Algebra Flashcards
Check a word, a formula or an equation on each card, then print any of ten sets on one sheet.
All 96 cards
Words: expressions and equations 12
2x + 5 < 11 is an ___ Inequality: two expressions compared with <, >, ≤ or ≥. 2x + 5 < 11 holds for every x below 3. 2x + 5 = 11 is an ___ Equation: two expressions joined by an equals sign. 2x + 5 = 11 is true only when x = 3. 2x + 5, with no equals sign Expression: numbers, variables and operations with no equals sign. You simplify it, never solve it. 3/4 and 4/3 are ___ Reciprocals: two numbers whose product is 1. Dividing by 3/4 is multiplying by 4/3. 3x² and −8x² are ___ Like terms: same variables, same powers, so they combine. 3x² − 8x² = −5x². 4x² and 9x in 4x² + 9x Terms: the parts of an expression that are added or subtracted. 4x² + 9x has two terms. 5 and −5 are ___ Opposites: the same distance from 0 on either side. They add to 0: 5 + (−5) = 0. |−7| = 7 shows the ___ Absolute value: distance from 0 on the number line, so it is never negative. |−7| = 7. In 3x + 7, the letter x Variable: a letter that stands for a number whose value can change. In 3x + 7 it is x. In 5x + 3, the number 3 Constant: a term with no variable, so its value never changes. In 5x + 3 the constant is 3. In 5x + 3, the number 5 Coefficient: the number that multiplies a variable. In 5x + 3 it is 5; in −x it is −1. x = 3, for 2x + 5 = 11 Solution: a value of the variable that makes the equation true. Check: 2(3) + 5 = 11.
Show all 96 cards (84 more)
Words: expressions and equations
Words: graphs and functions
Words: polynomials and powers
Exponent laws
Number properties
Line formulas
Quadratics and factoring
One-step equations
Two-step equations
Both sides and parentheses
Words: graphs and functions 11
(3, −2) is an ___ Ordered pair: (x, y), the x-coordinate first. (3, −2) is 3 right and 2 down. A quarter of the xy-plane Quadrant: one of four regions made by the axes, numbered I to IV counterclockwise from the upper right. All the inputs of a function Domain: the set of all x-values, the inputs. For y = 1/x it is every number except 0. All the outputs of a function Range: the set of all y-values, the outputs. For y = x² it is y ≥ 0. Each x is paired with one y Function: a relation that gives each input exactly one output. Its graph passes the vertical line test. In y = 2x + 1, the number 2 Slope: rise over run, the change in y for each step of 1 in x. In y = mx + b it is m. The point (0, 0) Origin: the point (0, 0), where the x-axis and the y-axis cross. The point (0, 1) on y = 2x + 1 y-intercept: the point (0, b) where a line crosses the y-axis. Set x = 0 to find it. The point where y = 0 x-intercept: the point (a, 0) where a graph crosses the x-axis. For y = 2x − 6 it is (3, 0). The U-shaped graph of y = x² Parabola: the graph of a quadratic equation. It opens upward when a > 0, downward when a < 0. y = 2x and x + y = 9 together System of equations: two or more equations solved together. Here x = 3, y = 6 fits both.
Words: polynomials and powers 9
Highest power in a polynomial Degree: the highest degree of all the terms. 4x³ − x + 9 has degree 3; a constant has degree 0. In 3 · 4 = 12, the 3 and the 4 Factors: numbers or expressions multiplied to make a product. x² + 5x + 6 has factors (x + 2) and (x + 3). In x⁵, the small raised 5 Exponent: how many times the base is used as a factor. x⁵ = x · x · x · x · x. In x⁵, the x Base: what is raised to the power. In −3² the base is 3, so −3² = −9, while (−3)² = 9. Monomials added or subtracted Polynomial: one monomial, or several joined by + or −, like 4x³ − x + 9. One term, such as 7x³ Monomial: a polynomial with exactly one term, a constant times a whole-number power of a variable. Three terms: x² + 5x + 6 Trinomial: a polynomial with exactly three terms. x² + 5x + 6 factors into (x + 2)(x + 3). Two terms, such as x + 5 Binomial: a polynomial with exactly two terms. (x + 5)(x − 5) multiplies two binomials. x² − 5x + 6 = 0 is a ___ Quadratic equation: ax² + bx + c = 0 with a not 0. This one factors: x = 2 or x = 3.
