Quiz about Semester 2 ('24) Final Review

Question 1

Use substitution to solve the system.

$$6x-2y\ =\ 20$$

$$4x-y\ =\ 4$$

Accepted Answer

(-6, -28)

Answer

(2,4)

Answer

(2, -4)

Answer

(1, -6)

Question 2

Use elimination to solve the system.

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

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

Accepted Answer

(-4,3)

Answer

(0,6)

Answer

(3,4)

Answer

(4,3)

Question 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.

Accepted Answer

4 five-dollar bills,

10 one-dollar bills

Answer

3 five-dollar bills,

15 one-dollar bills

Answer

5 five-dollar bills,

5 one-dollar bills

Answer

5 five-dollar bills,

9 one-dollar bills

Question 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?

Accepted Answer

65 wraps

Answer

79 wraps

Answer

89 wraps

Answer

64 wraps

Question 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?

Accepted Answer

300 copies

Answer

196 copies

Answer

301 copies

Answer

195 copies

Question 6

Which ordered pair is a solution of the inequality?

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

Accepted Answer

(1,1)

Answer

(3,4)

Answer

(2,1)

Answer

(3,0)

Question 7

Which ordered pair is a solution of the inequality?

$$y\ +1\ <3x$$

Accepted Answer

(5, -4)

Answer

(5, 14)

Answer

(-1, 3)

Answer

(-5, 11)

Question 8

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

$$y=x+1$$

$$y\ =4x-2$$

Accepted Answer

Question 9

Graph the inequality.

$$y<4x-2$$

Accepted Answer

Question 10

Which inequality represents the graph?

Accepted Answer

$$y\le-3x\ +4$$

Answer

$$y\le-3x-4$$

Answer

$$y\ge-3x+4$$

Answer

$$y\ge-3x-4$$

Question 11

What system of inequalities is represented by the graph?

Accepted Answer

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

Answer

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

Answer

$$y\le x+3$$

$$y\ge2x-6$$

Answer

$$y\ge x+3$$

$$y\le2x-6$$

Question 12

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

Accepted Answer

1

Answer

-1

Answer

-8.9

Answer

0

Question 13

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

Accepted Answer

Question 14

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

Accepted Answer

Question 15

Simplify:

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

Accepted Answer

Question 16

Simplify:

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

Accepted Answer

Question 17

Simplify:

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

Accepted Answer

16

Answer

64

Answer

80

Answer

32

Question 18

Simplify:

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

Accepted Answer

3

Answer

81

Answer

27

Answer

9

Question 19

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

Accepted Answer

$$1\cdot10^{-6}$$

Answer

$$10\cdot10^{-6}$$

Answer

$$1\cdot10^{-9}$$

Answer

$$1\cdot10^{-8}$$

Question 20

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

Accepted Answer

Question 21

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

Accepted Answer

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

Answer

$$8h^{100000}$$

Answer

$$8h^{-50}$$

Answer

$$32768h^5$$

Question 22

Simplify:

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 23

Simplify:

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

Accepted Answer

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

Answer

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

Answer

$$x^6y^5$$

Answer

$$x^{-7}y^4$$

Question 24

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

Accepted Answer

Question 25

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

Accepted Answer

$$-\frac{1}{128}$$

Answer

$$\frac{10}{3}$$

Answer

$$128$$

Answer

$$-128$$

Question 26

What is the simplified form of the expression:

$$\sqrt[5]{243}$$

Accepted Answer

$$3$$

Answer

$$243$$

Answer

$$243^5$$

Answer

$$\sqrt[]{243^5}$$

Question 27

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

Accepted Answer

Question 28

What is the degree of the monomial?

$$7m^6n^5$$

Accepted Answer

11

Answer

5

Answer

6

Answer

7

Question 29

What is the degree of the monomial?

-5

Accepted Answer

0

Answer

-6

Answer

1

Answer

5

Question 30

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

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

Accepted Answer

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

cubic polynomial

Answer

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

cubic binomial

Answer

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

quadratic binomial

Answer

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

cubic polynomial

Question 31

Simplify.

Accepted Answer

Question 32

Simplify.

Accepted Answer

Question 33

Simplify.

