Algebra
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50 free Algebra trivia questions with answers — science & nature quiz, new questions added Oct 2026.
Algebra is the point where mathematics stops being about particular numbers and starts being about patterns. Replace a number with a letter and a single line can describe every case at once, which is why the subject sits underneath science, finance, engineering and computing. This quiz mixes practice with trivia. Expect questions on the properties of numbers, simplifying and expanding expressions, solving equations and inequalities, exponents, factoring, functions and straight-line graphs, the core of an Algebra I course. Alongside them are the stories: where the word algebra comes from, who chose the letter x for an unknown, and the scholars from the ancient world to modern times who shaped the subject. It suits students revising for a test, teachers who want a ready-made class quiz, and adults curious about how much school math has stuck. Every question comes with its answer and a short explanation.
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Q 01The word algebra comes from the Arabic al-jabr, a term for restoring that was also used for which medical treatment?
Bonesetting
Bonesetting was called algebra in English in the 15th and 16th centuries, a medical usage that probably came from Arab doctors in Spain.
Q 02Welsh mathematician Robert Recorde invented which symbol in 1557 because he was tired of writing the same words?
Equals sign
The equals sign made its debut in The Whetstone of Witte, where Recorde chose two parallel lines of one length because no two things can be more equal.
Q 03Which 9th-century Persian scholar wrote the book that named algebra and later gave his own name to the word algorithm?
Al-Khwarizmi
Al-Khwarizmi worked at the House of Wisdom in Baghdad around 820, and Latin translators later rendered his name as Algoritmi.
Q 04Which English shoemaker's son gives his name to the algebra of true and false values behind computer logic?
George Boole
George Boole set out the system in The Laws of Thought in 1854, and Claude Shannon later applied it to relay circuits, the forerunners of digital computers.
Q 05The graph of a quadratic function such as y = x² is which U-shaped curve, also traced by a thrown ball?
Parabola
A parabola also gives satellite dishes and car headlight reflectors their shape, because the curve gathers parallel rays at a single focal point.
Q 06In the straight-line equation y = mx + b, the letter m stands for which measure, often described as rise over run?
Slope
Slope has been written as m since at least 1844, when the letter first appears in an English textbook, yet nobody is sure why it was chosen.
Q 07Which Italian, famous for a sequence about breeding rabbits, spread Arabic algebra in Europe with his book Liber Abaci?
Fibonacci
Fibonacci was educated in what is now Algeria, where his father directed a trading post, and it was there that he learned the Hindu-Arabic numerals.
Q 08Following the order of operations taught as PEMDAS, what is the value of the expression 1 + 2 × 3?
7
The value is 7, because multiplication is done before addition. Working strictly left to right gives 9, the slip the PEMDAS mnemonic is meant to prevent.
Q 09The classroom mnemonic FOIL, short for first, outer, inner, last, is a method for multiplying two of what?
Binomials
Binomials are expressions with two terms, such as x + 3, so the method gives four products. FOIL is so familiar in American schools that it is used as a verb.
Q 10Solving x² = −1 needs which kind of number, made of a real part and a part once mocked as imaginary?
Complex
Complex numbers such as 3 + 2i were long written off as fictitious and useless, yet they are now everyday tools in electromagnetism and quantum mechanics.
Q 11Which British mathematician proved Fermat's Last Theorem, on the equation aⁿ + bⁿ = cⁿ, after years of secret work?
Andrew Wiles
Andrew Wiles unveiled his proof in 1993, some 350 years after Fermat claimed one too long for a book's margin, then had to repair an error before it was accepted.
Q 12Which ancient people left clay tablets, nearly 4,000 years old, that solve quadratic problems in cuneiform script?
Babylonians
The Babylonians counted in base 60, and one of their tablets gives the square root of 2 correct to about six decimal places.
Q 13The numbers produced by multiplying out (a + b)ⁿ fill the rows of which pattern, studied in China by Yang Hui?
Pascal's triangle
Q 21Under the associative property, (2 + 3) + 4 equals 2 + (3 + 4); which feature of the sum has changed?
