Quiz about 8th Algebra Spring Final Practice

Question 1

Simplify the product: $$3p^4(4p^4 + 7p^3 + 4p + 1)$$ .

Accepted Answer

$$12p^8 + 21p^7 + 12p^5 + 3p^4$$

Answer

$$12p^8 + 3p^7 + 4p^5 + p^4$$

Answer

$$7p^8 + 10p^7 + 7p^5 + 4p^4$$

Answer

$$12p^{16} + 21p^{12} + 15p^4$$

Question 2

Simplify the product: $$2n(n^2 + 3n + 4)$$ .

Accepted Answer

$$2n^3 + 6n^2 + 8n$$

Answer

$$2n^3 + 3n + 4$$

Answer

$$n^2 + 5n + 4$$

Answer

$$2n^2 + 6n + 8$$

Question 3

Simplify the product: $$4a^3(7a^2 - 6b^4)$$ .

Accepted Answer

$$28a^7 - 24a^6b^4$$

Answer

$$11a^{10} - 10a^5b^2$$

Answer

$$11a^7 - 10a^5b^2$$

Answer

$$28a^7 - 24a^5b^4$$

Question 4

Simplify the product: $$7x^3(8x^7 + 5y)$$ .

Accepted Answer

$$56x^{10} + 35xy^6$$

Answer

$$15x^{10} + 12x^3y^3$$

Answer

$$15x^{21} + 12x^3y^3$$

Answer

$$56x^{10} + 35x^3y^3$$

Question 5

Factor the polynomial: $$2x^3 + 4x^2 + 8x$$ .

Accepted Answer

$$x(2x^2 + 4x + 8)$$

Answer

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

Answer

2x(x + 2)(x + 4)

Answer

$$2x(x^2 + 2x + 4)$$

Question 6

Tell whether the ordered pair $(-3, 2)$ is a solution of the system of linear equations: $y = x + 5$ and $y = -4x - 10$.

Accepted Answer

No

Answer

Yes

Question 7

Tell whether the ordered pair $(0, -3)$ is a solution of the system of linear equations: $x + y = -3$ and $-4x - 2y = 8$.

Accepted Answer

No

Answer

Yes

Question 8

What is the solution to the system of equations: -6x + 2y = -10 and -2x - y = -5?

Accepted Answer

(2, 1)

Answer

(1, 2)

Answer

(0, 0)

Answer

(-1, -2)

Question 9

Simplify the expression: $$\frac{k^{13}}{k^{10}}$$ .

Accepted Answer

$$k^3$$

Answer

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

Answer

$$k^{130}$$

Answer

$$k^{23}$$

Question 10

Simplify the expression: $$y^8 \cdot 5y$$ .

Accepted Answer

$$5y^9$$

Answer

$$6y^8$$

Answer

$$6y^9$$

Answer

$$5y^8$$

Question 11

Simplify the expression: $$(5k^3)^4$$ .

Accepted Answer

$$625k^{12}$$

Answer

$$5k^{12}$$

Answer

$$5k^{81}$$

Answer

$$625k^7$$

Question 12

Simplify the expression: $$\frac{6^7}{6^6}$$ .

Accepted Answer

6

Answer

$$6^{13}$$

Answer

$$6^{42}$$

Answer

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

Question 13

Simplify the expression: $$(-3)^{-3}$$ .

Accepted Answer

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

Answer

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

Answer

$$3^3$$

Answer

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

Question 14

Simplify the expression: $$3^{-4} \cdot 5^0$$ .

Accepted Answer

$$\frac{1}{81}$$

Answer

-12

Answer

81

Answer

0

Question 15

Simplify the expression: $$(3xy^3)^2(xy)^6$$ .

Accepted Answer

$$9x^8y^{12}$$

Answer

$$9x^8y^9$$

Answer

$$2x^3y^{12}$$

Answer

$$3x^8y^{12}$$

Question 16

Simplify the expression: $$\frac{4k^6h^{-6}}{h^6}$$ .

