Getting your questions ready
Getting your questions ready
Beat the crowd
10 questions No timer
50 free Middle School Math trivia questions with answers — science & nature quiz, new questions added Aug 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 50 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 50 questions with answers and explanations. Play the quiz
Q 01Which property lets you compute 7 × 98 as 7 × 100 minus 7 × 2, the shortcut behind much mental arithmetic?
Distributive
Distributive multiplication over subtraction, a(b − c) = ab − ac, is the trick behind mental arithmetic like 7 × 98 = 700 − 14 = 686.
Q 02What is (−8) × (−6), a product that trips up anyone who expects two negatives to stay negative?
48
48 is the answer because the product of two negative numbers is positive, which is why squaring any negative number gives a positive result.
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: 5² + 12² = 169, and the square root of 169 is 13. Adding the legs gives 17, a common slip.
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, the shortcut cashiers use instead of subtracting.
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; forgetting the division gives 15, the most common wrong answer.
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 (1-6, 2-5, 3-4, 4-3, 5-2, 6-1) add to 7, which is why craps players dread a seven.
Q 10What is (−3)², a value that differs from −3² because the parentheses square the minus sign too?
9
9 is (−3)² since (−3) × (−3) is positive, while −3² means −(3²) = −9 by the usual convention that exponents bind before a 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 variable?
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 inequality solves −2x > 8, remembering that dividing by a negative number reverses the direction of the sign?
x < −4
x < −4 is the solution because dividing both sides by −2 flips the inequality; x > −4 is the answer of anyone who forgot the flip.
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 any triangle is exactly half a parallelogram with the same base and height, as Euclid proved.
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, and the same box has a surface area of 162 in², a figure students mix up with volume on tests.
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 x/5 must equal 7 after adding 3, and 7 × 5 = 35; multiplying before adding gives the tempting 20.
Q 19Which of these numbers is irrational, impossible to write exactly as one whole number over another?
√10
√10 is irrational, about 3.1623 with digits that never repeat, whereas √25 is simply 5 and 22/7 is only a rational approximation of pi.
Q 20Which transformation slides every point of a shape the same distance one way, without turning or flipping it?
Translation
Translation is the slide, the one rigid motion that keeps every segment parallel to its original; 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, since circumference equals pi times the diameter; using the 12 as a radius doubles it to 75.4.
Q 25By what percent did a class grow when it went from 60 pupils to 75, measured against the starting number?
25%
25% is the increase: the class gained 15 pupils, and 15 ÷ 60 = 0.25; dividing by the new size of 75 instead gives a misleading 20%.
Q 26What is the mode of 3, 3, 8, 12, 16, 20 and 22, a set whose mean and median both equal 12?
3
3 is the mode because it is the only value listed twice; a data set can have no mode at all, or several, which is why it is the least used average.
Q 27Which word describes two lines that meet at exactly 90°, like the hands of a clock at three o'clock?
Perpendicular
Perpendicular lines form four right angles where they cross, which is why a carpenter's square checks a corner with a single touch.
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 lower still.
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.