OAE Mathematics Flashcards
OAE Mathematics Flashcards: a free, printable set covering the topics you will see on the test, with answer keys included, so you can practice each topic one skill at a time and check your own work before test day.
Free OAE Mathematics review
Lock in every key OAE Mathematics formula, term, and concept with a free, interactive flashcard deck covering number theory, algebra and functions, exponential and logarithmic, trigonometry, analytic geometry, sequences and discrete, calculus: derivatives, calculus: integrals, probability and statistics, linear algebra and matrices.
Each card shows the rule or definition, a short explanation, and many include a quick diagram. Flip a card, filter by topic or card type, shuffle, and mark what you know so the cards you miss come back for review.
95flashcards
11topics covered
13cards with a diagram
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What These OAE Mathematics Flashcards Cover
This free deck collects the formulas, key terms, and concepts students use across the whole OAE Mathematics course, organized into 11 topics. Use the dropdown to study one topic at a time, or shuffle the full deck for mixed review before a test.
| Topic | Cards | What students review |
|---|---|---|
| Number Theory | 9 cards | Prime number, Fundamental theorem of arithmetic, GCD and LCM relationship, Modular arithmetic. |
| Algebra & Functions | 12 cards | Function, Domain and range, Function composition, Inverse function. |
| Exponential & Logarithmic | 6 cards | Exponent laws, Definition of a logarithm, Logarithm properties, Change of base. |
| Trigonometry | 10 cards | Sine, cosine, tangent, the unit circle, special triangles. |
| Analytic Geometry | 8 cards | Distance formula, Midpoint formula, Slope and line forms, Equation of a circle. |
| Sequences & Discrete | 8 cards | Arithmetic sequence, Arithmetic series, Geometric sequence, Geometric series. |
| Calculus: Derivatives | 12 cards | Limit, Continuity, Definition of the derivative, Power rule. |
| Calculus: Integrals | 8 cards | Power rule for integration, Definite integral, Fundamental theorem of calculus, Common antiderivatives. |
| Probability & Statistics | 10 cards | Measures of center, Spread: range, variance, SD, Probability of an event, Addition rule. |
| Linear Algebra & Matrices | 8 cards | Matrix addition and scalar multiples, Matrix multiplication, Identity matrix, Determinant of a 2×2. |
| Test Facts | 4 cards | Test format, question types, and calculator policy. |
Jump to a Topic
Number TheoryAlgebra & FunctionsExponential & LogarithmicTrigonometryAnalytic GeometrySequences & DiscreteCalculus: DerivativesCalculus: IntegralsProbability & StatisticsLinear Algebra & MatricesTest Facts
Number Theory
9 cards. This topic covers Prime number, Fundamental theorem of arithmetic, GCD and LCM relationship, Modular arithmetic, Rational vs. irrational, and Imaginary unit.
Algebra & Functions
12 cards. This topic covers Function, Domain and range, Function composition, Inverse function, Quadratic formula, and Discriminant.
Exponential & Logarithmic
6 cards. This topic covers Exponent laws, Definition of a logarithm, Logarithm properties, Change of base, Exponential growth and decay, and The number e.
Trigonometry
10 cards. The sine, cosine, and tangent ratios, the unit circle, special right triangles, and basic trig identities.
Analytic Geometry
8 cards. This topic covers Distance formula, Midpoint formula, Slope and line forms, Equation of a circle, Parabola, and Ellipse and hyperbola.
Sequences & Discrete
8 cards. This topic covers Arithmetic sequence, Arithmetic series, Geometric sequence, Geometric series, Binomial theorem, and Permutations.
Calculus: Derivatives
12 cards. This topic covers Limit, Continuity, Definition of the derivative, Power rule, Product rule, and Quotient rule.
Calculus: Integrals
8 cards. This topic covers Power rule for integration, Definite integral, Fundamental theorem of calculus, Common antiderivatives, u-substitution, and Area between curves.
Probability & Statistics
10 cards. This topic covers Measures of center, Spread: range, variance, SD, Probability of an event, Addition rule, Multiplication rule, and Conditional probability.
Linear Algebra & Matrices
8 cards. This topic covers Matrix addition and scalar multiples, Matrix multiplication, Identity matrix, Determinant of a 2×2, Inverse of a 2×2, and Solving systems with matrices.
Test Facts
4 cards. Quick facts about the OAE Mathematics test, the math question types, and the calculator policy.
How to Use These OAE Mathematics Flashcards
1
Pick one topic
Use the topic dropdown instead of facing all 95 cards at once. Start with the topics you find hardest.