Accepted Answer

$$\frac{4k^6}{h^6}$$

Answer

$$\frac{k^6}{4h^6}$$

Answer

$$4k^{-6}h^6$$

Answer

$$4kh^{-36}$$

Question 17

What is the result of $$\frac{4}{3y}$$ ?

Accepted Answer

$$\frac{16}{9y^2}$$

Answer

$$\frac{8}{6y^2}$$

Answer

$$\frac{16}{3y}$$

Answer

$$12y^2$$

Question 18

What is the result of $$(t^{-7})^3$$ ?

Accepted Answer

$$\frac{1}{t^{21}}$$

Answer

$$t^{21}$$

Answer

$$\frac{x}{21}$$

Answer

$$\frac{1}{t^{343}}$$

Question 19

What is the result of $$(-7.1)^0$$ ?

Accepted Answer

1

Answer

0

Answer

-7.1

Answer

-1

Question 20

Simplify $$\frac{m^3n^2}{m^1n^4}$$ .

Accepted Answer

$$m^3n^2$$

Answer

$$m^1n^7$$

Answer

$$\frac{n^{-1}}{n^{-7}}$$

Answer

$$\frac{m^8}{n^2}$$

Question 21

What is the result of $$(t^2)^4$$ ?

Accepted Answer

$$t^{16}$$

Answer

$$t^8$$

Answer

$$t^6$$

Answer

$$2t^8$$

Question 22

Simplify $$\frac{a^6}{a^8}$$ .

Accepted Answer

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

Answer

$$\frac{1}{a^{14}}$$

Answer

$$$a^2$$$

Answer

$$a^{14}$$

Question 23

What is the result of $$(5.63)^{-5} \cdot (5.63)^6$$ ?

Accepted Answer

1

Answer

$$-5.63^{11}$$

Answer

11

Answer

5.63

Question 24

Simplify $$\frac{7^2}{7^4}$$ .

Accepted Answer

$$\frac{1}{49}$$

Answer

49

Answer

$$\frac{1}{7^6}$$

Answer

$$7^6$$

Question 25

What is the result of $$(3)^{-4}$$ ?

Accepted Answer

$$\frac{1}{81}$$

Answer

81

Answer

-12

Question 26

Calculate $$15 \cdot 5^{-4}$$ .

Accepted Answer

$$\frac{3}{125}$$

Answer

625

Answer

-9,375

Answer

-300

Question 27

Solve the system using elimination: 3x - 4y = 9 -3x + 2y = 9

Accepted Answer

(-3, -6)

Answer

(-27, -9)

Answer

(3, 9)

Answer

(-9, -9)

Question 28

Solve the system using elimination: 3x - y = 28 3x + y = 14

Accepted Answer

(8, -4)

Answer

(-7, 7)

Answer

(-4, 8)

Answer

(7, -7)

Question 29

Which graph represents the following system of equations? y = -3x + 3 y = -x - 1

Accepted Answer

Graph b

Answer

Graph a

Answer

Graph c

Answer

Graph d

Question 30

Write an equation of a line with the given slope and y-intercept: m = 4, b = 1

Accepted Answer

y = 4x + 1

Answer

y = x + 4

Answer

y = -4x + 1

Answer

y = 4x - 1

Question 31

Solve the system of linear equations: -4x - 2y = 6 and 16x + 8y = -24.

Accepted Answer

infinitely many solutions

Answer

no solution

Answer

(1, -5)

Answer

(4, 5)

Question 32

Solve the system of linear equations: y = x + 1 and y = x + 9.

Accepted Answer

no solution

Answer

(1, 1)

Answer

(1, 9)

Answer

infinitely many solutions

Question 33

Solve the system of linear equations: x - 2y = 8 and -x + 2y = 8.

Accepted Answer

(-4, -2)

Answer

no solution

Answer

(4, -2)

Answer

infinitely many solutions

Question 34

Solve the system of linear equations: y = -4x + 9 and y = 4x - 7.

Accepted Answer

(-2, 17)

Answer

no solution

Answer

infinitely many solutions

Answer

(2, 1)

Question 35

By what number should you multiply the first equation to solve using elimination? -5x - 2y = 6, -20x + 3y = 46.

