YOUR HSPT STUDY COMPANION
HSPT Math Flashcards (Free Online: Formulas, Terms & Concepts)
HSPT Math 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.
HSPT Math 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 HSPT Math review
Lock in every key HSPT Math formula, term, and concept with a free, interactive flashcard deck covering numbers and operations, fractions and decimals, percent, ratios and proportions, exponents and roots, algebra, linear equations, quadratics, geometry, coordinate geometry, statistics and probability.
No calculator, so build your mental-math toolkit. 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.
72flashcards
12topics covered
44formula cards
Freeonline, progress saved
What These HSPT Math Flashcards Cover
This free deck collects the formulas, key terms, and concepts students use across the whole HSPT Math course, organized into 12 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 |
|---|---|---|
| Numbers & Operations | 7 cards | Integers, order of operations, factors, primes, GCF and LCM. |
| Fractions & Decimals | 5 cards | Add or subtract fractions, Multiply fractions, Divide fractions, Convert a fraction to a decimal. |
| Percent | 6 cards | Percent of a number, What percent is one number of another, Percent change, Find the original after a percent change. |
| Ratios & Proportions | 5 cards | Ratios, proportions, unit conversion, simple interest, average speed. |
| Exponents & Roots | 7 cards | Exponent rules, square roots, radicals, scientific notation. |
| Algebra | 6 cards | Equations, like terms, FOIL, factoring, the quadratic formula, inequalities. |
| Linear Equations | 6 cards | Slope between two points, Slope-intercept form, Point-slope form, Standard form of a line. |
| Quadratics | 5 cards | Quadratic formula, Discriminant & what it tells you, Vertex of a parabola y = ax squared + bx + c, Vertex form. |
| Geometry | 13 cards | Area, perimeter, volume, the Pythagorean theorem, angle rules. |
| Coordinate Geometry | 3 cards | Slope, line equations, distance and midpoint, parallel and perpendicular. |
| Statistics & Probability | 5 cards | Mean (average), Median, mode, range, Probability of an event, Probability of independent events (both). |
| Test Facts | 4 cards | Test format, question types, and calculator policy. |
Jump to a Topic
Numbers & OperationsFractions & DecimalsPercentRatios & ProportionsExponents & RootsAlgebraLinear EquationsQuadraticsGeometryCoordinate GeometryStatistics & ProbabilityTest Facts
Numbers & Operations
7 cards. Integers, real numbers, order of operations, factors and primes, GCF and LCM, and the distributive property.
Fractions & Decimals
5 cards. This topic covers Add or subtract fractions, Multiply fractions, Divide fractions, Convert a fraction to a decimal, and Convert a fraction to a percent.
Percent
6 cards. This topic covers Percent of a number, What percent is one number of another, Percent change, Find the original after a percent change, Simple interest, and Compound interest.
Ratios & Proportions
5 cards. Ratios, proportions, unit conversions, simple interest, and average speed.
Exponents & Roots
7 cards. The exponent rules, including product, quotient, power, zero, negative, and fractional exponents, plus square roots, simplifying radicals, and scientific notation.
Algebra
6 cards. Variables and expressions, solving one and two step equations, combining like terms, FOIL and special products, factoring, the quadratic formula, systems, and inequalities.
Linear Equations
6 cards. This topic covers Slope between two points, Slope-intercept form, Point-slope form, Standard form of a line, Parallel vs perpendicular slopes, and Solve a system of equations.
Quadratics
5 cards. This topic covers Quadratic formula, Discriminant & what it tells you, Vertex of a parabola y = ax squared + bx + c, Vertex form, and Zero-product property.
Geometry
13 cards. Area, perimeter, and volume formulas for common shapes, the Pythagorean theorem and triples, angle rules, and polygon interior angles.
Coordinate Geometry
3 cards. Slope, slope-intercept and point-slope form, the distance and midpoint formulas, and parallel and perpendicular lines.
Statistics & Probability
5 cards. This topic covers Mean (average), Median, mode, range, Probability of an event, Probability of independent events (both), and Mean vs median, which to use.
Test Facts
4 cards. Quick facts about the HSPT Math test, the math question types, and the calculator policy.
How to Use These HSPT Math Flashcards
1
Pick one topic
Use the topic dropdown instead of facing all 72 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.
