Updated CLEP Algebra Test questions
and answers with solutions
2024
What do you need to do to add / subtract fractions? - correct Answers ✔✔
-Get a common denominator
How do you multiply fractions? - correct Answers ✔✔ -Multiply numerators
and multiply denominators
How do you divide by a fraction / what do you do if you have a fraction in
the denominator? - correct Answers ✔✔ -Multiply the entire term by the
reciprocal fraction
Compute.
(1/3) + (7/5) - correct Answers ✔✔ -(1/3) + (7/5)
(5+21)/15
= 26/15
Compute.
[(3x-1) / (x^2-2)] + [1/(x-1)] - correct Answers ✔✔ -[(3x-1) / (x^2-2)] +
[1/(x-1)]
[(3x-1)(x+1) + (x^2-2)] / [(x^2-2)(x-1)
(3x^2 - 3x - x + 1 + x^2 - 2) / (x^3 - x^2 - 2x + 2)
= (3x^2 - 4x + 2) / x^3 - x^2 - 2x + 2)
What is another way to write √x ? - correct Answers ✔✔ -x^(1/2)
(√x)^2 = ? - correct Answers ✔✔ -x
,T or F
Roots and powers undo each other. - correct Answers ✔✔ -True
Properties of Exponents
How do you multiply 2 terms with the same base but different exponents?
- correct Answers ✔✔ -Add the exponents
Properties of Exponents
How do you multiply 2 terms with different bases but the same
exponents? - correct Answers ✔✔ -1) Multiply the bases
2) Raise this to the exponent
Properties of Exponents
How do you solve a term with an exponent, and that whole term is raised
to another exponent? - correct Answers ✔✔ -Multiply the exponents
Properties of Exponents
How do you divide terms with exponents? - correct Answers ✔✔ -Subtract
the exponents
Simplify.
[(4√9)^8] / [(4^2)-(3√8)] - correct Answers ✔✔ -[(4√9)^8] / [(4^2)-(3√8)]
[(9^(1/4))^8] / (16-2)
[9^((1/4)(8))] / 14
(9^2) / 14
=
Simplify.
[(-2)/((x^2)-1)] + [1/(x+1)] - [1/(x-1)] - correct Answers ✔✔ -[(-2)/((x^2)-
1)] + [1/(x+1)] - [1/(x-1)]
(-2+x-1-x-1) / [(x^2)-1]
= -4 / [(x^2)-1]
Simplify.
[(a^4)(b^3)] / [(a^3)(b^3)] - correct Answers ✔✔ -[(a^4)(b^3)] / [(a^3)
(b^3)]
=a
Simplify.
(a^b)^c - correct Answers ✔✔ -(a^b)^c
a^(bc)
,Degree of Polynomial - correct Answers ✔✔ -The highest exponent of x in
the polynomial
Constants are degree ___ polynomials. - correct Answers ✔✔ -0
What is the format for first degree polynomials? - correct Answers ✔✔ -y =
ax + b
What does the graph of a first degree polynomial look like? - correct
Answers ✔✔ -
What is the more common name for a second degree polynomial? -
correct Answers ✔✔ -Quadratic
What is the format for second degree polynomials? - correct Answers ✔✔ -
ax^2 + bx + c = 0
What does the graph of a second degree polynomial look like? - correct
Answers ✔✔ -
What are the steps to graphing polynomials? - correct Answers ✔✔ -1)
Plug in ± values for x (start with 0 and go outward from there) and solve
for y
2) Plot these points on the graph
What is another way of saying, "Find the zeroes of the polynomial"? -
correct Answers ✔✔ -Find the roots of the polynomaial
What are the ways you can find the roots of quadratics / second degree
polynomials? - correct Answers ✔✔ --Factoring
-Quadratic Formula
When factoring, the numbers must __________ to form the middle term and
__________ to form the last term of a quadratic. - correct Answers ✔✔ --add
-multiply
Write the quadratic formula. - correct Answers ✔✔ -
Factor.