Accepted Answer

4

Answer

3

Answer

-20

Answer

-5

Question 36

The solutions given by the quadratic formula are _______ integers.

Accepted Answer

sometimes

Answer

always

Answer

never

Answer

only

Question 37

Factor the expression: $$$d^2 + 14d + 40$$$ .

Accepted Answer

$(d + 4)(d + 10)$

Answer

$(d - 4)(d + 10)$

Answer

$(d - 4)(d - 10)$

Answer

$(d + 4)(d - 10)$

Question 38

Factor the expression: $$$w^2 + 18w + 77$$$ .

Accepted Answer

$(w + 7)(w + 11)$

Answer

$(w - 7)(w + 11)$

Answer

$(w + 1)(w + 77)$

Answer

$(w - 7)(w - 11)$

Question 39

Factor the expression: $$$x^2 - 10xy + 24y^2$$$ .

Accepted Answer

$(x - 6y)(x - 4y)$

Answer

$(x - 2y)(x + 12y)$

Answer

$(x + 6y)(x + 4y)$

Answer

$(x + 2y)(x - 12y)$

Question 40

Factor the expression: $$k^2 + 7kf - 8f^2$$ .

Accepted Answer

$(k - 8)(k + f)$

Answer

$(k + 8)(k + f)$

Answer

$(k - 8)(k - f)$

Answer

$(k + 8)(k - f)$

Question 41

Find the product: $(2n + 2)(2n - 2)$.

Accepted Answer

$$$4n^2 - 4$$

Answer

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

Answer

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

Answer

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

Question 42

Find the product: $(j + 7)(j - 7)$.

Accepted Answer

$$j^2 - 49$$

Answer

$$j^2 + 14j - 49$$

Answer

$$j^2 - 14j - 49$$

Answer

$$j^2 + 14j - 49$$

Question 43

Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms: $$2 - 11x^2 - 8x + 6x^2$$ .

Accepted Answer

$$-5x^2 - 8x + 2$$ ; quadratic trinomial

Answer

$$-5x^2 - 8x - 2$$ ; cubic polynomial

Answer

$$$5x^2 - 8x - 2$$ ; quadratic trinomial

Answer

$$$6x^2 - 8x + 2$$ ; cubic trinomial

Question 44

Graph each system. Tell whether the system has no solution, one solution, or infinitely many solutions: $y = -3x - 4$ $y = -5x - 2$.

Accepted Answer

one solution

Answer

no solutions

Answer

infinitely many solutions

Question 45

Which system of equations has one solution?

Accepted Answer

$ y = -2x - 3 $, $ y = -2x - 5 $

Answer

$ y = -2x - 3 $, $ y = -2x - 4 $

Answer

$ y = -2x - 5 $, $ y + 5 = -2x $

Question 46

Which number is NOT written in scientific notation?

Accepted Answer

$$25.67 imes 10^{-2}$$

Answer

$$8.7 imes 10^{-5}$$

Answer

$$$ 6.7 \times 10^3 $$$

Answer

$$$ 3 \times 10^{-8} $$$

Question 47

Find the slope and y-intercept of the line $$y = \frac{6}{5}x + 1$$ .

Accepted Answer

Slope: $$\frac{6}{5}$$ , y-intercept: 1

Answer

Slope: $$\frac{5}{6}$$ , y-intercept: -1

Answer

Slope: -1, y-intercept: $$\frac{6}{5}$$

Answer

Slope: $$\frac{6}{5}$$ , y-intercept: $$\frac{1}{5}$$

Question 48

Simplify the sum: $$(3u^3 + 4u^2 + 6) + (2u^3 - 6u + 8)$$ .

Accepted Answer

$$5u^3 + 4u^2 - 6u + 14$$

Answer

$$$ 1u^3 - 6u^2 + 4u - 14 $$$

Answer

$$14 - 6u + 4u^2 + 5u^3$$

Answer

$$$ 1u^3 + 4u^2 - 6u + 14 $$$

Question 49

Find the product: $ (3c - 7)(4c - 7) $.

