I taught algebra at a community college for several years (recently switched to CS), and this was largely my goal for weekly quizzes (given in online multiple-choice format via Blackboard). Roughly half the questions were directly computational or symbolic manipulations, with the other half an attempt at being conceptual. I've taken my quiz source document for the intermediate algebra class and cut it down to most of the conceptual prompts/examples here:
Name the result of the operation.
1) The result of a subtraction operation is called a ____.
Identify the correct word.
2) Any written combination of numbers and operations (with no equal sign) is called a(n) ____.
Write the sentence as an equation, using n to represent the unknown number.
5) Eight times the difference of 12 and a number is -56.
Identify the false statement regarding signed numbers.
6) Select the statement regarding signed numbers which is false.
A) adding a positive and a negative may result in a number of either sign
B) multiplying two negatives results in a positive number
C) multplying a positive and a negative results in a negative number
D) adding two negatives results in a positive number
Characterize the set of numbers.
11) When a rational number is expressed in decimal notation, which of the following is not a possibility?
A) an infinite, non-repeating decimal B) a terminating decimal
C) a repeating decimal D) a non-terminating decimal
List all numbers from the given set that are of the indicated type.
12) Rationals in {9, -15, 0, (2/3), 0.overbar(5), 0.47, π}
Identify the property illustrated by the statement.
13) (4 ∙ 3) ∙ 2 = 4 ∙ (3 ∙ 2)
Find the inverse.
14) Find the multiplicative inverse of 3(8/9).
Analyze the form of the expression.
15) Why can we not say that this expression is "simplified"?
3((2/3)x + 8) + (6/15)x
A) fractions not reduced B) parentheses not removed
C) like terms not combined D) all of the above
Identify the incorrect rule of exponents.
16) According to the Fundamental Rule of Exponents, which of the following shortcuts on same-base powers is incorrect?
A) exponents add powers B) multiplying adds powers
C) division subtracts powers D) radicals divide powers
Identify the correct rule of distribution.
17) According to the General Distribution Rule, which of the following operations will distribute piecewise?
A) exponents over addition B) radicals over subtraction
C) radicals over multiplication D) exponents over subtraction
Identify the polynomial by its degree and number of terms.
21) 15s^2 + 9s + 6
A) quadratic monomial B) linear trinomial C) cubic binomial D) quadratic trinomial
Identify the well-defined real number.
31) Which of the following is well-defined as a real number?
A) sqrt(-9) B) (6/0) C) 0 to power of ((-3)) D) (0/8)
Find any real number for which the rational expression is undefined.
32) (25x to power of ((2)) - 64/2x - 8)
Indicate the quadrant in which the point belongs.
46) (11, -7)