Exponent laws 7
(a/b)ᵐ = ? Quotient to a power: (a/b)ᵐ = aᵐ/bᵐ, b not 0. Top and bottom both take it: (x/2)³ = x³/8. (ab)ᵐ = ? Product to a power: (ab)ᵐ = aᵐbᵐ. Every factor takes the exponent: (3x)² = 9x². aᵐ · aⁿ = ? Product property: aᵐ · aⁿ = aᵐ⁺ⁿ. Same base, so add the exponents: x² · x³ = x⁵. aᵐ ÷ aⁿ = ? Quotient property: aᵐ ÷ aⁿ = aᵐ⁻ⁿ, a not 0. Subtract the exponents: x⁷ ÷ x³ = x⁴. (aᵐ)ⁿ = ? Power property: (aᵐ)ⁿ = aᵐⁿ. A power of a power multiplies the exponents: (x²)³ = x⁶. a⁰ = ? Zero exponent: a⁰ = 1 for every a except 0. So 7⁰ = 1 and (−3x)⁰ = 1. a⁻ⁿ = ? Negative exponent: a⁻ⁿ = 1/aⁿ, a not 0. It makes a reciprocal, not a negative: 2⁻³ = 1/8.
Number properties 6
−2x < 6, so x is ___ than −3 Greater: x > −3. Multiplying or dividing an inequality by a negative number reverses the sign. a + 0 = a and a · 1 = a Identity property: adding 0 or multiplying by 1 changes nothing. 0 and 1 are the identities. a + b = b + a Commutative property: order does not change a sum or a product. 3 + 8 = 8 + 3, and ab = ba. (a + b) + c = a + (b + c) Associative property: grouping does not change a sum or a product. (2 + 3) + 4 = 2 + (3 + 4). a(b + c) = ? Distributive property: a(b + c) = ab + ac. Multiply every term inside: 3(x + 4) = 3x + 12. If a = b, then a + c = ? Addition property of equality: a + c = b + c. Do the same to both sides and the equation stays true.
Line formulas 8
Point-slope form Point-slope form: y − y₁ = m(x − x₁), a line with slope m through the point (x₁, y₁). Slope formula: m = ? Slope formula: m = (y₂ − y₁)/(x₂ − x₁), rise over run. From (1, 2) to (3, 8), m = 6/2 = 3. Slope of a horizontal line 0. A horizontal line y = b has no rise, so its slope is 0 divided by the run. Slope of a vertical line Undefined. A vertical line x = a has no run, and the rise cannot be divided by 0. Slope-intercept form Slope-intercept form: y = mx + b. m is the slope and (0, b) is the y-intercept. Slopes of parallel lines Equal: m₁ = m₂. Same slope, different y-intercepts: y = 2x + 1 and y = 2x − 4 never meet. Slopes of perpendicular lines m₁ · m₂ = −1: the slopes are negative reciprocals, such as 2 and −1/2. Standard form of a line Standard form: Ax + By = C, A and B not both 0. Set x = 0, then y = 0, to find the intercepts.
