Middle School Math Quiz: Opposites And Absolute Value

9 questions · exam conditions

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Opposites And Absolute ValueQuestion 1 of 9

A submarine starts at sea level and descends 150 feet, then ascends 75 feet, then descends another 200 feet. If the absolute value of the submarine's final depth equals the distance a helicopter is above sea level, and the helicopter's altitude and the submarine's depth are opposites, what is the helicopter's altitude?

275 feet above sea level

275 feet below sea level

225 feet above sea level

150 feet above sea level

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Middle School Math Quiz

Middle School Math Quiz: Opposites And Absolute Value

Practice Opposites And Absolute Value in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Opposites And Absolute Value, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

275 feet above sea level (correct answer)
275 feet below sea level
225 feet above sea level
150 feet above sea level

Explanation: The submarine's path: starts at 0, goes to -150, then to -75, then to -275 feet. The final depth is -275 feet, so |−275| = 275. Since the helicopter's altitude and submarine's depth are opposites, the helicopter is at +275 feet above sea level. Choice B gives the wrong direction. Choice C incorrectly calculates the final depth as -225. Choice D uses only the initial descent.

Question 2

A bank account shows three transactions: a withdrawal of $85, a deposit that is the opposite of the withdrawal, and another withdrawal of $120. If the absolute value of the account's net change equals the absolute value of the change in a savings account, and these net changes are opposites, what happened to the savings account?

The savings account decreased by exactly $120
The savings account increased by exactly $85
The savings account decreased by exactly $85
The savings account increased by exactly $120 (correct answer)

Explanation: When you encounter problems involving opposite values and absolute values, you're working with integers and their relationships on the number line. The key insight is that opposite numbers have the same absolute value but different signs. Let's track the bank account's transactions step by step. Start with a withdrawal of

85, which gives us -

85. Next comes "a deposit that is the opposite of the withdrawal." The opposite of -

85 is +

85, so we add $85 back. Finally, there's another withdrawal of

120, giving us -

120. The net change is:

-85 + 85 + (-120) = -120

The absolute value of this net change is

|-120| = 120

. Now, the problem states that the savings account's net change has the same absolute value ($120) but is the opposite of the bank account's change. Since the bank account decreased by $120, the savings account must have increased by $120. Looking at the wrong answers: Choice A suggests the savings account decreased by $120, but this would be the same change as the bank account, not the opposite. Choice B proposes an increase of $85, which matches the absolute value of individual transactions but ignores the net effect. Choice C suggests a decrease of $85, which again focuses on individual transactions rather than the overall result. Study tip: When problems mention "opposites" and "absolute values" together, always calculate the complete net change first, then apply the opposite relationship. Don't get distracted by individual transaction amounts.

Question 3

Point $A$ is located at $-12$ on a number line. Point $B$ is the same distance from zero as point $A$ , but in the opposite direction. Point $C$ is located so that the distance from $C$ to zero equals the distance from $A$ to $B$ . How many possible locations are there for point $C$ ?

Exactly one location for point $C$
Exactly four locations for point $C$
Exactly three locations for point $C$
Exactly two locations for point $C$ (correct answer)

Explanation: When you encounter problems about points on a number line and distances, focus on understanding absolute value and how distance works in both directions from any reference point. Let's work through this step by step. Point A is at

-12

. Since point B is the same distance from zero as A but in the opposite direction, B must be at

+12

. The distance from A to zero is

|-12| = 12

, so B is 12 units on the positive side. Now find the distance from A to B: from

-12

+12

12 - (-12) = 24

units total. Point C must be located so that its distance from zero equals this distance from A to B, which is 24 units. Since distance is always positive, C could be either 24 units to the right of zero (at

+24

) or 24 units to the left of zero (at

-24

). That gives us exactly two possible locations for point C. Answer choice A is wrong because there isn't just one location—distance from zero creates two possibilities. Answer choice B incorrectly suggests four locations, which would happen if you mistakenly counted distances in multiple directions or made calculation errors. Answer choice C suggests three locations, which has no mathematical basis for this type of distance problem. Remember: whenever a problem asks for points at a specific distance from zero (or any reference point), there are typically two solutions—one in each direction along the number line, unless the point is exactly at the reference point itself.

Question 4

Which statement is always true about any real number $x$ and its opposite?