2
Flip, then mark
Read the front, say the rule or definition out loud, then flip. Mark Know it only when you can explain it, not just recognize it.
3
Practice right away
After a set, solve a few problems that use those rules. Flashcards build recall; worked practice turns them into test-day tools.
Best Order for Studying
If the deck feels like a lot, study the foundational topics first, such as numbers, fractions and percents, and exponents, then move on to algebra, geometry, and data, and review the test facts last. This moves from the skills every other topic builds on to the ones that appear in specific problem types.
Most Important Formulas and Facts to Know First
- Order of operations: the sequence that keeps every calculation consistent.
- Exponent rules: product, quotient, power, zero, and negative exponents.
- Fraction operations: and converting between fractions, decimals, and percents.
- Percent of a number and percent of change: the backbone of word problems.
- Slope and slope-intercept form: for reading and writing linear graphs.
- Area, perimeter, and volume: the core geometry formulas.
- The Pythagorean theorem: for right triangles and distance.
- Factoring and the quadratic formula: for solving quadratics.
- Mean, median, mode, and range: the four measures that summarize data.
- Probability of an event: favorable outcomes over total outcomes.
Common Mistakes These Cards Help Fix
- Ignoring order of operations and simply working left to right.
- Adding or subtracting fractions without a common denominator.
- Confusing area with perimeter, or surface area with volume.
- Flipping an inequality sign at the wrong time, instead of only when multiplying or dividing by a negative.
- Mixing up mean, median, and mode.
- Treating a negative exponent as a negative number instead of a reciprocal.
- Applying the Pythagorean theorem to triangles that are not right triangles.
Frequently Asked Questions
How do you use math flashcards effectively?
Use math flashcards effectively by saying the answer out loud or writing it down before you flip, so you practice real recall instead of just recognizing it. With the OAE Mathematics deck, filter to one topic, such as exponent laws, mark each card, and come back to the review pile the next day. Ten focused minutes daily beats a weekend cram.
How do you make math flashcards?
Make math flashcards by writing a prompt on the front, like “midpoint formula,” and the answer on the back: ((x₁ + x₂)/2, (y₁ + y₂)/2), plus one worked example. Keep cards short and focused on a single idea. If you are reviewing for the OAE, add cards for any formula you missed on a practice test, since those gaps matter most.
Can you make flashcards online?
Yes, you can make or use flashcards online, which makes shuffling and tracking progress easy. The OAE Mathematics deck already covers 95 cards across 11 topics, from number theory to linear algebra, so you can start studying right away. Your marks are saved in your browser, which means the cards you flag for review come back on your next visit.
Are there free math flashcards online?
Yes, free math flashcards are available online, including this OAE Mathematics deck, which costs nothing to use. It mixes formula, term and concept cards, and 13 of them include a diagram such as a coordinate grid or right triangle. Pair the cards with free practice problems so you can apply each rule, not just memorize it.
What are the uses of flashcards?
Flashcards are used to memorize facts, formulas and vocabulary through quick, repeated recall. In math they are especially useful for rules you must know cold, like the change of base formula, logₐx = log x ÷ log a, or the equation of a circle, (x − h)² + (y − k)² = r². For the OAE, they free up test time for harder reasoning questions.
All 102 Flashcards, Text Version
Every card from the deck above, listed as text so you can read, search, or print it without the flip player.