HSPT Math for Beginners 2026: The Ultimate Step by Step Guide to Preparing for the HSPT Math Test
Recommended when a student needs more than flashcards: a step-by-step HSPT Math study path with lessons, worked examples, and practice to use alongside the deck.
- Every topic taught from the ground up, not just listed.
- Pairs naturally with these flashcards and the free practice tests.
- Great for rebuilding weak skills before a test.
Frequently Asked Questions
Are these HSPT Math flashcards free?
Yes. The HSPT Math flashcards are free to use online, and your progress is saved in your browser so the cards you mark for review come back later.
What is on the HSPT Math flashcards?
The deck covers formulas, key terms, and concepts across 12 topics, including numbers and operations, fractions and decimals, percent, ratios and proportions, exponents and roots, algebra, linear equations, quadratics, geometry, coordinate geometry, statistics and probability.
Is this a formula sheet or a flashcard deck?
It is an interactive flashcard deck built for active recall. Each card pairs the rule or definition with a short explanation, and many include a diagram, so you learn when each one applies instead of just reading a list.
Do the flashcards include diagrams?
Many cards include a worked example or a short visual explanation to make the rule concrete.
How many cards are in the HSPT Math deck?
There are 72 cards organized into 12 topics, with formula, term, and concept cards mixed in each topic.
Do these flashcards match the HSPT Math test?
Yes. The formulas, terms, and concepts are aligned to the math content HSPT Math students are expected to know. After memorizing them, practice full problems so the rules become solving skills.
How should students study these flashcards?
Pick one topic, flip each card and predict the answer, mark each card as Know it or Review again, then restudy the missed cards. After that, use worksheets or a practice test.
Explore more free review tools in our math flashcards hub.
All 105 Flashcards, Text Version
Every card from the deck above, listed as text so you can read, search, or print it without the flip player.
Numbers & Operations
| Front | Back |
|---|---|
| Order of operations (PEMDAS)? | Parentheses, Exponents, Multiply/Divide (left→right), Add/Subtract (left→right). |
| What is an integer? | Any whole number and its negative, including zero: …, −2, −1, 0, 1, 2, … |
| Prime number? | A whole number greater than 1 with exactly two factors: 1 and itself (2, 3, 5, 7, 11, …). 2 is the only even prime. |
| Rules for multiplying/dividing signed numbers? | Same signs → positive. Different signs → negative. (−)(−)=+, (−)(+)=− |
| Absolute value | x |? | The distance of x from 0 on the number line; always ≥ 0. |−7| = 7, |7| = 7. |
| Distributive property? | a(b + c) = ab + acMultiply the outside term by each term inside the parentheses. |
| LCM vs GCF? | GCF = greatest factor shared by numbers. LCM = smallest multiple shared by numbers. |
Fractions & Decimals
| Front | Back |
|---|---|
| Add or subtract fractions? | ab ± cd = ad ± bcbdGet a common denominator, then add/subtract numerators. |
| Multiply fractions? | ab × cd = acbdMultiply across; simplify. |
| Divide fractions? | ab ÷ cd = ab × dcMultiply by the reciprocal (flip the second fraction). |
| Convert a fraction to a decimal? | Divide the numerator by the denominator. 34 = 3 ÷ 4 = 0.75. |
| Convert a fraction to a percent? | Convert to a decimal, then multiply by 100. 14 = 0.25 = 25%. |
Percent
| Front | Back |
|---|---|
| Percent of a number? | part = percent × wholee.g. 20% of 80 = 0.20 × 80 = 16. |
| What percent is one number of another? | percent = partwhole × 100 |
| Percent change? | % change = new − oldold × 100Positive = increase, negative = decrease. |
| Find the original after a percent change? | Divide by the multiplier. After a 25% increase: original = new1.25. |
| Simple interest? | I = P r tP = principal, r = rate (decimal), t = time. Total = P + I. |
| Compound interest? | A = P(1 + rn)ntn = times compounded per year, t = years. |
Ratios & Proportions
| Front | Back |
|---|---|
| What is a ratio? | A comparison of two quantities, written a : b, a to b, or ab. |
| Solve a proportion? | ab = cd → ad = bcCross-multiply, then solve. |