Quadratics and factoring 7
(a + b)² = ? Perfect square trinomial: (a + b)² = a² + 2ab + b², never a² + b². (x + 3)² = x² + 6x + 9. (a − b)² = ? Perfect square trinomial: (a − b)² = a² − 2ab + b². So (x − 5)² = x² − 10x + 25. Axis of symmetry: x = ? Axis of symmetry: x = −b/2a. The vertex of y = ax² + bx + c sits on this line. a² − b² = ? Difference of squares: a² − b² = (a + b)(a − b). So x² − 9 = (x + 3)(x − 3). The discriminant Discriminant: b² − 4ac. Positive gives 2 real solutions, zero gives 1, negative gives none. If ab = 0, then ? Zero product property: a = 0 or b = 0. So (x − 2)(x + 5) = 0 gives x = 2 or x = −5. Quadratic formula: x = ? Quadratic formula: x = (−b ± √(b² − 4ac)) / 2a solves ax² + bx + c = 0, a not 0.
One-step equations 12
Solve: 3x = 27 x = 9. Divide both sides by 3. Solve: 8x = 56 x = 7. Divide both sides by 8. Solve: x + 7 = 12 x = 5. Subtract 7 from both sides. Solve: x + 9 = 4 x = −5. Subtract 9 from both sides: 4 − 9 = −5. Solve: x + 15 = 40 x = 25. Subtract 15 from both sides. Solve: x − 4 = −10 x = −6. Add 4 to both sides: −10 + 4 = −6. Solve: x − 6 = 9 x = 15. Add 6 to both sides. Solve: x − 13 = 8 x = 21. Add 13 to both sides. Solve: x/4 = 6 x = 24. Multiply both sides by 4. Solve: x/7 = 12 x = 84. Multiply both sides by 7. Solve: x/9 = 5 x = 45. Multiply both sides by 9. Solve: −4x = −32 x = 8. Divide both sides by −4. A negative divided by a negative is positive.
Two-step equations 12
Solve: 2x + 3 = 11 x = 4. Subtract 3 (2x = 8), then divide by 2. Solve: 3x + 5 = 26 x = 7. Subtract 5 (3x = 21), then divide by 3. Solve: 4x − 7 = 21 x = 7. Add 7 (4x = 28), then divide by 4. Solve: 5x + 8 = 3 x = −1. Subtract 8 (5x = −5), then divide by 5. Solve: 6x − 9 = 45 x = 9. Add 9 (6x = 54), then divide by 6. Solve: 7x − 10 = 60 x = 10. Add 10 (7x = 70), then divide by 7. Solve: 9 − 2x = 17 x = −4. Subtract 9 (−2x = 8), then divide by −2. Solve: 20 − 3x = 5 x = 5. Subtract 20 (−3x = −15), then divide by −3. Solve: x/2 + 4 = 10 x = 12. Subtract 4 (x/2 = 6), then multiply by 2. Solve: x/3 + 7 = 12 x = 15. Subtract 7 (x/3 = 5), then multiply by 3. Solve: x/4 − 6 = −3 x = 12. Add 6 (x/4 = 3), then multiply by 4. Solve: x/5 − 2 = 4 x = 30. Add 2 (x/5 = 6), then multiply by 5.
Both sides and parentheses 12
Solve: 2(x − 7) = 12 x = 13. Divide by 2 (x − 7 = 6), then add 7. Solve: 2x + 15 = 6x − 9 x = 6. Subtract 2x (15 = 4x − 9), add 9, divide by 4. Solve: 3(x + 4) = 27 x = 5. Divide by 3 (x + 4 = 9), then subtract 4. Solve: 3x + 4x = 56 x = 8. Combine like terms (7x = 56), then divide by 7. Solve: 4(x − 3) = 2x + 6 x = 9. Distribute (4x − 12 = 2x + 6), subtract 2x, add 12, divide by 2. Solve: 5(x + 2) = 4x + 18 x = 8. Distribute (5x + 10 = 4x + 18), subtract 4x, subtract 10. Solve: 5x + 2 = 3x + 10 x = 4. Subtract 3x (2x + 2 = 10), subtract 2, divide by 2. Solve: 6x + 5 − 2x = 33 x = 7. Combine like terms (4x + 5 = 33), subtract 5, divide by 4. Solve: 7x − 4 = 4x + 11 x = 5. Subtract 4x (3x − 4 = 11), add 4, divide by 3. Solve: 8x − 5 = 3x − 20 x = −3. Subtract 3x (5x − 5 = −20), add 5, divide by 5. Solve: 9x + 6 = 5x + 30 x = 6. Subtract 5x (4x + 6 = 30), subtract 6, divide by 4. Solve: −3(x − 4) = 18 x = −2. Divide by −3 (x − 4 = −6), then add 4.
