)

$4\ \sqrt[]{3}$

d)

$2\ \sqrt[]{12}$

66.

Simplify: $\sqrt[]{\frac{15}{4p^2}}$

a)

$\frac{\sqrt[]{15}}{2\ \sqrt[]{p^2}}$

b)

$\frac{\sqrt[]{15}}{2p^2}$

c)

$\frac{15}{2p^2}$

d)

$2p^2\ \sqrt[]{15}$

67.

Simplify:

$\sqrt[]{6\ }\ +7\ \sqrt[]{6}$

a)

$6\ \sqrt[]{6}$

b)

$6\ \sqrt[]{12}$

c)

$8\ \sqrt[]{12}$

d)

$8\ \sqrt[]{6}$

68.

Simplify:

$4\ \sqrt[]{7}-4\ \sqrt[]{28}$

a)

$-4\ \sqrt[]{28}$

b)

$-4\ \sqrt[]{7}$

c)

$-12\ \sqrt[]{7}$

d)

$\sqrt[]{28}$

69.

Simplify:

$\left(7-\ \sqrt[]{6}\right)\left(7+\ \sqrt[]{6}\right)$

a)

$13$

b)

$43$

c)

$55+14\ \sqrt[]{6}$

d)

$49\ +\ \sqrt[]{6}$

70.

Solve: $\sqrt[]{p+2}=11$

a)

119

b)

20

c)

123

d)

9

71.

Solve:

$\sqrt[]{6x-8}=\ \sqrt[]{4x-2}$

a)

0

b)

2

c)

3

d)

-3

72.

Measures of Central Tendencies:

15, 7, 11, 4, 1, 10, 1, 14, 1, 12, 14

a)

Mean: 7.5

Median: 10

Mode: 8

b)

Mean: 8.2

Median: 10

Mode: 1

c)

Mean: 8.2

Median: 8

Mode: 1

d)

Mean: 7.5

Median: 10

Mode: none

73.

Use the discriminant determine number of solutions

$5x^2-10x-9=0$

a)

one solution

b)

two solutions

c)

no real solutions

d)

infinitely many solutions

74.

What are the solutions of the system?

$y\ =\ x^2+3x-5$

$y=-4x+3$

a)

(-8, 35) & (1, -1)

b)

(-8, 35) & (-1, 7)

c)

(-8, -1) & (1, 35)

d)

No solution

75.

What is the graph of the function?

$y\ =\ -\frac{1}{3}\cdot4^x$

a)

b)

c)

d)

Semester 2 ('24) Final Review

Total questions: 75

Worksheet time: 5hrs 45mins

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