| Unit rate? | unit rate = total amountnumber of unitse.g. miles ÷ hours = miles per hour. |
| Distance / rate / time? | d = r tso r = d/t and t = d/r. |
| Direct vs inverse variation? | Direct: y = kx (both rise together). Inverse: y = kx (one rises as the other falls). |
Exponents & Roots
| Front | Back |
|---|---|
| Product rule for exponents? | xa · xb = xa+bSame base → add exponents. |
| Quotient rule for exponents? | xaxb = xa−bSame base → subtract exponents. |
| Power of a power? | (xa)b = xabMultiply the exponents. |
| Negative exponent? | x−n = 1xnMove the base to flip the sign of the exponent. |
| Zero exponent & fractional exponent? | x0 = 1×1/n = n√xAny nonzero base to the 0 power is 1. |
| Scientific notation? | Written as a × 10n, where 1 ≤ a < 10. e.g. 47,000 = 4.7 × 104. |
| Simplify a square root? | √(ab) = √a · √bPull out perfect-square factors: √50 = √25·√2 = 5√2. |
Algebra
| Front | Back |
|---|---|
| Solve a one-variable equation? | Isolate the variable using inverse operations, doing the same thing to both sides. |
| Solving an inequality — key rule? | Solve like an equation, but flip the inequality sign when multiplying or dividing by a negative. |
| FOIL (multiply two binomials)? | (a+b)(c+d) = ac + ad + bc + bdFirst, Outer, Inner, Last. |
| Difference of squares? | a2 − b2 = (a + b)(a − b) |
| Perfect-square trinomials? | (a ± b)2 = a2 ± 2ab + b2 |
| Combine like terms? | Add/subtract terms with the same variable and exponent: 3x + 5x = 8x; 3x and 3x² are not alike. |
| Equivalent expression | Equivalent expressions have the same value for every allowed input, even when they look different. |
| Equation balance | An equation stays true when the same valid operation is performed on both sides. |
| Function input and output | A function assigns exactly one output to each allowed input. Evaluate by replacing the input variable carefully. |
| Slope as a rate of change | Slope compares vertical change with horizontal change and includes direction through its sign. |
Linear Equations
| Front | Back |
|---|---|
| Slope between two points? | m = y2 − y1x2 − x1Rise over run. |
| Slope-intercept form? | y = mx + bm = slope, b = y-intercept. |
| Point-slope form? | y − y1 = m(x − x1) |
| Standard form of a line? | Ax + By = C |
| Parallel vs perpendicular slopes? | Parallel lines: equal slopes. Perpendicular lines: slopes are negative reciprocals (m1·m2 = −1). |
| Solve a system of equations? | Use substitution or elimination. The solution (x, y) is where the two lines intersect. |
Quadratics
| Front | Back |
|---|---|
| Quadratic formula? | x = −b ± √(b2 − 4ac)2aSolves ax² + bx + c = 0. |
| Discriminant & what it tells you? | D = b2 − 4acD > 0 → 2 real roots; D = 0 → 1; D < 0 → none (real). |
| Vertex of a parabola y = ax² + bx + c? | x = −b2aPlug back in to get the y-value of the vertex. |
| Vertex form? | y = a(x − h)2 + kVertex is (h, k). |
| Zero-product property? | If (x − r)(x − s) = 0, then x = r or x = s. Used to solve factored quadratics. |
Geometry
| Front | Back |
|---|---|
| Area of a triangle? | A = 12bhb = base, h = perpendicular height. |
| Area & perimeter of a rectangle? | A = lwP = 2l + 2w |
| Area of a circle? | A = πr2 |
| Circumference of a circle? | C = 2πr = πd |
| Area of a parallelogram & trapezoid? | Parallelogram: A = bhTrapezoid: A = 12(b1 + b2)h |
| Pythagorean theorem? | a2 + b2 = c2Right triangles only; c = hypotenuse. |
| Volume of a rectangular prism (box)? | V = lwh |
| Volume of a cylinder? | V = πr2h |
| Volume of a cone & sphere? | Cone: V = 13πr2hSphere: V = 43πr3 |
| Volume of a pyramid? | V = 13(base area)(height) |
| Angles in a triangle & on a line? | Triangle interior angles sum to 180°. Angles on a straight line sum to 180°. Around a point: 360°. |
| Complementary vs supplementary angles? | Complementary add to 90°. Supplementary add to 180°. |
| Sum of interior angles of a polygon? | (n − 2) × 180°n = number of sides. |
| Draw and label | Sketch the figure, label known measurements and the unknown, and mark equal or perpendicular parts before selecting a formula. |
| Area versus perimeter | Perimeter measures boundary length in linear units; area measures covered surface in square units. |