Number Theory
| Front | Back |
|---|---|
| Prime number | A whole number greater than 1 whose only factors are 1 and itself: 2, 3, 5, 7, 11, 13, … |
| Fundamental theorem of arithmetic | Every integer greater than 1 has a unique prime factorization (apart from order). Example: 60 = 2² · 3 · 5. |
| GCD and LCM relationship | For positive integers a and b: GCD(a,b) · LCM(a,b) = a · b. |
| Modular arithmetic | a ≡ b (mod n) means n divides (a − b); a and b have the same remainder when divided by n. Example: 17 ≡ 2 (mod 5). |
| Rational vs. irrational | Rational = a ratio p/q of integers (q ≠ 0), with a terminating or repeating decimal. Irrational = nonrepeating, nonterminating: √2, π, e. |
| Imaginary unit | i = √(−1), so i² = −1. A complex number is a + bi with real part a and imaginary part b. i⁴ⁿ = 1 cycles every 4 powers. |
| Absolute value | |x| is the distance from 0: |x| = x if x ≥ 0, and −x if x < 0. |a − b| is the distance between a and b. |
| Mathematical induction | Prove a statement for all n ≥ 1 by (1) base case n = 1 and (2) assuming it holds for n = k and proving it for n = k + 1. |
| Divisibility tests | ÷3 if the digit sum is divisible by 3; ÷9 if the digit sum is divisible by 9; ÷4 if the last two digits are; ÷8 if the last three digits are. |
Algebra & Functions
| Front | Back |
|---|---|
| Function | A rule pairing each input with exactly one output. A graph is a function if it passes the vertical line test. |
| Domain and range | Domain = all allowed inputs (x). Range = all resulting outputs (y). Exclude inputs that make a denominator 0 or a square root negative. |
| Function composition | (f ∘ g)(x) = f(g(x)): apply g first, then f. In general f(g(x)) ≠ g(f(x)). |
| Inverse function | f⁻¹ undoes f: f(f⁻¹(x)) = x. Find it by swapping x and y and solving for y. Its graph reflects f over the line y = x. |
| Quadratic formula | For ax² + bx + c = 0: x = (−b ± √(b² − 4ac)) / (2a). |
| Discriminant | D = b² − 4ac. D > 0: two real roots. D = 0: one real (double) root. D < 0: two complex roots. |
| Sum and product of roots | For ax² + bx + c = 0: sum of roots = −b/a, product of roots = c/a. |
| Difference and sum of cubes | a³ − b³ = (a − b)(a² + ab + b²); a³ + b³ = (a + b)(a² − ab + b²). |
| Rational function asymptotes | Vertical asymptote where the denominator = 0 (and numerator ≠ 0). Horizontal asymptote from comparing degrees of numerator and denominator. |
| Graph transformations | f(x) + k shifts up k; f(x − h) shifts right h; −f(x) reflects over the x-axis; a·f(x) stretches vertically by a. |
| Solving inequalities | Solve like an equation, but reverse the inequality sign when multiplying or dividing both sides by a negative number. |
| Polynomial end behavior | Set by the leading term. Even degree: both ends go the same way. Odd degree: ends go opposite ways. Positive leading coefficient: right end rises. |
Exponential & Logarithmic
| Front | Back |
|---|---|
| Exponent laws | xᵃ · xᵇ = xᵃ⁺ᵇ; xᵃ ÷ xᵇ = xᵃ⁻ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁻ᵃ = 1/xᵃ; x^(1/n) = ⁿ√x; x⁰ = 1. |
| Definition of a logarithm | log_b(x) = y means bʸ = x. A logarithm is the inverse of an exponential. |
| Logarithm properties | log(xy) = log x + log y; log(x/y) = log x − log y; log(xⁿ) = n·log x. |
| Change of base | log_b(x) = ln(x) / ln(b) = log(x) / log(b). |
| Exponential growth and decay | A = A₀·eᵏᵗ. Growth when k > 0, decay when k < 0. Compound interest: A = P(1 + r/n)ⁿᵗ. |
| The number e | e ≈ 2.718, the base of natural logarithms. ln x = log_e x, and d/dx eˣ = eˣ. |
Trigonometry
| Front | Back |
|---|---|
| SOH CAH TOA | In a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. |
| Radian measure | π radians = 180°. To convert: radians = degrees · π/180. Arc length s = rθ (θ in radians). |
| Pythagorean identity | sin²θ + cos²θ = 1. Dividing gives 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ. |
| Reciprocal identities | csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ, tan θ = sin θ/cos θ. |
| Sum and difference formulas | sin(A ± B) = sin A cos B ± cos A sin B; cos(A ± B) = cos A cos B ∓ sin A sin B. |
| Double-angle formulas | sin 2θ = 2 sin θ cos θ; cos 2θ = cos²θ − sin²θ = 2cos²θ − 1 = 1 − 2sin²θ. |
| Law of sines | a/sin A = b/sin B = c/sin C. Use when you know two angles and a side, or two sides and a non-included angle. |