Accepted Answer

Question 34

Find the GCF.

$$8x^6+36x^2$$

Accepted Answer

$$4x^2$$

Answer

$$4x^6$$

Answer

$$x^2$$

Answer

$$8x^6$$

Question 35

Factor.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 36

Factor.

$$24w^9+64w^4$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 37

F.O.I.L.

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

Accepted Answer

$$16h^2+16h-21$$

Answer

$$16h^2-40h+21$$

Answer

$$16h^2+40h+21$$

Answer

$$16h^2-16h-21$$

Question 38

F.O.I.L.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

Write in simpler form.

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 40

Write in simpler form.

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

Accepted Answer

$$4x^2-24x+36$$

Answer

$$4x^2+36$$

Answer

$$4x^2-8x+36$$

Answer

$$4x^2-12x+36$$

Question 41

Write in simpler form.

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

Accepted Answer

$$4n^2-4$$

Answer

$$4n^2+2n-4$$

Answer

$$4n^2-4n-4$$

Answer

$$4n^2+4n-4$$

Question 42

Factor

$$d^2-8d+12$$

Accepted Answer

(d-6)(d-2)

Answer

(d+6)(d-2)

Answer

(d-6)(d+2)

Answer

(d+6)(d+2)

Question 43

Factor.

$$x^2-x-42$$

Accepted Answer

(x-7)(x+6)

Answer

(x+7)(x-6)

Answer

(x+7)(x+6)

Answer

(x-7)(x-6)

Question 44

Factor.

$$d^2+d-6$$

Accepted Answer

(d+3)(d-2)

Answer

(d+3)(d+2)

Answer

(d-3)(d-2)

Answer

(d-3)(d+2)

Question 45

Factor.

$$6x^2+5x+1$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 46

Factor.

$$20x^2+22x-12$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 47

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

Accepted Answer

4x+3

Answer

-4x+3

Answer

3x+4

Answer

4x-3

Question 48

Factor.

$$32x^2-50$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 49

Identify the vertex. Is it a maximum or minimum?

Accepted Answer

(-1, 1) minimum

Answer

(-1, 1) maximum

Answer

(1, -1) minimum

Answer

(1, -1) maximum

Question 50

Order the quadratic functions from widest to narrowest graphs

Accepted Answer

Question 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.

Accepted Answer

1.25 sec

35 feet

Answer

1.25 sec

40 feet

Answer

2.5 sec

10 feet

Answer

1.25 sec

85 feet

Question 52

Graph the function. Identify the vertex and axis of symmetry

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

Accepted Answer

Question 53

Solve using square roots.

$$3x^2-243\ =0$$

Accepted Answer

$$-9,\ 9$$

Answer

$$-81,\ 81$$

Answer

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

Answer

No real number solutions

Question 54

Solve the equation using the Zero-Product Property.

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

Accepted Answer

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

Answer

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

Answer

$$-4,\ 7$$

Answer

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

Question 55

Solve the equation using the Zero-Product Property

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 56

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

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

Accepted Answer

8, 3

Answer

-8, 3

Answer

8, -3

Answer

-8, -3

Question 57

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

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

Accepted Answer

-1, 2

Answer

-2, -2

Answer

-2, 2

Answer

-1, -2

Question 58

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

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

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 59

What are the solutions of the equation?

(Solve by graphing, factoring, or quadratic formula)

$$x^2-3x=4$$

Accepted Answer

4, -1

Answer

-4, 1

Answer

1.58, -1.58

Answer

7.75, -4.75

Question 60

Using the Quadratic Formula to solve the equation.

$$x^2-4=5x$$

Accepted Answer

-.7, 5.7

Answer

-.7, -5.7

Answer

.7, -5.7

Answer

.7, 5.7

Question 61

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

Accepted Answer

49

Answer

196

Answer

-7

Answer

98

Question 62

Use Completing the Square to solve equation.

$$x^2+7x=11$$

Accepted Answer

-8.32, 1.32

Answer

8.32, -1.32

Answer

-8.32, -1.32

Answer

8.32, 1.32

Question 63

Simplify: $$\sqrt[]{98}$$

Accepted Answer

$$7\sqrt[]{2}$$

Answer

$$5$$

Answer

$$14$$

Answer

$$7\sqrt[]{5}$$

Question 64

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

Accepted Answer

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

Answer

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

Answer

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

Answer

$$cd\ \sqrt[]{20}$$

Semester 2 ('24) Final Review

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