The sum of $x$ and its opposite equals twice the absolute value of $x$
The absolute value of $x$ equals the absolute value of its opposite (correct answer)
The product of $x$ and its opposite is always positive when $x \neq 0$
The difference between $x$ and its opposite equals the absolute value of $x$

Explanation: For any real number x, its opposite is -x, and |x| = |-x| is always true. Choice A is false since x + (-x) = 0, not 2|x|. Choice C is false since x·(-x) = -x² which is negative when x ≠ 0. Choice D is false since x - (-x) = 2x, which equals |x| only when x ≥ 0.

Question 5

The temperature in Fairbanks changed by $-15°F$ in the morning and $+8°F$ in the afternoon. If the absolute value of the total temperature change equals the absolute value of a second city's temperature change, and the two cities' changes are opposites, what was the second city's temperature change?

$-7°F$ decrease in temperature
$+7°F$ increase in temperature (correct answer)
$-23°F$ decrease in temperature
$+23°F$ increase in temperature

Explanation: Fairbanks' total change: -15 + 8 = -7°F. The absolute value is |-7| = 7. Since the cities' changes are opposites, the second city's change is +7°F. Choice A gives the same change as Fairbanks, not the opposite. Choice C uses |-15| + |8| = 23 incorrectly. Choice D uses the same incorrect calculation but with wrong sign reasoning.

Question 6

A stock price changed by $x$ dollars on Monday and by the opposite amount on Tuesday. On Wednesday, it changed by an amount whose absolute value equals $|x|$ . If the net change over three days was $+12$ dollars, what was Wednesday's change?

Wednesday's change was exactly $+12$ dollars (correct answer)
Wednesday's change was exactly $-12$ dollars
Wednesday's change could be either $+12$ or $-12$ dollars
Wednesday's change was exactly $0$ dollars

Explanation: Monday: +x, Tuesday: -x, Wednesday: ±|x|. Net change: x + (-x) + (±|x|) = ±|x| = +12. Since the net change is positive 12, Wednesday's change must be +12 (which equals +|x|). Choice B gives the wrong sign. Choice C suggests both are possible, but the net change constraint determines it uniquely. Choice D ignores the given net change.

Question 7

Two hikers start at base camp (elevation 0). Hiker 1 goes to an elevation where the absolute value is 450 feet. Hiker 2 goes to the opposite elevation of Hiker 1. Then Hiker 2 climbs an additional 200 feet up. Which statement must be true?

Hiker 2 could end up at either 250 feet or 650 feet above base camp
Hiker 2 could end up at either -250 feet or -650 feet below base camp
Hiker 2 could end up at either -250 feet or 650 feet relative to base camp (correct answer)
Hiker 2 must end up at exactly 650 feet above base camp

Explanation: Hiker 1 is at elevation with |elevation| = 450, so at +450 or -450 feet. Hiker 2 goes to the opposite: -450 or +450 feet respectively. After climbing 200 feet up: (-450) + 200 = -250 feet, or (+450) + 200 = 650 feet. Choice A assumes Hiker 1 starts below ground. Choice B ignores the upward climb. Choice D assumes only one possibility.

Question 8

Consider the expression $|a - b|$ where $a = -8$ and $b$ is the opposite of $a$ . What is the value of this expression?

The expression equals zero since opposites cancel
The expression equals $8$ since $|a| = 8$
The expression equals $16$ since $|-8 - 8| = 16$ (correct answer)
The expression equals $-16$ since $a - b = -16$

Explanation: Since a = -8, its opposite b = 8. Therefore |a - b| = |-8 - 8| = |-16| = 16. Choice A confuses this with a + b = 0. Choice B incorrectly uses just |a|. Choice D forgets that absolute value is always non-negative.

Question 9

The absolute value of a number is 15. If you subtract 8 from the opposite of this number, what are the possible results?

Only $-23$ is possible as the result
Only $7$ is possible as the result
Both $-23$ and $7$ are possible results (correct answer)
Both $23$ and $-7$ are possible results

Explanation: If |x| = 15, then x = 15 or x = -15. The opposites are -15 and 15 respectively. Subtracting 8: (-15) - 8 = -23, and (15) - 8 = 7. Both results are possible. Choice A considers only one case. Choice B considers only the other case. Choice D incorrectly calculates the arithmetic.