| Law of cosines | c² = a² + b² − 2ab·cos C. Use with two sides and the included angle, or all three sides. |
| Unit circle | Circle of radius 1; a point at angle θ is (cos θ, sin θ). Key angles 0, π/6, π/4, π/3, π/2 give the standard sine and cosine values. |
| Inverse trig functions | sin⁻¹, cos⁻¹, tan⁻¹ return the angle with a given ratio, on restricted ranges so each output is unique. |
Analytic Geometry
| Front | Back |
|---|---|
| Distance formula | d = √((x₂ − x₁)² + (y₂ − y₁)²). It comes from the Pythagorean theorem. |
| Midpoint formula | M = ((x₁ + x₂)/2, (y₁ + y₂)/2). |
| Slope and line forms | Slope m = (y₂ − y₁)/(x₂ − x₁). Slope-intercept: y = mx + b. Point-slope: y − y₁ = m(x − x₁). Standard: Ax + By = C. |
| Equation of a circle | (x − h)² + (y − k)² = r², center (h, k), radius r. |
| Parabola | y = a(x − h)² + k has vertex (h, k). Opens up if a > 0, down if a < 0. |
| Ellipse and hyperbola | Ellipse: (x−h)²/a² + (y−k)²/b² = 1. Hyperbola: (x−h)²/a² − (y−k)²/b² = 1, asymptote slopes ±b/a. |
| Vector magnitude | For v = ⟨x, y⟩, |v| = √(x² + y²). Add vectors componentwise. |
| Dot product | a · b = a₁b₁ + a₂b₂ = |a||b|cos θ. The vectors are perpendicular when a · b = 0. |
Sequences & Discrete
| Front | Back |
|---|---|
| Arithmetic sequence | Common difference d. nth term: aₙ = a₁ + (n − 1)d. |
| Arithmetic series | Sum of n terms: Sₙ = (n/2)(a₁ + aₙ) = (n/2)(2a₁ + (n − 1)d). |
| Geometric sequence | Common ratio r. nth term: aₙ = a₁·r^(n−1). |
| Geometric series | Finite: Sₙ = a₁(1 − rⁿ)/(1 − r). Infinite (|r| < 1): S = a₁/(1 − r). |
| Binomial theorem | (a + b)ⁿ = Σ_{k=0}^{n} C(n,k) a^(n−k) bᵏ, where C(n,k) are the binomial coefficients. |
| Permutations | Ordered arrangements: nPr = n! / (n − r)!. |
| Combinations | Unordered selections: nCr = n! / (r!(n − r)!). |
| Sets and logic | Union A ∪ B = in either set; intersection A ∩ B = in both. Contrapositive of ‘if p then q’ is ‘if not q then not p’ (logically equivalent). |
Calculus: Derivatives
| Front | Back |
|---|---|
| Limit | lim_{x→a} f(x) = L means f(x) gets arbitrarily close to L as x approaches a. The limit can exist even if f(a) is undefined. |
| Continuity | f is continuous at a if f(a) is defined, the limit exists, and lim_{x→a} f(x) = f(a) — no breaks, holes, or jumps. |
| Definition of the derivative | f′(x) = lim_{h→0} [f(x + h) − f(x)] / h. It gives the slope of the tangent line and the instantaneous rate of change. |
| Power rule | d/dx (xⁿ) = n·x^(n−1). Example: d/dx (x³) = 3x². |
| Product rule | (f·g)′ = f′·g + f·g′. |
| Quotient rule | (f/g)′ = (f′·g − f·g′) / g². |
| Chain rule | d/dx f(g(x)) = f′(g(x))·g′(x). Differentiate the outside, then multiply by the derivative of the inside. |
| Derivatives of trig functions | d/dx sin x = cos x; d/dx cos x = −sin x; d/dx tan x = sec²x. |
| Derivatives of eˣ and ln x | d/dx eˣ = eˣ; d/dx ln x = 1/x; d/dx aˣ = aˣ·ln a. |
| Critical points and extrema | Critical points occur where f′(x) = 0 or is undefined. f′ changing + to − marks a local maximum; − to + a local minimum. |
| Second derivative and concavity | f″ > 0: concave up (cup); f″ < 0: concave down (cap). An inflection point is where concavity changes. |
| Mean value theorem | If f is continuous on [a, b] and differentiable on (a, b), some c has f′(c) = (f(b) − f(a))/(b − a). |
Calculus: Integrals
| Front | Back |
|---|---|
| Power rule for integration | ∫ xⁿ dx = x^(n+1)/(n + 1) + C, for n ≠ −1. Always add the constant C for indefinite integrals. |
| Definite integral | ∫_a^b f(x) dx is the signed area between the curve and the x-axis from a to b. |
| Fundamental theorem of calculus | ∫_a^b f(x) dx = F(b) − F(a), where F is an antiderivative of f. Differentiation and integration are inverse processes. |
| Common antiderivatives | ∫ (1/x) dx = ln|x| + C; ∫ eˣ dx = eˣ + C; ∫ cos x dx = sin x + C; ∫ sin x dx = −cos x + C. |
| u-substitution | Reverse of the chain rule: let u = inside function, du = u′ dx, rewrite the integral in u, integrate, then substitute back. |
| Area between curves | A = ∫_a^b [top(x) − bottom(x)] dx over the interval where they overlap. |
| Volume of revolution (disks) | Rotating about the x-axis: V = π ∫_a^b [R(x)]² dx, where R(x) is the radius at x. |
