Hello, budding mathematicians! Ready to tackle our free Absolute Value Test and prove your mastery of positive and negative numbers? This friendly math integer quiz challenges you with integer absolute value problems designed to sharpen your absolute value practice and boost your confidence. Whether you're prepping for an exam or simply love a numbers challenge, you'll learn tricks to simplify computations and deepen your understanding of integers. Dive into our interactive notebook for guided tips, then strengthen your skills with targeted practice exercises . Get started now and ace those integers!
What is the absolute value of -5?
5
10
-5
0
The absolute value of a number is its distance from zero on the number line, which is always nonnegative. Since -5 is five units away from zero, its absolute value is 5. It cannot be negative or zero. For more detail, see Absolute Value.
What is |0|?
1
-1
Undefined
0
Absolute value measures distance from zero, and zero is zero units away from itself. Therefore, |0| = 0. It is neither positive nor undefined. See Absolute Value.
Which of the following is equal to |3|?
3
0
-3
±3
|3| represents the distance of 3 from zero, which is 3. It cannot be negative or zero. The notation ±3 denotes two values, but absolute value yields a single nonnegative result. More at Absolute Value.
What is the value of |-8| + |4|?
12
4
-12
-4
Absolute values are always nonnegative. |-8| = 8 and |4| = 4, so their sum is 12. Negative sums cannot occur in this context. For more examples, see Absolute Value.
Which expression gives the smallest value when x = -2?
-x
|x|
x
All give the same value
Plugging x = -2 gives |x| = 2, -x = 2, and x = -2. The smallest of these is x itself, which equals -2. The absolute expressions are always nonnegative, so they cannot be smallest. Learn more at Absolute Value.
What is |?7 + 2|?
7
5
-5
2
First compute the interior: -7 + 2 = -5. Then take the absolute value to get 5. Absolute values turn negatives to positives. Additional info at Absolute Value.
If a = -3, what is |a| + |?a|?
6
0
-6
3
With a = -3, |a| = 3 and |?a| = |3| = 3, so the sum is 6. Absolute values are nonnegative distances. Negative sums are not possible here. See Absolute Value.
Which of these inequalities is always true for any real x?
|x| ? x
|x| = x for all x
|x| > 0
|x| ? 0
By definition, absolute value is a distance and cannot be negative, so |x| ? 0 always holds. It may equal zero when x = 0, so |x| > 0 is not always true. Other options fail for certain x. More at Absolute Value.
Evaluate |?12| ? |5|.
-17
17
7
-7
|?12| = 12 and |5| = 5, so the expression is 12 ? 5 = 7. Absolute value converts negatives to positives. Negative results aren't possible if the minuend is greater. For more, see Khan Academy.
Compute |3 ? 8| + |?2|.
7
3
5
1
Inside the absolute values, 3?8 = -5 so |3?8| = 5, and |?2| = 2. Their sum is 5 + 2 = 7. Absolute values make each term nonnegative. See Khan Academy.
What is |x| if x² = 49?
7
-7
49
±7
If x² = 49 then x = 7 or x = -7, and the absolute value of either is 7. Absolute value always yields the positive root. It does not return ±7 as a single value. Learn more at Khan Academy.
Simplify |?3 * 4|.
12
7
-7
-12
First compute ?3 * 4 = -12, then take the absolute value to get 12. Absolute value removes the negative sign. It always returns a nonnegative result. For more, visit Khan Academy.
Which of the following equals |a ? b|?
|b - a|
b - a
a - b
|a + b|
Absolute value ignores order of subtraction, so |a - b| = |b - a|. Direct subtraction may yield a negative if a < b, which would not match the absolute value. The sum form is unrelated. Read more at Khan Academy.
Solve |x| > 3.
x > 3
-3 < x < 3
x < -3 or x > 3
x < -3
The inequality |x| > 3 means x is more than 3 units from zero, so x > 3 or x < -3. The interval between -3 and 3 is excluded. Absolute value inequalities split into two cases. Details at Khan Academy.
Compute |2?5| * |?1|.
-1
-3
1
3
|2?5| = |?3| = 3 and |?1| = 1, so the product is 3 × 1 = 3. Absolute values ensure nonnegative factors. Negative results cannot occur here. More at Khan Academy.
Which expression represents the distance between points x and y on a number line?
|x - y|
|y + x|
x - y
y - x
Distance on a number line is always nonnegative, so it's |x - y|. Direct subtraction may yield a negative value if x < y. The sum form is unrelated. Read more at Khan Academy.
What is the sum of the solutions to |2x - 3| = 7?
2
-2
-3
3
Set 2x - 3 = 7 ? x = 5, and 2x - 3 = -7 ? x = -2. The sum is 5 + (-2) = 3. Absolute value equations yield two cases. More at Khan Academy.
Find the sum of solutions to 2|x| + 4 = 10.
