Free Printable Fall 2023 Final exam review Part 2: Equations

1.

Solve for the value of x:

$\sqrt[]{2x+3}+\sqrt[]{x-2}=2$

(if no solutions exists type: no solution)

(a)

2.

Solve for the value of x:

$\sqrt[]{3x+1}+3=7$

(if no solutions exists type: no solution)

(a)

3.

Solve for the value of x:

$\sqrt[]{x+1}-3x=1$

(if no solutions exists type: no solution)

(a)

4.

Find the extraneous solution for the following equation:

$2x+9\sqrt[]{x}-5=0$

(a)

5.

a)

$x=2$

b)

$x=\frac{3}{4}$

c)

$x=4$

d)

$x=\frac{1}{2}$

6.

a)

$-\frac{25}{3}$

b)

4

c)

-6

d)

$\frac{25}{3}$

7.

Solve for x

a)

x = 5

b)

x = $\frac{4}{5}$

c)

x = 1

d)

x = - 4

8.

Solve for v

a)

$-\frac{7}{6}$

b)

$-\frac{9}{5}$

c)

$\frac{9}{5}$

d)

$-3$

9.

Solve for the value of x:

$\left(x+5\right)^{\frac{1}{3}}=\left(x-1\right)^{\frac{2}{3}}$

Write answers as a set using {}

(a)

10.

Solve for the value of x:

$\sqrt[]{x}-\sqrt[]{x-5}=1$

(if no solutions exists type: no solution)

(a)

11.

Solve for the value of x in the equation:

$\left(4x+4\right)^{\frac{1}{3}}+2=0$

12.

$\sqrt[3]{2x+1}+8=0$

13.

Determine any extraneous solutions for the equation:

$\sqrt[]{2x+3}+\sqrt[]{x-2}=2$

(if no solutions are extraneous type: none)

(a)

14.

Classify this polynomial by its degree and number of terms: x² + 6

a)

Linear polynomial

b)

Quadratic trinomial

c)

Quadratic binomial

d)

Cubic binomial

15.

Classify this polynomial by its degree and number of terms: x² + 2x + 6

a)

Linear polynomial

b)

Quadratic trinomial

c)

Quadratic binomial

d)

Cubic trinomial

16.

Classify this polynomial by its degree and number of terms: 4x³

a)

Cubic monomial

b)

Linear binomial

c)

Cubic binomial

d)

6th degree (sextic) monomial

17.

x⁴+2

a)

Quadratic binomial

b)

Quadratic monomial

c)

Quartic binomial

d)

Quartic trinomial

18.

Classify by degree of polynomial:

3x⁵ – 6x

a)

Constant

b)

Linear

c)

Quadratic

d)

fifth degree

19.

When a polynomial is written in standard form, the coefficient of the first term is called the _____________.

a)

Boss coefficient

b)

Leading coefficient

c)

Best coefficient

d)

Greatest common coefficient

20.

The following polynomial is written in standard form:

x² - 10x+ 8x - 5

a)

True

b)

False

21.

$-9x^2y^4z^6$ Find the degree of the monomial.

a)

Degree: 10

b)

Degree: 12

c)

Degree: 6

d)

Degree: 4

22.

$8x^6y^4z$ Find the degree of the monomial.

a)

Degree: 11

b)

Degree: 10

c)

Degree: 6

d)

Degree: 12

23.

$4x^3y+5x^2y^2-7$ Name each expression based on its degree and number of terms.

a)

Fourth degree trinomial.

b)

Cubic trinomial.

c)

Quadratic trinomial

d)

Cubic binomial.

24.

$9x^4y\ -3x^3y^2+7x^2y^4-5xy^5$ Name each expression based on its degree and number of terms.

a)

sixth degree polynomial of four terms.

b)

sixth degree trinomial.

c)

twenty second degree polynomial of four terms.

d)

fifth degree polynomial of four terms.

25.

Which is an example of a cubic binomial?

a)

x³ + 5

b)

x² + 3

c)

x² + 5x - 6

d)

5x³

26.

Which is an example of a quadratic monomial?

a)

x³ + 5

b)

x² + 3

c)

x² + 5x - 6

d)

-5x²

27.

Find the degree of the monomial -6

a)

Degree: 1

b)

Does not have a degree.

c)

Degree: 0

d)

It is not a monomial.

28.

What is the leading coefficient of the following polynomial?

5x² - 3x + 6

a)

2

b)

-3

c)

5

d)

6

29.