| Average value of a function | The average value of f on [a, b] is (1/(b − a)) ∫_a^b f(x) dx. |
Probability & Statistics
| Front | Back |
|---|---|
| Measures of center | Mean = sum ÷ count. Median = middle value (ordered). Mode = most frequent value. |
| Spread: range, variance, SD | Range = max − min. Variance = average of squared deviations from the mean. Standard deviation σ = √variance. |
| Probability of an event | P(E) = favorable outcomes / total equally likely outcomes, a value from 0 to 1. |
| Addition rule | P(A ∪ B) = P(A) + P(B) − P(A ∩ B). For mutually exclusive events, P(A ∩ B) = 0. |
| Multiplication rule | P(A ∩ B) = P(A)·P(B | A). If A and B are independent, P(A ∩ B) = P(A)·P(B). |
| Conditional probability | P(A | B) = P(A ∩ B) / P(B). |
| Expected value | E(X) = Σ x·P(x): multiply each outcome by its probability and add. |
| Normal distribution (empirical rule) | Bell-shaped and symmetric: about 68% of data lie within 1 SD of the mean, 95% within 2 SD, 99.7% within 3 SD. |
| z-score | z = (x − μ) / σ: how many standard deviations a value is from the mean. |
| Correlation vs. causation | A correlation coefficient r (from −1 to 1) measures linear association. Correlation alone does not prove that one variable causes the other. |
Linear Algebra & Matrices
| Front | Back |
|---|---|
| Matrix addition and scalar multiples | Add matrices of the same size entry by entry. Multiply by a scalar by multiplying every entry. |
| Matrix multiplication | (AB) is defined when A is m×n and B is n×p; entry (i,j) is the dot product of row i of A with column j of B. AB ≠ BA in general. |
| Identity matrix | I has 1’s on the main diagonal and 0’s elsewhere. AI = IA = A. |
| Determinant of a 2×2 | For [[a, b],[c, d]], det = ad − bc. The matrix is invertible exactly when det ≠ 0. |
| Inverse of a 2×2 | [[a,b],[c,d]]⁻¹ = (1/(ad − bc)) · [[d, −b],[−c, a]], when ad − bc ≠ 0. |
| Solving systems with matrices | Write Ax = b. Solve by Gaussian elimination on the augmented matrix, by x = A⁻¹b, or by Cramer’s rule using determinants. |
| Determinant of a 3×3 | Expand along a row using cofactors: alternate + and − signs, each times the 2×2 minor formed by deleting that entry’s row and column. |
| Vectors and linear combinations | A vector has magnitude and direction. A linear combination is c₁v₁ + c₂v₂ + …; the span is all such combinations. |
Test Facts
| Front | Back |
|---|---|
| What is the OAE Mathematics (027)? | OAE Mathematics (027) is the content assessment for Integrated Mathematics, grades 7–12, in Ohio. Middle Grades Mathematics is a separate assessment (030). |
| How many questions and how long? | 150 multiple-choice questions with 4 hours and 15 minutes of testing time. The test-center appointment is 4 hours and 30 minutes; online proctoring adds an optional 15-minute break for a 4-hour-and-45-minute appointment. |
| What score do you need? | You need a scaled score of at least 220 to pass. |
| Calculator and format | An on-screen scientific calculator and a formulas page are provided. Computer-based testing and online proctoring are available; the passing score is 220. |
Reasoning
| Front | Back |
|---|---|
| Estimate before calculating | Predict the size and sign of an answer first. The estimate helps catch a misplaced decimal, wrong operation, or impossible result. |
| Check with an inverse operation | Undo the operation when possible: addition with subtraction, multiplication with division, and squaring with a square root plus a sign check. |
| Use units as evidence | Carry units through the work. A final unit that does not match the question often reveals an incorrect setup. |
| Translate one phrase at a time | Name the unknown, translate each relationship, and only then combine the pieces into an equation or expression. |
| Test a simple case | Use an easy valid number to check whether a rule or algebraic statement behaves the way you expect. |
| Eliminate impossible choices | Reject answers with the wrong sign, scale, unit, domain, or relationship before doing detailed arithmetic. |
| Distinguish exact and approximate | Keep exact forms such as fractions and radicals during the work; round only when the question or context requires it. |
Explore more free review tools in our math flashcards hub.
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