2
4
-2
0
First, 2|x| = 6 ? |x| = 3 so x = 3 or x = -3. The sum of solutions is 3 + (-3) = 0. Absolute value creates two symmetric cases. Details at Khan Academy.
How many solutions does |x - 1| = 0 have?
Infinitely many
0
2
1
|x - 1| = 0 only when x - 1 = 0, so x = 1 is the sole solution. Absolute value equals zero only at its center. There are no other solutions. For more, see Khan Academy.
Solve the inequality |x + 2| < 5.
-5 < x < 2
x < -2
x > 3
-7 < x < 3
Rewrite as -5 < x + 2 < 5, then subtract 2: -7 < x < 3. This gives the open interval of solutions. Absolute value inequalities split into two chained inequalities. More at Khan Academy.
Solve |x - 4| ? 2.
x ? 2 or x ? 6
x ? 2 and x ? 6
x > 6
2 < x < 6
|x - 4| ? 2 splits to x - 4 ? 2 ? x ? 6, or x - 4 ? -2 ? x ? 2. Thus the solution is x ? 2 or x ? 6. Distance is at least 2 from 4. See Khan Academy.
What is the simplified form of |x| + |x - 1| for x ? 1?
x
2x - 1
-2x + 1
1 - x
For x ? 1, both x and x - 1 are nonnegative, so |x| = x and |x - 1| = x - 1. Their sum is x + (x - 1) = 2x - 1. Piecewise definitions guide this simplification. More at Khan Academy.
What is the y-intercept of the graph y = |x|?
Undefined
-1
0
1
The y-intercept occurs at x = 0, so y = |0| = 0. This gives the point (0, 0). Absolute value graphs are V-shaped with vertex at the origin. Learn more at Absolute Value Graph.
Compute |3?2| + |2?5| - |5?3|.
2
-2
0
3
|3?2| = 1, |2?5| = 3, and |5?3| = 2. So 1 + 3 - 2 = 2. Absolute values ensure each term is nonnegative before combining. More at Khan Academy.
How many integer solutions satisfy |2x - 5| ? 7?
8
6
9
7
Solve -7 ? 2x - 5 ? 7. Adding 5 gives -2 ? 2x ? 12, so -1 ? x ? 6. The integers from -1 to 6 inclusive are 8 values. Counting endpoints yields 8 solutions. See Khan Academy.
Evaluate the sum ?_{i=-2}^{2} |i|.
5
6
4
7
Compute |?2| + |?1| + |0| + |1| + |2| = 2 + 1 + 0 + 1 + 2 = 6. Each term is nonnegative by definition of absolute value. Summation yields 6. More examples at Absolute Value.
For which x is f(x) = |x+1| - |x-1| equal to 0?
All real x
-1
1
0
Set |x+1| = |x-1|. The midpoint between -1 and 1 is 0, which is the only point equidistant from both. Thus f(x) = 0 only at x = 0. For piecewise reasoning, see Khan Academy.
0
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AI Study Notes
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Study Outcomes
Understand Absolute Value Concepts -
Grasp the definition and key properties of absolute value for integers, setting a strong foundation for more complex calculations.
Calculate Integer Absolute Values -
Perform quick and accurate computations of absolute values for positive and negative integers to build speed and confidence.
Apply Absolute Value Operations -
Use absolute value rules to solve integer-based problems, ensuring precision in each step of your calculations.
Analyze Integer Expressions -
Break down expressions involving absolute values to determine magnitude relationships and solve for unknowns.
Track Quiz Performance -
Monitor your scores in real time, identify areas for improvement, and enhance your speed on the absolute value test.
Evaluate Problem-Solving Strategies -
Assess various techniques for tackling integer absolute value problems under time constraints to boost overall accuracy.
Cheat Sheet
Definition of Absolute Value -
Absolute value measures the distance of an integer from zero, always yielding a non-negative result based on the rule |x| = x if x ≥ 0 and |x| = - x if x < 0, as highlighted by Khan Academy.
Ordering Integers with Absolute Values -
When comparing values in an integer quiz, use a number line to place each |x| point; for example, | - 3| = 3 sits the same distance from zero as |3|, demonstrating symmetry (University of Waterloo).
Key Strategies for Absolute Value Equations -
When you see an equation like |x - 4| = 7 on your absolute value test or integer quiz, split it into x - 4 = 7 and x - 4 = - 7 to find both solutions; this two”case method is a staple in Purplemath lessons.
Solving Absolute Value Inequalities -
Translate |x| < 5 into - 5 < x < 5 or |x| ≥ 3 into x ≤ - 3 or x ≥ 3 by remembering that "less than" yields a range and "greater than" yields two rays, as described by the National Council of Teachers of Mathematics.
Real-World Word Problems -
Absolute value often models real distances - like "John is at point x, 8 units from home," so |x - 0| = 8 has two practical solutions - an approach endorsed by the Mathematical Association of America for solid absolute value practice.
