Algebra Practice Test
2024 Edition
Test your knowledge of introductory Algebra with this Algebra practice exam. Whether you are studying for a school math test or looking to test your math skills, this free practice test will challenge your knowledge of algebra.
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Diane Dean, LPC, RNBC, MA, is a licensed professional counselor and educator with 20 years of experience...
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Our Practice exam covers the actual NCE Domains:
The NCE contains 200 multiplechoice, nonsectioned questions. There are different versions of the test. Test questions.
There are different versions of the text. Test questions come from a pool of questions that have been extensively reviewed and researched for content accuracy and clarity
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Free Sample Questions
Free Sample Questions
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1.  3ab + 4ac  2ad = (3ab  4ac + 2ad)  




3ab + 4ac  2ad = (3ab  4ac + 2ad)
3ab + 4ac  2ad = 3ab + 4ac  2ad
Incorrect answer. Please choose another answer.




2.  A father gave $500 to his two sons. He gave X dollars to one son. Which of the following expressions correctly shows the amount he gave to the other son.  








If X represents the amount given to one son, $500  X represents the amount given to the other son.
Incorrect answer. Please choose another answer.




3.  Solve X where 5X = 20.  








5X = 20
X = 20 ÷ 5 X = 4
Incorrect answer. Please choose another answer.




4.  Solve X where X  5 = 15.  








X  5 = 15
X = 15 + 5 X = 20
Incorrect answer. Please choose another answer.




5.  Solve X where 3X + 7  2 = 8.  








3X + 7  2 = 8
3X + 5 = 8 3X = 3 X = 3 ÷ 3 X = 1
Incorrect answer. Please choose another answer.




6.  Irene is N years old. If Tom is twice as old, which of the following algebraic statements shows his age now?  








If Irene is N years old and Tom is twice as old as Irene, the algebraic formula to show how old Tom is would be 2 x N or 2N.
Incorrect answer. Please choose another answer.




7.  John has B bats and buys C bats more. He then gives away D bats. Which of the following algebraic statements corretly shows how many bats John has left?  








If John starts with B bats and buys C more bats, the total number of bats John has would be represented by the formula B + C.
When John gives D bats away, the sum of B + C would subtract D bats to determine how many he has left. So, the formula is B + C  D.
Incorrect answer. Please choose another answer.




8.  What is the representation algebraically of the cost of L feet of lumber at Y dollars per foot?  








There are a variety of ways to show multiplication, L x Y.
LY L · Y (L)(Y)
Incorrect answer. Please choose another answer.




10.  5a + 2b  b + 4a =  








5a + 2b  b + 4a =
5a + 4a + 2b  b = 9a + b
Incorrect answer. Please choose another answer.




11.  Find the value of 3abc, where a = 2, b = 3 and c = 4.  








If a = 2, b = 3 and c = 4,
3abc = 3(2)(3)(4) = 6 x 12 = 72
Incorrect answer. Please choose another answer.




12.  The sum of a certain number and 3 times the number is 40. What is the number?  








8 + 3(8) = 32
9 + 3(9) = 36 10 + 3(10) = 40 11 + 3(11) = 44
Incorrect answer. Please choose another answer.




13.  Joe is lending Frank $500 and Frank has 4 years to pay it back. Joe is charging 6% interest. Frank wants to determine how much interest he'll pay over the 4 years. He sets up the formula, interest (i) = loan amount (l) x rate (r) x time (t). Find i.  








i = l x r x t
l = $500, r = 6% and t = 4 years l = $500 x .06 x 4 i = $30 x 4 i = $120
Incorrect answer. Please choose another answer.




14.  In V = 2m  3, V is which of the following?  








A dependent variable is a variable that depends on one or more other variables. In this equation, V depends on the value of m.
An independent variable is a variable that can have its value chosen without considering the values of other variables. In this equation, m is an independent variable.
Incorrect answer. Please choose another answer.




15.  In B = 3 + 4w, 3 is which of the following?  








A constant is a value that does not change. In this equation, 3 is a fixed number that will not change.
A coefficient is a number used to multiple a variable. In this equation, 4 is a coefficient of the independent variable w.
Incorrect answer. Please choose another answer.




16.  V = bdt. Solve the formula for d.  








v = bdt
v = d bt
Incorrect answer. Please choose another answer.




17. 
B = 1hm. Solve the formula for h. 2 









B = 1hm
2 2B = 1hm 2B = h m
Incorrect answer. Please choose another answer.




18.  The absolute value of 14 is 14.  




The absolute value of a number, even a negative number, is a positive number.
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19.   3 + (14) =  








 3 + (14) =
 3  14 =  17
Incorrect answer. Please choose another answer.




21.  Add the following: 3x  2y + 2y + 3z + 2z  4x  5y.  








3x  2y + 2y + 3z + 2z  4x  5y =
3x  4x  2y  5y + 2y + 3z + 2z = x  5y + 5z
Incorrect answer. Please choose another answer.




22.  6x  10 = 4(x + 3). Solve for x.  








6x  10 = 4(x + 3)
6x  10 = 4x + 12 6x = 4x + 22 2x = 22 x = 11
Incorrect answer. Please choose another answer.




23.  x  6 = 17. Solve for x.  








x  6 = 17
x = 17 + 6 x = 23
Incorrect answer. Please choose another answer.




24.  Which of the following is not a grouping symbol?  








Grouping symbols such as parentheses, brackets and braces in math will contain numbers, variables and operations. The grouping symbol tells you to do the operation first. An arrow, on the other hand, is an implicaiton notation to show that both sides of an notation are equal.
Incorrect answer. Please choose another answer.




25.  A minus sign that precedes a parenthesis causes the sign of each term within the parentheses to change when the parentheses are removed.  




If a minus sign appears outside of a parentheses, the minus sign changes the terms within the parentheses when the parentheses is removed. For example,
 (2x  4y) 2x + 4y
Incorrect answer. Please choose another answer.




26.  If X equals 5, what is the value of 6X + 2X  X?  








If x = 5,
6x + 2x  x = 6(5) + 2(5)  5 = 30 + 10  5 = 35
Incorrect answer. Please choose another answer.




27.  If 10 is separated into two parts, one of which is y, represent the second part.  








If 10 is separated into two parts, one of which is y, the second part will be 10  y.
Incorrect answer. Please choose another answer.




28.  Find 3 consecutive numbers such that 3 times the first is equal to 8 more than the sum of the other two.  








x = 1st number
x + 1 = 2nd number x + 2 = 3rd number 3x = x + 1 + x + 2 + 8 3x = 2x + 11 x = 11
Incorrect answer. Please choose another answer.




29.  The ratio of the height of two buildings is 7 to 5. The first building is 210 feet tall. How tall is the second building?  








7/5 = 210/x
7x = 1,050 x = 150
Incorrect answer. Please choose another answer.




30.  Factor the polynomial 5x  15.  








When factoring, look to see what you can take out of a parentheses to put out front of it. It is the opposite of distributing in polynomial expressions.
The first term 5x can be factored (5)(x). The second term 15 can be factored (5)(3). 5 is the only factor common to both terms. Divide out the 5 from the terms and move the common factor to the front of the parentheses. Remember, when dividing 15 by 5, a 3 is left over. 5x/5  15/5 = x  3 Move the common factor to the front. 5(x  3)
Incorrect answer. Please choose another answer.