x^2 - 6x + 9 - correct Answers ✔✔ -x^2 - 6x + 9
(x-3)(x-3)
= (x-3)^2
, On the CLEP exam, if asked to factor a problem, what is a short cut I can
do? - correct Answers ✔✔ -Expand the multiple choice answers until I get
the polynomial in the question
Factor.
x^2 + 6x + 8 - correct Answers ✔✔ -x^2 + 6x + 8
= (x+4)(x+2)
Find the roots of the following equation:
x^2 + 7x + 9 - correct Answers ✔✔ -x^2 + 7x + 9
x = [(-7) ± √((7^2)-(4⋅1⋅9)] / (2⋅1)
x = [(-7) ± √(49-36)] / 2
x = [(-7) ± √13] / 2
Factor.
x^2 - 4 - correct Answers ✔✔ -x^2 - 4
= (x+2)(x-2)
What are the steps to factor higher order polynomials? - correct Answers
✔✔ -1) Factor out any common factors
2) Guess and check until you factor the problem correctly
Factor.
x^3 - x - correct Answers ✔✔ -x^3 - x
x(x^2 - 1)
= x(x+1)(x-1)
How do you expand polynomials? - correct Answers ✔✔ -FOIL
Expand.
(x-7)(2x+3) - correct Answers ✔✔ -(x-7)(2x+3)
2x^2 + 3x -14x - 21
= 2x^2 -11x - 21
Expand.
(x^2 - 7x +1)(x^2 + 2x + 2) - correct Answers ✔✔ -(x^2 - 7x +1)(x^2 +
2x + 2)
x^4 + 2x^3 + 2x^2 - 7x^3 - 14x^2 - 14x + x^2 + 2x + 2
= x^4 - 5x^3 - 11x^2 - 12x + 2
Find the roots / zeroes of:
x^3 - 9x - correct Answers ✔✔ -x^3 - 9x
x(x^2 - 9)
and answers with solutions
2024
What do you need to do to add / subtract fractions? - correct Answers ✔✔
-Get a common denominator
How do you multiply fractions? - correct Answers ✔✔ -Multiply numerators
and multiply denominators
How do you divide by a fraction / what do you do if you have a fraction in
the denominator? - correct Answers ✔✔ -Multiply the entire term by the
reciprocal fraction
Compute.
(1/3) + (7/5) - correct Answers ✔✔ -(1/3) + (7/5)
(5+21)/15
= 26/15
Compute.
[(3x-1) / (x^2-2)] + [1/(x-1)] - correct Answers ✔✔ -[(3x-1) / (x^2-2)] +
[1/(x-1)]
[(3x-1)(x+1) + (x^2-2)] / [(x^2-2)(x-1)
(3x^2 - 3x - x + 1 + x^2 - 2) / (x^3 - x^2 - 2x + 2)
= (3x^2 - 4x + 2) / x^3 - x^2 - 2x + 2)
What is another way to write √x ? - correct Answers ✔✔ -x^(1/2)
(√x)^2 = ? - correct Answers ✔✔ -x
,T or F
Roots and powers undo each other. - correct Answers ✔✔ -True
Properties of Exponents
How do you multiply 2 terms with the same base but different exponents?
- correct Answers ✔✔ -Add the exponents
Properties of Exponents
How do you multiply 2 terms with different bases but the same
exponents? - correct Answers ✔✔ -1) Multiply the bases
2) Raise this to the exponent
Properties of Exponents
How do you solve a term with an exponent, and that whole term is raised
to another exponent? - correct Answers ✔✔ -Multiply the exponents
Properties of Exponents
How do you divide terms with exponents? - correct Answers ✔✔ -Subtract
the exponents
Simplify.
[(4√9)^8] / [(4^2)-(3√8)] - correct Answers ✔✔ -[(4√9)^8] / [(4^2)-(3√8)]
[(9^(1/4))^8] / (16-2)
[9^((1/4)(8))] / 14
(9^2) / 14
=
Simplify.
