Middle School Math Trivia
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100 free Middle School Math trivia questions with answers — science & nature quiz, new questions added Oct 2026.
Middle school is where arithmetic turns into mathematics. Negative numbers appear, letters stand in for unknowns, and a triangle's sides start obeying a rule with a Greek name. It is also the material quiz bowl buzzer rounds lean on hardest, because every problem has a single clean answer and a ten-second solve. These 100 questions mix computation with vocabulary the way a real quiz bowl packet does: integer arithmetic and order of operations, ratios and percent change, solving for an unknown, area, volume and circumference, exponents and scientific notation, probability with dice and marbles, and the mean, median, mode and range of small data sets. The vocabulary questions cover the terms a middle school course expects students to use, from the names of angle pairs to the word for a slide on a coordinate grid. Play it to see how much has stuck since seventh grade, hand it to a student as buzzer practice, or print it for a classroom round. Each answer comes with a one-line worked solution or the fact that makes the term worth knowing.
30 of 100 questions with answers and explanations. Play the quiz
Q 01Which property lets you compute 7 × 98 as 7 × 100 minus 7 × 2?
Distributive
Distributive is the property: multiplying spreads across a bracket, a(b − c) = ab − ac, the trick behind mental arithmetic like 7 × 98 = 700 − 14 = 686.
Q 02What is (−8) × (−6), the product of two negative numbers?
Positive 48
Positive 48, because each minus sign reverses direction on the number line and two reversals cancel, just as losing eight debts of 6 leaves you 48 better off.
Q 03What is the longest side of a right triangle with shorter sides 5 and 12, a classic whole-number triple?
13
13 completes the 5-12-13 triple, since 5² + 12² = 169 and the square root of 169 is 13; stopping at 169 forgets the root and gives a side longer than both legs laid end to end.
Q 04What is 7⁰, the value every nonzero number takes when raised to the power zero?
1
1 is the value of 7⁰ because each drop of one in the exponent divides by 7: 7² = 49, 7¹ = 7, and 7 ÷ 7 = 1.
Q 05What is 30% of 70, the discount on a $70 jacket in a sale that takes 30 percent off?
$21
$21 comes from 0.30 × 70; the sale price is then $49, which is 70% of the original, so multiplying by 0.7 gets there in one step.
Q 06Which numbered region of the coordinate plane holds the point (−3, 5), counting anticlockwise from the upper right?
II
II is the upper-left region, where x is negative and y is positive; the numbering runs counterclockwise from I in the upper right.
Q 07What value of x solves 3x + 7 = 22, an equation solved by undoing the addition before the multiplication?
x = 5
x = 5 because 22 − 7 leaves 3x = 15, and 15 ÷ 3 = 5; stopping at 15 forgets the final division, and multiplying by 3 instead gives 45.
Q 08Which name do the equal angles facing each other across the crossing point of two straight lines go by?
Vertical
Vertical is the name, from the shared vertex rather than any up-and-down direction, and the two angles in each pair are always equal.
Q 09What is the probability that two fair dice total 7, the sum that has more ways to come up than any other?
1/6
1/6 is the chance because six of the thirty-six equally likely pairs, from 1-6 round to 6-1, add to 7, making it the likeliest total and the roll that wins outright on a craps shooter's first throw.
Q 10What is (−3)², where the parentheses mean the minus sign is squared too?
Positive 9
Positive 9, since (−3) × (−3) multiplies two negatives, while −3² without parentheses means −(3²) = −9, because in written maths the power is applied before the minus sign.
Q 11What is the mean of the scores 6, 12, 16, 20 and 41, a figure dragged upward by one high score?
19
19 is the mean: the scores sum to 95 and 95 ÷ 5 = 19, while the median stays at 16, which is why one extreme value can mislead an average.
Q 12What is 12 boys to 18 girls as a ratio in simplest form, found by dividing both counts by a shared factor?
2:3
2:3 is the ratio once 12 and 18 are both divided by 6; 4:6 and 6:9 are equal to it but not fully reduced, and 3:2 reverses the order.
Q 13Which name does the 4 in the term 4x go by, the number that multiplies the letter?