What is the constant of this polynomial? 2x³ - 8x² + 3x - 7

a)

2

b)

-8

c)

3

d)

-7

30.

Terms in a polynomial are separate by what?

a)

A. Parenthesis

b)

B. multiplication/division

c)

C. constant

d)

D. addition/ subtraction

31.

Polynomial terms are made up of

a)

coefficients or constants

b)

variables

c)

radicals

d)

positive exponents

e)

logartithms

32.

Simplify: $7(p^3-4)^0$

a)

7

b)

1

c)

28

d)

3

33.

According to exponent rules, when we multiply the expressions we _______ the exponents.

a)

add

b)

subtract

c)

multiply

d)

divide

34.

Simplify the expression. $x^4(x^{-\frac{3}{2}})$

a)

$\sqrt[]{x^5}$

b)

$\sqrt[5]{x^2}$

c)

$x^{-6}$

d)

$\sqrt[]{x^{11}}$

35.

Rewrite using positive exponents: $\frac{1}{\sqrt[-3]{5x}}$

36.

Re-write the expression in radical form. $x^{\frac{2}{3}}$

a)

$\sqrt[3]{x^2}$

b)

$\sqrt[]{x^3}$

c)

$\frac{1}{x}$

d)

$\sqrt[3]{x}$

37.

$9^{-\frac{1}{2}}\left(9^{\frac{3}{2}}\right)$

38.

Simplify . Your answer should contain only positive exponents. $\left(a^{\frac{1}{2}}b^{\frac{1}{2}}\right)^{-1}$

a)

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

b)

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

c)

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

d)

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

39.

$\frac{\sqrt[3]{80}}{\sqrt[3]{10}}$

40.

Simplify:

$\left(\frac{49}{25}\right)^{-\frac{3}{2}}$

41.

Simplify:

$\sqrt[3]{\sqrt[2]{729}}-\sqrt[]{\sqrt[]{16}}$

(a)

42.

$\left(5^{\frac{1}{2}}x^{\frac{1}{4}}\right)^8$

43.

Divide: $\frac{2x^4-9x^3+21x^2-26x+12}{2x-3}$

a)

$x^3-3x^2+6x-4$

b)

$2x^3-6x^2+12x-8$

c)

$x^4-3x^3+6x^2-4x$

d)

$2x^4-6x^3+12x^2-8x^{ }$

44.

Divide: $\frac{27x^3+64}{3x+4}$

a)

$27x^2-36x+48$

b)

$9x^2-12x+16$

c)

$27x^2+28x$

d)

$27x^2+28$

45.

Divide: $\frac{2x^3-9x^2+15}{2x-5}$

a)

$2x^2-4x-10-\frac{10}{2x-5}$

b)

$x^2-2x-5-\frac{10}{2x-5}$

c)

$x^2-2x-5-\frac{5}{2x-5}$

d)

$2x^2-4x+5$

46.

Divide: $\frac{9x^3+12x^2+15x+4}{3x+1}$

a)

$9x^2+9x+12-\frac{8}{3x+1}$

b)

$3x^2+3x+12-\frac{8}{3x+1}$

c)

$9x^2+9x+12$

d)

$3x^2+3x+4$

47.

Find the Difference:

(3x² + 4x - 2) - (5x + 7)

a)

3x² - x - 9

b)

2x² - 9

c)

3x² + 9x - 5

d)

3x² - x + 5

48.

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

a)

3y³+ 7y²- 4y + 3

b)

4y² + 3y³ - y + 3

c)

-y⁴ + 2y³-y - 4

d)

4y³+ 3y²-3y + 1

49.

Find the product.

5x(2x + 3)

a)

10x²+ 15x

b)

7x + 15x

c)

7x² + 8x

d)

25x²

50.

Find the product
(x - 3)(x +10)

a)

x² - 7x + 13

b)

x² - 6x - 30

c)

x² + 7x - 30

d)

x² + 13x + 30

51.

$(4x-3)(x^2-x+5)$

a)

$4x^3-7x^2+23x-15$

b)

$4x^3-x^2+17x+15$

c)

$x^2+3x+2$

d)

$x^3-x^2+5x$

52.

Factor Completely

a)

(2x⁸ + 49)²

b)

2x⁶(x - 7)²

c)

2x⁶(x - 7)(x + 7)

d)

2x⁶(x²-14x+49)

53.

Factor Completely

a)

5x⁵(x + 4)(x - 4)

b)

(x + 4)(x - 4)

c)

5x⁵ (x² - 16)

d)

(5x⁵ +16)²

54.