The grouping
The grouping is all that moves: the parentheses shift while the numbers stay in line. Subtraction lacks the property, since (10 − 5) − 3 is 2 but 10 − (5 − 3) is 8.
Q 22Zero is called the additive what, because adding it to any number leaves that number unchanged?
Identity
Identity is the title, and multiplication has one too: the number 1, since multiplying by 1 changes nothing.
Q 23Which name is given to a number's multiplicative inverse, such as 1/5 for 5, since the pair multiply to 1?
Reciprocal
Reciprocal is the everyday name, and it explains the rule for dividing by a fraction: flip the fraction and multiply instead.
Pascal's triangle builds each entry by adding the two numbers above it, and it was studied in India, Persia and China centuries before Blaise Pascal wrote about it.
Q 14What name is given to a rectangular array of numbers in rows and columns, from a Latin word for womb?
Matrix
Matrix was coined for the purpose by James Joseph Sylvester in 1850, who pictured the array as a parent giving birth to the values called determinants.
Q 15Which French philosopher's book La Géométrie began the habit of using x, y and z for unknown quantities?
René Descartes
René Descartes also pioneered the raised numbers used for powers, such as the small 2 in x², while reserving a, b and c for known quantities.
Q 16Which property of addition, whose name comes from a word for exchanging, guarantees that a + b always equals b + a?
Commutative
Commutative operations ignore order, which is why 3 + 5 and 5 + 3 match. Subtraction and division fail the test, since 3 − 5 is not 5 − 3.
Q 17In the algebraic term 5x, what name is given to the 5, the number written in front that multiplies the letter?
Coefficient
Coefficient is the name for that multiplier, and when none is written, as in x², it is understood to be 1.
Q 18Using the distributive property to remove the parentheses, 3(x + 5) expands to which expression?
3x + 15
The result is 3x + 15, because the 3 outside multiplies every term inside the parentheses. Stopping at 3x + 5 is a common slip.
Q 19What value of x solves the two-step equation 2x + 5 = 17, where the unknown is doubled and then increased?
6
The answer is 6: taking 5 from both sides leaves 2x = 12, and halving gives x. Treating both sides alike at every step keeps the equation balanced.
Q 20The two vertical bars in |−8| = 8 denote which quantity, a number's distance from zero on the number line?
Absolute value
Absolute value strips away the sign, so −8 and 8 both give 8. The bar notation was introduced by Karl Weierstrass in 1841.
Q 24If a = b and b = c, then a = c: which property of equality appears in Euclid's Elements?
Transitive
Transitive reasoning links a chain of equal quantities end to end. Euclid put it as things equal to the same thing being equal to one another.
Q 25Combining like terms, which share the same letter and power, what does 3x + 5x + 2 simplify to?
8x + 2
It becomes 8x + 2, because 3x and 5x count the same thing and can be added, while the lone 2 has no partner and stays as it is.
Q 26Which algebraic expression matches the phrase five less than twice a number n, where the subtraction comes last?
2n − 5
It is 2n − 5: twice the number comes first, then 5 is taken away. Writing 5 − 2n follows the word order but subtracts the wrong way round.
Q 27What is the value of 2x² when x = 3, given that the power is worked out before the multiplication?
18
The value is 18, because the 3 is squared to give 9 before being doubled. Doubling first and then squaring gives 36, which is the value of (2x)² instead.
Q 28By the product rule for exponents, x² × x³ simplifies to which single power of x?
x⁵
The answer is x⁵, since x² is two copies of x and x³ is three more, five in all. Exponents multiply only when a power is itself raised to a power.
Q 29Powers of 2 halve as the exponent falls, from 8 to 4 to 2, so 2 to the power 0 equals what?
1
It equals 1, and the same holds for every non-zero base. The convention keeps the laws of exponents consistent, since dividing any power by itself must give 1.
Q 30The pattern a² − b² = (a − b)(a + b), a shortcut for mental math, is known by which name?
Difference of squares
The difference of squares turns 21 × 19 into (20 + 1)(20 − 1), which is 400 − 1 = 399, with no long multiplication needed.