Regents Prep: Math A
Multiple-Choice Questions
Regents Prep Math A: Topical Multiple-Choice Question Archive
Use of Topical Archive Multiple-Choice Questions
Teachers:

Feel free to copy and paste any of the multiple-choice questions below for use in creating your own Regents-style assessments.

Graphics are easily downloaded by right-clicking on the desired image and selecting either Save Picture As... (Internet Explorer) or Save Image As... (Netscape).

Numbers & Numeration: Question 1 of 14
Which equation is an illustration of the additive identity property?
  1. (x)•(1) = x
  2. x + 0 = x
  3. x - x = 0
  4. (x)•(1/x) = 1

Correct Answer Number: 2

Explanation: Zero is the additive identity. Adding zero to any number will give an answer equal to the original number.


Numbers & Numeration: Question 2 of 14
If the relationship shown below is true, then t could be
 

  1. -(1/4)
  2. 0
  3. 1/4
  4. 4

Correct Answer Number: 3

Explanation: The easiest way to see the solution to this problem is to substitute the answers into the expression and determine which one is true.


Numbers & Numeration: Question 3 of 14
If a and b are both odd integers, which of the following MUST also be an odd integer?
  1. a+b
  2. a-b
  3. a•b
  4. a/b

Correct Answer Number: 3

Explanation: Problems such as this one are best tackled with trial and error. Choose two odd integers, say 15 and 5, and perform the operations of addition, subtraction, multiplication and division to see what the results look like. In this case, multiplication gives another odd integer.


Numbers & Numeration: Question 4 of 14
Which property is illustrated by the statement 4 • 1 = 4?
  1. additive identity
  2. multiplicative identity
  3. commutative property
  4. multiplicative inverse

Correct Answer Number: 2

Explanation: One is the multiplicative identity. Multiplying any number by one will give an answer equal to the original number.


Numbers & Numeration: Question 5 of 14
If x(y+z)= w and x, y, z, and w are all integers, which of the following must be true?
  1. x(y + z) > 0
  2. xy + z = w
  3. xy + xz = w
  4. x, y, z and w are all positive

Correct Answer Number: 3

Explanation: Choice 3 shows the distributive property at work. While the other choices may or may not be true, the distributive property is always true.


Numbers & Numeration: Question 6 of 14
Which of the following are true for all real numbers x, y and z?
I. x(y + z) = xy + xz
II. x + y + z = z + y + x
III. x - y - z = z - y - z
  1. I only
  2. II only
  3. I and II only
  4. I, II and III

Correct Answer Number: 3

Explanation: I. the distributive property is always true.
II. addition is commutative for all values.
III. subtraction is not commutative. Imagine 5-2 = 2-5. This is NOT true, since 3 does not equal -3.

More Information


Numbers & Numeration: Question 7 of 14
If a(b + c)=d and a, b, c and d are all integers, then which of the following MUST be true?
  1. ab + c = d
  2. ab + ac = d
  3. a(b + c) > 0
  4. ab < d

Correct Answer Number: 2

Explanation: This problem utilizes the distributive property. a(b+c)=d becomes ab+ac=d. The a is multiplied times each of the elements inside of the parentheses.

More Information


Numbers & Numeration: Question 8 of 14
If x³ < x² < x then the value of x could be
  1. 0
  2. 1
  3. 1/3
  4. square root of 3

Correct Answer Number: 3

Explanation: For choice 3, the expression reads 1/27 < 1/9 < 1/3.


Numbers & Numeration: Question 9 of 14
Which of the following systems is NOT commutative?
  1. Addition for whole numbers
  2. Multiplication of integers
  3. Subtraction of whole numbers
  4. Addition for integers

Correct Answer Number: 3

Explanation: Consider the following example:
3 - 5 = 5 - 3
This sentence is not true. Under subtraction, the commutative property may not yield the same result.

More Information


Numbers & Numeration: Question 10 of 14
Which of the following is a rational number?
  1. pi
  2. square root of 2
  3. square root of 64
  4. none of the above

Correct Answer Number: 3

Explanation: A rational number can be expressed as a fraction. The square root of 64 is equal to 8, which can be expressed as 8/1.

More Information


Numbers & Numeration: Question 11 of 14
If x and y are both odd integers, which of the following MUST also be an odd integer?
  1. x + y
  2. x • y
  3. x/y
  4. x - y

Correct Answer Number: 2

Explanation: Consider an example. Let x=3 and y=5.
3 + 5 = 8 (not odd)
3 • 5 = 15 (odd)
3/5 = 0.6 (not odd, not integer)
3 - 5 = -2 Multiplication is the only operation which will yield another odd integer.


Numbers & Numeration: Question 12 of 14
What is the identity element for addition?
  1. 0
  2. 1
  3. -1
  4. There is no identity element for addition.

Correct Answer Number: 1

Explanation: The identity element for addition will return the same element to which it was added.

More Information


Numbers & Numeration: Question 13 of 14
If the square root of x is greater than x, then x could be
  1. 0
  2. 1/2
  3. 2
  4. 4

Correct Answer Number: 2

Explanation: Consider each possible answer:
1. square root of zero is 0 which is not greater than 0
2. square root of 1/2 is .707 which is greater than 1/2 (.5)
3. square root of 2 is 1.414 which is not greater than 2
4. square root of 4 is 2 which is not greater than 2


Numbers & Numeration: Question 14 of 14
The statement
( x + 5 )•( 7 + x ) = ( x + 5 )•( 7 )+( x + 5 )•( x )
is an example of which property?
  1. associative property of addition
  2. commutative property of multiplication
  3. associative property of multiplication
  4. distributive property

Correct Answer Number: 4

Explanation: The (x+5) is being multiplied by each element inside of the parentheses (7+x). This is the distributive property.

More Information
Copyright © 1999-2011 Oswego City School District Regents Exam Prep Center
RegentsPrep and StudyZone are FREE educational resources.