| Scale-factor effect | If every length is multiplied by k, perimeter scales by k, area by k squared, and volume by k cubed. |
Coordinate Geometry
| Front | Back |
|---|---|
| Distance between two points? | d = √[(x2−x1)2 + (y2−y1)2] |
| Midpoint of a segment? | (x1+x22, y1+y22) |
| Equation of a circle (center (h,k), radius r)? | (x − h)2 + (y − k)2 = r2 |
Statistics & Probability
| Front | Back |
|---|---|
| Mean (average)? | mean = sum of valuesnumber of values |
| Median, mode, range? | Median = middle value (ordered). Mode = most frequent. Range = max − min. |
| Probability of an event? | P = favorable outcomestotal outcomesAlways between 0 and 1. |
| Probability of independent events (both)? | P(A and B) = P(A) × P(B) |
| Mean vs median — which to use? | Median resists outliers; mean is pulled toward extreme values. Skewed data → median is often more representative. |
Test Facts
| Front | Back |
|---|---|
| How is HSPT math structured? | Mathematics: 64 questions in 45 minutes. Quantitative Skills: 52 questions in 30 minutes. |
| Is a calculator allowed on the HSPT? | No. Calculators are not permitted (unless an approved accommodation applies). |
| What does HSPT math cover? | Arithmetic, basic algebra, and geometry, plus number-series and reasoning items in Quantitative Skills. |
| How is the HSPT scored? | As scaled scores and percentile ranks used by high schools for admissions and placement. |
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. |
| Read every label | For a table, graph, diagram, or formula, identify the title, variables, units, scale, and restrictions before calculating. |
| Find the hidden constraint | Check for limits such as positive length, nonzero denominator, integer count, defined radical, or realistic time. |
| Explain the deciding step | After solving, state why the method fits. A short explanation reveals whether the answer came from understanding or a lucky pattern. |
Number Sense
| Front | Back |
|---|---|
| Percent as a multiplier | An increase of r% multiplies by 1+r/100; a decrease multiplies by 1-r/100. Repeated changes use repeated multiplication. |
| Ratio as a relationship | A ratio compares quantities in a stated order. Equivalent ratios scale both terms by the same nonzero factor. |
| Rate and unit rate | A rate compares quantities with different units. Divide to find the amount for one unit, then scale as needed. |
| Order of operations | Work through grouping, exponents, multiplication or division left to right, then addition or subtraction left to right. |
| Negative-number sense | A negative sign may describe direction, loss, or a value below zero. Interpret the context before applying sign rules. |
Data
| Front | Back |
|---|---|
| Center versus spread | A measure of center describes a typical location; a measure of spread describes how far values vary around it. |
| Correlation is not causation | A pattern between two variables does not by itself prove that changing one variable causes the other to change. |
| Outlier influence | An extreme value can pull the mean strongly while often changing the median less. Choose a summary that fits the distribution. |
Test Strategy
| Front | Back |
|---|---|
| Review guesses as well as misses | A correct guess can hide the same weakness as a missed question. Review every answer you could not fully justify. |
| Use a two-pass approach | Answer clear questions first, mark slower items, and return with the remaining time and a calmer view. |
| Reread the actual question | Before choosing, identify exactly what is requested: a value, expression, reason, comparison, or best estimate. |
| Verify in the original problem | Substitute or interpret the result in the original statement, not only in a transformed equation. |
| Keep an error log | For each miss, record the topic, the deciding idea, the error type, and one action that would prevent the same mistake. |
Foundations
| Front | Back |
|---|---|
| Study decision 1: Name the goal | State what the question asks for before choosing a formula or operation. |
| Study decision 2: List what is known | Write the given values, relationships, and units so no condition is lost. |
| Study decision 3: Define the unknown | Use a symbol or clear phrase for the quantity you must find. |
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