8th Grade Math
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49 free 8th Grade Math trivia questions with answers — science & nature quiz, new questions added Oct 2026.
Eighth grade is where math turns algebraic: lines get slopes and intercepts, equations come in systems, functions get their rules, exponents go negative, numbers go irrational and triangles obey Pythagoras. These 49 questions hit the big ideas of the year without needing a calculator. Expect slope and y-intercept, solving two-variable systems, what makes a relation a function, the laws of exponents and scientific notation, square roots, cube roots and perfect squares, rational versus irrational numbers, the Pythagorean theorem and the 3-4-5 triangle, translations, rotations, reflections and dilations, congruence and similarity, transversals and the angle sum of polygons, the volumes of cylinders, cones and spheres, and reading scatter plots. Every answer is tied to a reference page we checked and each explanation shows the working. Play it solo, use it for a review day, or print it for a classroom quiz.
30 of 49 questions with answers and explanations. Play the quiz
Q 01Slope is defined as rise over what?
Run
Run. Dividing the change up or down by the change across turns steepness into one number, so a slope of 2 means two units up for every unit along.
Q 02What is the slope of the line through the points (1, 2) and (3, 14)?
6
6. The line climbs 12 while moving only 2 across, and 12 ÷ 2 = 6; dividing the wrong way round, the classic slip, gives 1/6.
Q 03Which letter is traditionally used for slope in the equation y = mx + b?
m
m. Nobody knows why that letter was chosen: the popular link to the French monter, 'to climb', has no evidence behind it, and Descartes, who was French, never used it.
Q 04What does a line with positive slope do as you read it from left to right?
It goes up
It goes up. A positive slope means y grows as x grows, and the bigger the number the steeper the climb; a slope below zero runs downhill instead.
Q 05Where does the graph of y = 2x + 6 cross the y-axis?
At (0, 6)
At (0, 6). On the y-axis x is zero, so the 2x term vanishes and only the constant is left, which is why that constant is called the y-intercept.
Q 06A line with a slope of 0 is what kind of line?
Horizontal
Horizontal. With zero slope y never changes, so the line runs flat; a line straight up and down is the opposite case, with a slope that is undefined.
Q 07What is a solution to a system of linear equations?
Values that satisfy every equation at once
Values that satisfy every equation at once. On a graph that is the point where the lines cross, which is why parallel lines, which never meet, give no solution.
Q 08Which test tells whether a graph shows a function?
Vertical line test
Vertical line test. A function gives each input only one output, so no upright line may cross its graph twice: a U-shaped parabola passes and a circle fails.
Q 09Which of these sets of ordered pairs is a function?
{(1, 2), (2, 2), (3, 2)}
{(1, 2), (2, 2), (3, 2)}. Outputs may repeat as often as they like; what a function forbids is one input paired with two outputs, which each of the other sets has.
Q 10In a directly proportional relationship, what stays constant?
The ratio of the two quantities
The ratio of the two quantities. Double one and the other doubles, so y divided by x never changes; when it is the product that stays fixed instead, the two are inversely proportional.
Q 11What is 2 to the power of 5?
32
32. Each extra power of 2 doubles the last (2, 4, 8, 16, 32), so the 5 counts doublings rather than multiplying 2 by 5.
Q 12What is 3 to the power of −2 equal to?
1/9
1/9. A negative power means divide rather than make negative: stepping down the powers of 3 (9, 3, 1, 1/3, 1/9) divides by 3 each time.
Q 13Which of these numbers, written in scientific notation, is the largest?
2 × 10^6
2 × 10^6. The power of ten outweighs the digit in front: two million beats nine hundred thousand, so compare the powers of ten first.
Q 14How is 4,500,000 written in scientific notation?
Q 21Which repeating decimal is exactly equal to 1?
0.999…
0.999… with the nines going on forever. A third is 0.333…, and three of those make 0.999…, yet three thirds are exactly 1.
Q 22A decimal that repeats or terminates represents what kind of number?
Rational
Rational. Every such decimal can be turned back into a fraction of two whole numbers: 0.25 is 1/4, and 0.272727… is 3/11.
Q 23Which of these numbers cannot be written as a fraction of two integers?
√2
√2. No fraction squares to exactly 2, and in one telling Hippasus, the follower of Pythagoras sometimes credited with the proof, was drowned at sea for revealing it.
4.5 × 10^6
4.5 × 10^6. The decimal point hops six places to the left to leave a single digit in front, and the 6 simply counts the hops.
Q 15In the number 6.022 × 10^23, what is the 23 called?
The exponent
The exponent. Calculators that can't show a raised number print it after an E instead, so the same value appears as 6.022E23.
Q 16Which root does √9 mean?
The positive root
The positive root. The radical sign always means the principal root, here 3, which is why formulas that need both roots have to write ± in front of it.
Q 17Which two numbers are square roots of 16?
4 and −4
4 and −4. A negative times a negative is positive, so every positive number has two square roots, mirror images on either side of zero.
Q 18√50 lies between which two whole numbers?
7 and 8
7 and 8. Since 7 × 7 is 49 and 8 × 8 is already well past 50, the root sits just above 7, at about 7.07.
Q 19What is the cube root of 64?
4
4. Three 4s multiplied together make 64, so a cube built from 64 small blocks is exactly 4 blocks along every edge; 8 is the square root instead.
Q 20Which of these numbers has a real cube root but no real square root?
−27
−27. Three negatives multiply back to a negative, so −3 cubed is −27, but no real number squared can ever come out below zero.
Q 24What is (3 + 5)²?
64
64. The parentheses make the sum happen first, so it is 8 squared; without them only the 5 would be squared and the answer would drop to 28.
Q 25Pi is a circle's circumference divided by its what?
Diameter
Diameter. Every circle, from a coin to the equator, is about 3.14159 times as far around as it is across, which is why one number serves them all.
Q 26Which of these equations has no solution?
x + 1 = x + 2
x + 1 = x + 2. Take x from both sides and it claims that 1 equals 2, which no value of x can repair; x + 1 = 1 + x is the opposite case, true for every x.
Q 27The square on the hypotenuse equals what?
The sum of the squares on the other two sides
The sum of the squares on the other two sides. Though named for Pythagoras, the rule was in everyday use in Babylon more than a thousand years before he was born.
Q 28What is the hypotenuse of a right triangle whose legs are 3 and 4?
5
5. The squares on the legs, 9 and 16, add to 25, and it works backwards too: mark out any triangle with sides 3, 4 and 5 and you have made a perfect right angle.
Q 29Which of these Pythagorean triples is just a smaller triple scaled up?
(6, 8, 10)
(6, 8, 10). Every side is even, so halving gives (3, 4, 5); the other three have no common factor, which is what makes a triple primitive.
Q 30Which of these equations graphs as a curve rather than a straight line?
y = x²
y = x². Squaring makes y grow faster and faster as x grows, so the graph bends into a parabola; the other three change by the same amount for every step along.