How this list was compiled: Own deck of 96 cards: 32 words, 28 rules and formulas and 36 equations to solve. The choice of cards and the examples are our own. Each definition, property and formula was checked on 2026-09-19 against the key terms and key concepts of OpenStax Elementary Algebra 2e, chapters 1, 2, 4, 5, 6, 7 and 10 (https://openstax.org/books/elementary-algebra-2e/pages/1-key-terms , https://openstax.org/books/elementary-algebra-2e/pages/1-key-concepts , https://openstax.org/books/elementary-algebra-2e/pages/2-key-concepts , https://openstax.org/books/elementary-algebra-2e/pages/4-key-terms , https://openstax.org/books/elementary-algebra-2e/pages/4-key-concepts , https://openstax.org/books/elementary-algebra-2e/pages/6-key-concepts , https://openstax.org/books/elementary-algebra-2e/pages/7-key-concepts , https://openstax.org/books/elementary-algebra-2e/pages/10-key-concepts ), and function, domain and range against OpenStax Intermediate Algebra 2e, chapter 3 (https://openstax.org/books/intermediate-algebra-2e/pages/3-key-terms ). The seven exponent laws carry the names OpenStax uses: product, quotient, power, product to a power, quotient to a power, zero exponent and negative exponent. The 36 equations were written for this deck; each answer was put back into its equation with exact fraction arithmetic, which confirmed that no other whole number from −60 to 100 also works. Licence: own work
How it works These algebra flashcards come in three kinds: 32 words such as coefficient and y-intercept, 28 rules and formulas from the exponent laws to the quadratic formula, and 36 equations to solve. Flip a card, type the answer, or print a set.
Read the full guide
Pick one of ten sets
Word cards show an example (In 5x + 3, the number 5) and the back names it: coefficient. Rules split into Exponent laws , Number properties , Line formulas and Quadratics and factoring . The solve cards climb from one-step to two-step equations, then both sides and parentheses. Three more chips gather all 32 words, all 28 rules and all 36 solves.
Print a set on one sheet
Each of the ten sets has 12 cards or fewer, so it fits one sheet of Letter or A4: fronts on one side, backs on the other with the rows mirrored. Print double-sided, flip on the long edge, and y = mx + b lands behind Slope-intercept form. All 96 take 8 sheets.
The base card hides a classic slip: −3² is −9, since the exponent belongs to 3 alone; (−3)² is 9.
Before solving, sort the 36 equation cards by first move: add, subtract, multiply, divide, distribute or combine like terms.
Six solve cards have negative answers, such as x + 9 = 4. In quiz mode, 5 is marked wrong.
Questions and answers
Are these cards for pre-algebra or Algebra 1?
Grade 6 through Algebra 1. The Common Core puts one-step equations in grade 6, two-step equations in grade 7, exponent laws and y = mx + b in grade 8, and the quadratic formula in high school. That is our reading, not an official alignment.
How do I type a formula in quiz mode?
On one line with no spaces: y=mx+b, a^(m+n), b^2-4ac. Spaced out the way the card prints it, y = mx + b passes too. Capital letters do not matter, but the minus sign does. For a solve card, type -5 or x = -5.
Which exponent rules are on the cards?
Seven: the product, quotient and power properties, product to a power, quotient to a power, the zero exponent and the negative exponent. Each back names the law and works one example, such as x² · x³ = x⁵. The names follow OpenStax Elementary Algebra.