Factor Completely

a)

(m + 3)³

b)

(m - 3)³

c)

(m + 3)(m² - 3m + 9)

d)

(m + 3)(m² + 3m +9)

55.

Factor Completely

a)

(a - 5)(a² + 5a + 25)

b)

(a - 5)³

c)

(a + 5)³

d)

(a - 5)(a² - 5a + 25)

56.

Factor Completely

a)

(x² + 8)(x + 7)

b)

(x - 4)(x+4)(x+7)

c)

x²(x³+7x²+8x+56)

d)

Not Factorable

57.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

58.

If you are missing a term in your polynomials (both dividend and divisor), you must put a zero as a coefficient place holder for that term.

a)

True

b)

False

c)

Only for the dividend

d)

Only for the divisor

59.

If 𝒙³+2𝒙²-1 is divided by 𝒙-𝟐, then what is the remainder?

a)

7

b)

1

c)

-1

d)

15

60.

What is the quotient when (10n²- 37n - 12) is divided by (n - 4)?

a)

(10n - 3)

b)

(3n - 10)

c)

(10n + 3)

d)

(3n + 10)

61.

Simplify $\frac{x+9}{x^2-81}$

a)

$\frac{x-9}{x+9}$

b)

$\frac{1}{x-9}$

c)

$x+9$

d)

$\frac{1}{x+9}$

62.

$\frac{x^2+10x+24}{x^2-x-20}$ Simplify.

a)

$\frac{x+6}{x+4}$

b)

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

c)

$x+6$

d)

$\frac{x+6}{x-5}$

63.

Factor the expression:
$\frac{x^2\ -5x\ +\ 6}{x^2-4}\cdot\frac{\left(x\ +6\right)\left(x\ +\ 5\right)}{x^2+2x\ -15}$

a)

$\frac{\left(x\ -\ 3\right)\left(x\ -\ 2\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ +\ 5\right)\left(x\ -\ 3\right)}$

b)

$\frac{\left(x\ +\ 6\right)\left(x\ -\ 1\right)}{\left(x\ +\ 2\right)\left(x\ -\ 2\right)}\cdot\frac{\left(x\ +\ 6\right)\left(x\ +\ 5\right)}{\left(x\ -5\right)\left(x\ -3\right)}$

64.

$\frac{\left(x-3\right)\left(x-2\right)}{\left(x+2\right)\left(x-2\right)}\div\frac{\left(x+5\right)\left(x-3\right)}{\left(x+6\right)\left(x+5\right)}$

a)

$\frac{x+6}{x+2}$

b)

$\frac{x+2}{x+6}$

c)

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

65.

$\frac{b-4}{b^2-14b+40}\div\frac{b^2+6b+8}{b^2-3b-70}$

a)

$\frac{b-3}{6}$

b)

$\frac{2b}{9}$

c)

$\frac{5b\left(b-6\right)}{7}$

d)

$\frac{b+7}{\left(b+4\right)\left(b+2\right)}$

66.

Peter can mow the lawn in 40 minutes and John can mow the lawn in 60 minutes. How long will it take for them to mow the lawn together?

a)

48 minutes

b)

50 minutes

c)

24 minutes

d)

12 minutes

67.

Which of the following is true - select all that apply - if you know that I can dig a hole in 4 days and my friend Steve can dig it in 5 days.

a)

I have the quicker rate.

b)

Steve has the quicker rate.

c)

If we work together to complete the job, the equation will equal 1.

d)

This is a subtraction problem.

68.

Joan can clean the store in five hours. If Dan helps, it takes them four hours. Without help, how long would it take Dan to complete this job ?

a)

10

b)

25

c)

20

d)

15

69.

Subtract the following fractions:

$\frac{x}{x^2+5x+6}-\frac{1}{x^2-2x-8}$

a)

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

b)

$\frac{x^2-5x-3}{\left(x+2\right)\left(x+3\right)\left(x-4\right)}$

c)

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

d)

$\frac{x-1}{2x^2+3x-2}$

70.

Add the fractions:

$\frac{x-3}{x^2+6x+5}+\frac{x+4}{x^2-4x-5}$

a)

$\frac{2x^2+x+35}{2x^2+2x}$

b)

$\frac{2x^2+x+35}{\left(x+1\right)\left(x-5\right)\left(x+5\right)}$

c)

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

d)

$\frac{2x+1}{\left(x+1\right)^2\left(x-5\right)\left(x+5\right)}$

Fall 2023 Final exam review Part 2: Equations

Total questions: 70

Worksheet time: 4hrs 29mins

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