7th Grade Math
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50 free 7th Grade Math trivia questions with answers — science & nature quiz, new questions added Oct 2026.
Seventh grade is the year math starts describing the real world. Ratios turn into rates and proportions, percentages show up as sale prices, tips and sales tax, and negative numbers stop being a curiosity and start behaving like everything else on the number line. This quiz follows a typical Math 7 course from the opening unit to the end-of-year review. It starts with rates and proportional relationships, moves through percent problems and operations with positive and negative real numbers, then turns to analyzing and comparing data sets and simple probability. Expressions, equations, inequalities, circles, scale and volume close it out, the way a final exam would. It suits a seventh grader revising for a unit test, a teacher who wants a ready-made warm-up or a printable review, and any adult curious about how much of middle school has stuck. Every answer comes with a short worked explanation, so a wrong guess still teaches the method.
30 of 50 questions with answers and explanations. Play the quiz
Q 01A $100 jacket is marked up 10%, then put on sale at 10% off; what is the final price?
$99
$99 is the final price because the 10% discount comes off the larger $110, removing $11 rather than $10. A rise and a fall of the same percentage never cancel out.
Q 02Sound covers roughly 343 metres a second; how far away is lightning whose thunder arrives 3 seconds later?
About 1 km
About 1 km is right, since 343 × 3 is 1,029 metres. Counting three seconds for every kilometre between the flash and the bang is a standard way to judge how close a storm is.
Q 03Which shape is the cross-section when an upright cylinder, like a soup can, is sliced straight down the middle?
Rectangle
Rectangle is the shape whenever the cut runs at right angles to the base; through the middle it is as tall as the can and as wide as its lid. Slice the same can parallel to the base and the face is a circle.
Q 04Pi Day is celebrated on which date, chosen because the month and day match the first three digits of π?
March 14
March 14 is written 3/14 in the American style, echoing 3.14. The celebration was founded in 1988 by Larry Shaw at the Exploratorium, a science museum in San Francisco.
Q 05When a billionaire walks into a small café, which measure of the customers' wealth barely changes?
Median
Median wealth barely moves because it is simply the middle value once everyone is lined up in order. The mean would leap into the millions, dragged up by a single extreme value.
Q 06A fair coin lands heads five times in a row; what is the probability that the sixth flip is heads?
1/2
1/2 is still the chance, because a coin has no memory and every flip is independent of the last. Expecting tails to be 'due' is the mistake known as the gambler's fallacy.
Q 07What is 68% of 50, a sum made simple by swapping it for 50% of 68?
34
34 is the answer either way round, because 68 × 50 and 50 × 68 are the same product. Any percentage can be flipped like this, which turns an awkward sum into simple halving.
Q 08When every side of a square is made 7 times as long, the square's area is multiplied by which number?
49
49 is the multiplier, because area grows with the square of the change in length: 7 times as wide and 7 times as tall. Volume grows faster still, by the cube.
Q 09Hot Wheels toy cars are made at about 1:64 scale; how long is the toy of a 16-foot car?
3 inches
3 inches is right: 16 feet is 192 inches, and 192 ÷ 64 = 3. The size is also called three-sixteenths scale, because 3/16 of an inch on the model stands for one foot.
Q 10Which two-word term describes a comparison such as 60 miles per hour, where the second quantity is exactly one?
Unit rate
Unit rate is the form that makes comparing easy: dividing 300 miles by 5 hours gives 60 miles for every single hour. A price per ounce on a shelf tag is one too.
Q 11Which name is given to k in the equation y = kx, the role speed plays when distance depends on time?
Constant of proportionality
Constant of proportionality is the full name, and y is always that many times x. For a car at a steady 50 miles an hour, k is 50, so the distance is 50 times the hours driven.
Q 12When pay is always the same multiple of hours worked, a graph of the two is a straight line through which point?
(0, 0)
(0, 0) is on every such graph because zero of one quantity always means zero of the other: no hours worked, no pay earned. A straight line that misses that point shows a fixed fee or a head start instead.
Q 13A 12-pack of soda costs $4.20; what is the price of each can, the figure shoppers use to compare pack sizes?
Q 21A phone's price falls from $200 to $150; what is the percent decrease, measured against the original price?
25%
25% is the decrease: the $50 drop is one quarter of the original $200. Measured against the new price of $150, the same $50 would be about 33%, which is why the starting value matters.