Accepted Answer

$$12c^2 - 28c + 49$$

Answer

$$12c^2 - 49c - 49$$

Answer

$$12c^2 + 49$$

Answer

$$$ 12c^2 - 49c + 49 $$$

Question 50

Write an equation of the line with the given slope and y-intercept: slope 4, y-intercept -6.

Accepted Answer

$ y = 4x - 6 $

Answer

$ y = 4m + 6 $

Answer

$ y = -6x - 4 $

Answer

$ y = -6x + 4 $

Question 51

Write the polynomial in standard form: $$7g - 5g^3 + 4g^2 - 1$$ .

Accepted Answer

$$-5g^3 + 4g^2 + 7g - 1$$

Answer

$$-1 + 7g + 4g^2 - 5g^3$$

Answer

$$5g^3 - 4g^2 + 7g - 1$$

Answer

$$4g^3 - 5g^2 + 7g - 1$$

Question 52

Solve the system of equations using substitution. y = 3x - 5 y = 4x - 9

Accepted Answer

(2, -1)

Answer

(-5, -19)

Answer

(2, 1)

Answer

(4, 7)

Question 53

Solve the system of equations using substitution. y = 4x + 8 y = 3x + 5

Accepted Answer

(3, 14)

Answer

(20, 3)

Answer

(3, 20)

Answer

(-3, -4)

Question 54

The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation.

Accepted Answer

25 dollars per day; the cost is $25 for each day.

Answer

75 dollars per day; the cost is $75 for each day.

Answer

1/25 dollars per day; the cost is $25 for each day.

Answer

1/150 dollars per day; the costs $1 for 150 days

Question 55

Write the number in standard notation. $$8 x 10^5$$

Accepted Answer

800,000

Answer

$$80^5$$

Answer

80,000

Answer

400

Question 56

Write the number in standard notation. $$2.04 imes 10^{-2}$$

Accepted Answer

0.0204

Answer

0.00204

Answer

0.204

Answer

-40.8

Question 57

Find the product. $$(x + 5)(x^2 - 2x + 3)$$

Accepted Answer

$$x^3 + 3x^2 - 7x + 15$$

Answer

$$x^3 + 3x^2 - 10x + 15$$

Answer

$$x^2 - 3x + 15$$

Answer

$$x^3 - 2x^2 + 15$$

Question 58

Find the sum: (3y + 6) + (-5y + 9)

Accepted Answer

-2y + 15

Answer

8y - 3

Answer

9y + 4

Answer

-2y + 6

Question 59

Find the degree of the monomial: 4.8

Accepted Answer

0

Answer

23.04

Answer

4.8

Answer

1

Question 60

Assume that the two lines are perpendicular. What is the slope-intercept equation for line A?

Accepted Answer

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

Answer

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

Answer

y = $$\frac{3}{2}x + 4$$

Answer

y = $$-\frac{3}{2}x + 4$$

Question 61

Assume that the two lines are perpendicular. What is the point-slope equation for line B?

Accepted Answer

y - 4 = $$\frac{3}{2}(x - 1)$$

Answer

y - 1 = $$\frac{3}{2}(x + 4)$$

Answer

y - 1 = $$\frac{3}{2}(x - 4)$$

Answer

y - 4 = $$\frac{3}{2}(x + 1)$$

Question 62

Which graph represents the function $ y = -3x + 2 $?

Accepted Answer

Graph a

Answer

Graph b

Answer

Graph c

Answer

Graph d

Question 63

What is the value of $$$ 8^0 $$$ ?

Accepted Answer

1

Answer

8

Answer

-8

Answer

0

Question 64

Evaluate the expression $$\frac{(-7)^{-4}}{(-9)^{-3}}$$ .

Accepted Answer

$$\frac{2401}{729}$$

Answer

$$\frac{729}{2401}$$

Answer

$$\frac{28}{27}$$

Answer

$$\frac{27}{28}$$

8th Algebra Spring Final Practice

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