Getting your questions ready
Getting your questions ready
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50 free 8th Grade Math trivia questions with answers — science & nature quiz, new questions added Aug 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 50 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 50 questions with answers and explanations. Play the quiz
Q 01Slope is defined as rise over what?
Run
It is usually written m; a line that goes up from left to right has positive slope.
Q 02What is the slope of the line through the points (1, 2) and (3, 8)?
3
Rise is 8 − 2 = 6 and run is 3 − 1 = 2, so the slope is 6/2 = 3.
Q 03Which letter is traditionally used for slope in the equation y = mx + b?
m
Nobody is sure why; it first appears in English in O'Brien's 1844 textbook.
Q 04What does a line with positive slope do as you read it from left to right?
It goes up
A larger absolute value of slope means a steeper line.
Q 05Where does the graph of y = 2x − 5 cross the y-axis?
At (0, −5)
Set x = 0 and you get y = −5; the y-intercept is the constant term in slope-intercept form.
Q 06A function with slope 0 has a graph that is what kind of line?
Horizontal
It is a constant function, f(x) = b, which some authors do not even count as linear.
Q 07What is the solution to the system x + y = 10 and x − y = 2?
x = 6, y = 4
Add the equations: 2x = 12, so x = 6, and then y = 4. Both equations must hold at once.
Q 08What is a solution to a system of linear equations?
Values that satisfy every equation at once
Graphically, it is where the lines cross; parallel lines give no solution.
Q 09A function assigns to each input how many outputs?
Exactly one
That is why a vertical line can only cross the graph of a function once.
Q 10Which set of ordered pairs is NOT a function?
{(1, 2), (1, 3), (2, 4)}
The input 1 is paired with two different outputs, 2 and 3, which a function cannot do.
Q 11In a directly proportional relationship, what stays constant?
The ratio of the two quantities
If the product is constant instead, the quantities are inversely proportional.
Q 12What is 2 to the power of 5?
32
It is 2 × 2 × 2 × 2 × 2, which you can read as "2 to the 5th".
Q 13What is 3 to the power of −2 equal to?
1/9
A negative exponent means the reciprocal of the positive power: 1 divided by 3 squared.
Q 14In scientific notation, the coefficient m is usually kept in what range?
Q 21How many real cube roots does every real number have?
Exactly one
Unlike square roots, negative numbers have a real cube root: the cube root of −8 is −2.
Q 22A number that can be written as a fraction of two integers is called what?
Rational
The denominator must be nonzero; 0.75 qualifies because it equals 3/4.
Q 23A decimal that repeats or terminates represents what kind of number?
Rational
0.333... is 1/3, and 0.25 is 1/4; an irrational number's decimal never repeats.
Q 24Which of these numbers cannot be written as a ratio of two integers?
Between 1 and 10
The integer power of ten is called the exponent and m is the significand or mantissa.
Q 15How is 4,500,000 written in scientific notation?
4.5 × 10^6
Move the decimal six places to get a coefficient between 1 and 10.
Q 16In the number 6.022 × 10^23, what is the 23 called?
The exponent
Calculators often display it as 6.022E23.
Q 17What is the principal square root of 9?
3
Both 3 and −3 square to 9, but the radical sign means the nonnegative one.
Q 18Which two numbers are square roots of 16?
4 and −4
Squaring either one gives 16; the principal root is the positive one.
Q 19The square root of a positive integer that is not a perfect square is always what kind of number?
Irrational
The ancient Greeks knew this; the square root of 2 is the classic example.
Q 20What is the cube root of 64?
4
A cube root is the number whose third power gives the original: 4 × 4 × 4 = 64.
√2
Pi, e and the golden ratio are also irrational; 22/7 is only an approximation of pi.
Q 25What is (3 + 5)²?
64
The parentheses force the addition first: 8 squared is 64, whereas 3 + 5² would be 28.
Q 26Pi is approximately equal to what?
3.14159
It is the ratio of a circle's circumference to its diameter; 2.71828 is e and 1.61803 is the golden ratio.
Q 27Who is credited with the first proof that some lengths cannot be written as a ratio of integers?
A Pythagorean, possibly Hippasus
He probably found them while studying the sides of a pentagram.
Q 28The Pythagorean theorem relates the square on the hypotenuse to what?
The sum of the squares on the other two sides
In symbols, a² + b² = c², where c is the side opposite the right angle.
Q 29A right triangle has legs of 3 and 4. How long is the hypotenuse?
5
9 + 16 = 25, and the square root of 25 is 5; (3, 4, 5) is the most famous Pythagorean triple.
Q 30Which of these is a Pythagorean triple but NOT a primitive one?
(6, 8, 10)
It is just (3, 4, 5) doubled; primitive triples share no common factor.