Coefficient
Coefficient is the word, and the unwritten 1 in front of a bare x is still a coefficient, which is why x + x = 2x.
Q 21What is the greatest common factor of 20 and 70, the largest number that divides both without a remainder?
10
10 is the greatest common factor, since 20 = 2 × 10 and 70 = 7 × 10 share nothing larger; 140 is their least common multiple instead.
Q 22What is the least common multiple of 6 and 8, the first number that appears in both times tables?
24
24 is the least common multiple: the sixes run 6, 12, 18, 24 and the eights 8, 16, 24, so 24 is where they first meet, well short of the product of the two.
Q 23Which of these values of x satisfies the inequality −2x > 8?
Negative 5
Negative 5 works, since −2 × −5 = 10; dividing an inequality by a negative number reverses its sign, so the solutions are the numbers below −4, not above it.
Q 14What is 2⁵, the number of different heads-or-tails outcomes when five coins are tossed at once?
32
32 is 2 × 2 × 2 × 2 × 2, and each extra coin doubles the count of outcomes, which is why ten coins already give 1,024 ways.
Q 15What is the area of a triangle with base 8 cm and height 7 cm, half that of the matching rectangle?
28 cm²
28 cm² is half of 8 × 7 = 56, because two copies of any triangle fit together into a parallelogram with the same base and height.
Q 16Which word describes two angles adding to 180°, such as the neighbouring pair formed when one line crosses another?
Supplementary
Supplementary is the term, and when the two angles sit side by side their outer arms form a straight line, a pairing geometry calls a linear pair.
Q 17What is the volume of a box 3 by 6 by 7 inches, the product of its three dimensions?
126 in³
126 in³ is 3 × 6 × 7: a 3-by-6 layer holds 18 inch cubes, and seven such layers stack up to fill the box.
Q 18What value of x solves x/5 − 3 = 4, where adding 3 to both sides comes before multiplying by 5?
x = 35
x = 35 because adding 3 to both sides leaves x/5 = 7, and 7 × 5 = 35; stopping at 7 forgets that x is still being divided by 5.
Q 19Which of these numbers is irrational, impossible to write exactly as one whole number over another?
√7
√7 is irrational, about 2.6458 with digits that never repeat, whereas √49 is simply 7 and 22/7 is only a rational stand-in for pi.
Q 20Which geometric move slides every point of a shape the same distance one way, without turning or flipping it?
Translation
Translation is the slide, a rigid motion that keeps every segment parallel to its starting position; a rotation turns and a reflection flips.
Q 24What is the distance around a circular table 12 feet across, found by multiplying the diameter by pi?
About 37.7 ft
About 37.7 ft is π × 12, because any circle is a little over three times as far around as it is across; treating the 12 as a radius doubles the answer to 75.4.
Q 25Which percent change is bigger, a class going from 60 pupils to 75 or from 75 to 60?
The increase
The increase is 25%, since 15 ÷ 60 = 0.25, while the same 15 pupils are only 20% of 75; a percent change always divides by the starting number.
Q 26What is the mode of the five values 3, 3, 8, 26 and 80?
3
3 is the mode because it is the only value listed twice; the median here is 8 and the mean 24, and unlike them a data set can have several modes or none at all.
Q 27Which word describes two lines that meet at exactly 90°, like the hands of a clock at three o'clock?
Perpendicular
Perpendicular lines cut the space around their crossing into four equal angles, each a right angle, so checking one corner with a set square checks them all.
Q 28What is −15 + 9 − (−4), an expression where subtracting a negative becomes adding a positive?
−2
−2 is the result: −15 + 9 = −6, then −6 − (−4) = −6 + 4 = −2; treating the double minus as a single subtraction drops the total to −10.
Q 29What is the slope of the line through (2, 3) and (5, 18), the rise between the points divided by the run?
5
5 is the slope: y rises 15 while x runs 3, and 15 ÷ 3 = 5, meaning the line climbs five units for every one it moves right.
Q 30Which name does the 7 in 63 ÷ 9 = 7 go by, the partner term to dividend and divisor?
Quotient
Quotient is the name, from the Latin quotiens, 'how many times', since 63 ÷ 9 asks how many times 9 fits into 63.