Q 2263 is 45% of which number, found by dividing 63 by 0.45 rather than multiplying?
140
140 is the whole: 63 ÷ 0.45 = 140, and 45% of 140 is 63 as a check. Multiplying instead gives 28.35, an answer smaller than the part it is supposed to contain.
Q 23How much simple interest does $500 earn in 3 years at 4% a year, with no interest reinvested?
$60
$60 is the interest: 4% of $500 is $20 a year, for three years. Simple interest is always worked out on the starting amount alone, which bankers call the principal.
$0.35
$0.35 comes from dividing $4.20 by 12. Stores usually post this price for a single item or ounce on the shelf tag, beside the price of the whole pack.
Q 14On a plan where 1 cm means 2 m, what is the real area of a room drawn 3 by 7 cm?
84 m²
84 m² is the real area, because the room measures 6 m by 14 m. Both sides have to be scaled up: multiplying the drawing's 21 by 2 only once gives 42, half the true figure.
Q 15A recipe uses 3 cups of flour for 2 dozen cookies; how many cups do 5 dozen cookies need?
7.5
7.5 is right: each dozen takes 1.5 cups, and 5 × 1.5 = 7.5. Adding one cup for each of the 3 extra dozen, a common slip, gives 6 and leaves the dough short.
Q 16A nurse counts 18 heartbeats in 15 seconds; what is the patient's heart rate in beats per minute?
72 bpm
72 bpm is the rate, since a minute holds four 15-second counts and 18 × 4 = 72. That sits comfortably inside the normal resting adult span of 60 to 100.
Q 17A sprinter who runs 100 metres in 10 seconds averages which speed in kilometres per hour?
36 km/h
36 km/h is the answer: 10 metres a second, times the 3,600 seconds in an hour, is 36,000 metres. Multiplying metres per second by 3.6 always converts to kilometres per hour.
Q 18What is a 20% tip on a $65 restaurant bill, found quickly by doubling one-tenth of the total?
$13
$13 is the tip: one-tenth of $65 is $6.50, and doubling that gives $13. Sliding the decimal point one place to the left finds 10% of any amount.
Q 19An $80 pair of sneakers is sold where sales tax is 6%; what is the total at the register?
$84.80
$84.80 is the total: 6% of $80 is $4.80, added to the shelf price. Multiplying $80 by 1.06 does both steps at once.
Q 20After a 20% discount a pair of running shoes costs $96; what was the price before the sale?
$120
$120 was the original price: the $96 is the 80% left after the discount, and 96 ÷ 0.80 = 120. Adding 20% of $96 back on gives only $115.20, because that 20% is taken from a smaller amount.
Q 24Which word describes numbers such as π and the square root of 2, whose decimals never end or repeat?
Irrational
Irrational numbers cannot be written as one whole number over another. In one legend the Greek Hippasus was thrown overboard at sea by fellow Pythagoreans for discovering them.
Q 25Which name, from the Latin for 'whole', covers zero, the counting numbers and the negatives of those numbers?
Integers
Integers have no fractional part, so −3, 0 and 8 qualify but 2.5 does not. Mathematicians label the set with a Z, from Zahlen, the German word for numbers.
Q 26Which two-word term names a number's distance from zero on the number line, written with vertical bars?
Absolute value
Absolute value is never negative, so −7 and 7 share the same one: 7. The vertical-bar notation was introduced by the German mathematician Karl Weierstrass in 1841.
Q 27Which term names a number's opposite, such as −9 for 9, the partner that brings the sum to zero?
Additive inverse
Additive inverse pairs sit equally far from zero on opposite sides of the number line. Zero is the only number that is its own.
Q 28Which word describes a decimal such as 0.375 that stops, unlike 0.333… which goes on forever?
Terminating
Terminating decimals come only from fractions whose simplest-form denominator has no prime factors other than 2 and 5. That is why eighths end neatly while thirds never do.
Q 29What is the value of 8 − (−11)?
19
19 is the result, because taking away a debt of 11 is the same as gaining 11: 8 + 11 = 19. Dropping one of the minus signs gives −3 instead.
Q 30What is (−4) × (−3) × (−2), a product whose sign depends on there being three negative factors?
−24
−24 is the product: the first two negatives multiply to a positive 12, and the third flips the sign back. An odd count of negative factors always leaves a negative result.