[(-2)/((x^2)-1)] + [1/(x+1)] - [1/(x-1)] - correct Answers ✔✔ -[(-2)/((x^2)-
1)] + [1/(x+1)] - [1/(x-1)]
(-2+x-1-x-1) / [(x^2)-1]
= -4 / [(x^2)-1]
Simplify.
[(a^4)(b^3)] / [(a^3)(b^3)] - correct Answers ✔✔ -[(a^4)(b^3)] / [(a^3)
(b^3)]
=a
Simplify.
(a^b)^c - correct Answers ✔✔ -(a^b)^c
a^(bc)
,Degree of Polynomial - correct Answers ✔✔ -The highest exponent of x in
the polynomial
Constants are degree ___ polynomials. - correct Answers ✔✔ -0
What is the format for first degree polynomials? - correct Answers ✔✔ -y =
ax + b
What does the graph of a first degree polynomial look like? - correct
Answers ✔✔ -
What is the more common name for a second degree polynomial? -
correct Answers ✔✔ -Quadratic
What is the format for second degree polynomials? - correct Answers ✔✔ -
ax^2 + bx + c = 0
What does the graph of a second degree polynomial look like? - correct
Answers ✔✔ -
What are the steps to graphing polynomials? - correct Answers ✔✔ -1)
Plug in ± values for x (start with 0 and go outward from there) and solve
for y
2) Plot these points on the graph
What is another way of saying, "Find the zeroes of the polynomial"? -
correct Answers ✔✔ -Find the roots of the polynomaial
What are the ways you can find the roots of quadratics / second degree
polynomials? - correct Answers ✔✔ --Factoring
-Quadratic Formula
When factoring, the numbers must __________ to form the middle term and
__________ to form the last term of a quadratic. - correct Answers ✔✔ --add
-multiply
Write the quadratic formula. - correct Answers ✔✔ -
Factor.
x^2 - 6x + 9 - correct Answers ✔✔ -x^2 - 6x + 9
(x-3)(x-3)
= (x-3)^2
, On the CLEP exam, if asked to factor a problem, what is a short cut I can
do? - correct Answers ✔✔ -Expand the multiple choice answers until I get
the polynomial in the question
Factor.
x^2 + 6x + 8 - correct Answers ✔✔ -x^2 + 6x + 8
= (x+4)(x+2)
Find the roots of the following equation:
x^2 + 7x + 9 - correct Answers ✔✔ -x^2 + 7x + 9
x = [(-7) ± √((7^2)-(4⋅1⋅9)] / (2⋅1)
x = [(-7) ± √(49-36)] / 2
x = [(-7) ± √13] / 2
Factor.
x^2 - 4 - correct Answers ✔✔ -x^2 - 4
= (x+2)(x-2)
What are the steps to factor higher order polynomials? - correct Answers
✔✔ -1) Factor out any common factors
2) Guess and check until you factor the problem correctly
Factor.
x^3 - x - correct Answers ✔✔ -x^3 - x
x(x^2 - 1)
= x(x+1)(x-1)
How do you expand polynomials? - correct Answers ✔✔ -FOIL
Expand.
(x-7)(2x+3) - correct Answers ✔✔ -(x-7)(2x+3)
2x^2 + 3x -14x - 21
= 2x^2 -11x - 21
Expand.
(x^2 - 7x +1)(x^2 + 2x + 2) - correct Answers ✔✔ -(x^2 - 7x +1)(x^2 +
2x + 2)
x^4 + 2x^3 + 2x^2 - 7x^3 - 14x^2 - 14x + x^2 + 2x + 2
= x^4 - 5x^3 - 11x^2 - 12x + 2
Find the roots / zeroes of:
x^3 - 9x - correct Answers ✔✔ -x^3 - 9x
x(x^2 - 9)
