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For teachers

Create worksheets with answer key

Pick the formulas and how many questions of each, and the sheet is put together as you go. The answer key gets its own page — hand out the first and keep the second.

Choose formulas

20 questions on the sheet

How the sheet is written

Calculator

Answer key and print

On the answer key

Writing space

Figures

Paper

Contrast

What this does

With the formula printed, the sheet tests substitution. Without it, it tests whether the student knows the formula. The answer key always shows it.

With names the questions spell out what each quantity is called — Base rather than b — and the student has to find which letter in the formula the word belongs to. With names and letters the letter follows in brackets, Base (b), so that link is given.

As a story, each question becomes a short situation with plausible numbers — a cinnamon bun for $3, a bicycle wheel with a radius of 33 cm — and the reader works out which number is which quantity. Formulas that have no story are written with names.

With nothing on the sheet, what you said in the room stands — that is the ordinary sheet. Choose either and it prints at the top, beside the instruction, and travels in the link.

With the first one worked, the key shows the full working for the first question on each formula — step by step, with the sheet’s own numbers. The rest keep just the answer, so the key is still quick to mark with.

Empty room under each question to work in. 40 mm is usually enough for a question with a few steps. The sheet gets longer — that is the point.

High contrast prints all text in black and makes the lines heavier — for pupils who read faint grey text poorly, and for photocopiers that lose it.

Which sheet

What this does

The link in the address bar holds your choice. Keep it and you get exactly the same sheet again — next term, or on another computer.

Which stage

646 of 646 formulas

Arithmetic

20 questions

Algebra

Geometry

Trigonometry

Functions and graphs

Straight lines

Polynomials

Exponential change

Indices and series

Calculus

Statistics and probability

Motion

Mechanics

Electricity

Thermodynamics

Waves and optics

Modern physics

Stoichiometry

Solutions and concentration

Gas laws

Acids and bases

Interest

Borrowing and repayment

Business

Tax and VAT

Household

The body

Questions in several steps

Preview of the sheet

The print dialogue lists "Save as PDF" among the printers. Only the sheet and its answer key go on the paper — the rest of this page is left off.

Drawing the sheet …

The questions and the key come from one draw, so they cannot disagree. Every formula on the sheet also has a page here, where it calculates in whichever direction you need.

Ready-made worksheets

Sheets already put together, with their answer keys. Open one to see the questions, print it as it is, or change it here in the generator.

Lower secondary

  • Fractions: addition and subtraction

    Sixteen questions with unlike denominators, answered as fractions in lowest terms. Answer key on its own sheet.

  • Fractions: multiplication and division

    Eight products and eight quotients of fractions, answered in lowest terms. Answer key on its own sheet.

  • Percent

    Eighteen questions of three kinds: the share as a percentage, the change in percent and the price after a discount. Calculator allowed.

  • Pythagoras' theorem

    Twelve right triangles, mixed: sometimes the hypotenuse is asked for, sometimes a leg. The key works the first question step by step.

  • Area of plane figures

    Eighteen questions on four figures. Sometimes the area is asked for, sometimes a side or the height when the area is given. Quantities carry name and letter.

  • Area and circumference of a circle

    Eight areas and eight circumferences. Answers round to one decimal, so a calculator is allowed and the sheet says so.

  • Volume of solids

    Twenty questions on four solids. The volume is asked for in most; in some the volume is given and an edge or the height is asked for instead.

  • Linear equations

    Ten equations of the form ax + b = c and six with x on both sides. The answers are whole numbers, some of them negative. Writing space under each question, and the first one worked in the key.

  • Probability

    Six questions of each kind: favourable outcomes over possible ones, the chance that something does not happen, and two independent events both happening.

  • Speed, distance and time

    Twelve questions on one relation, but what is asked for changes: sometimes the speed, sometimes the distance, sometimes the time. The key works the first one.

  • Density and pressure

    Eight questions on density and eight on pressure. Each is one quantity divided by another, and in both the one asked for changes. Calculator allowed.

  • Ohm's law and electric power

    Eight questions on Ohm's law, six on power and four on energy. Voltage, current, resistance and power take turns being asked for. Calculator allowed.

  • Scale

    Twelve questions where drawing, reality and scale swap places: sometimes the scale is asked for, sometimes the real length, sometimes the length on the drawing.

  • Perimeter

    Sixteen questions on the perimeter of rectangles, squares, triangles and regular polygons. Sometimes a side is asked for when the perimeter is given.

  • Angles in triangles and polygons

    Sixteen questions on the angle sum of triangles, quadrilaterals and polygons, and on vertical angles. Mostly a missing angle is asked for.

  • Similar triangles and scale factors

    Six questions on similar triangles and ten on how area and volume change when the lengths change.

  • Negative numbers

    Sixteen questions with negative numbers: adding, subtracting, multiplying and dividing. The sign rules are what is practised.

  • Fractions, decimals and percent

    Sixteen questions on converting between fractions, decimals and percent, and on mixed numbers.

  • Proportion and ratio

    Six questions on direct proportion, six on sharing in a given ratio and four on equal fractions.

  • Surface area

    Sixteen questions on the surface area of cubes, cuboids and prisms.

  • Volume of pyramids and spheres

    Eight questions on the volume of a pyramid, four on a sphere and four on a cube. Sometimes the height or the radius is asked for.

  • Electricity cost, power and energy

    Six questions on what electricity costs, five on power and five on energy. The units change in every question. Calculator allowed.

  • Mean, median and mode

    Sixteen lists of numbers: six means, five medians and five modes. No calculator. The first one is worked.

  • GCD and LCM

    Sixteen pairs of numbers: eight greatest common divisors and eight least common multiples. No calculator. The first one is worked.

Upper secondary

  • Squares of binomials and the difference of squares

    Six questions per rule. The formulas are hidden on the sheet, so it tests whether the rules are known; the key prints them.

  • Laws of exponents

    Twenty questions across five laws, no calculator. The answer is a number rather than a power, so the laws have to be used to get there.

  • Logarithm laws

    Five questions per law, no calculator: the numbers are chosen so the logarithms come out exact and the laws are the only way to the answer.

  • Quadratic equations with the pq formula

    Eight equations of the form x² + px + q = 0, four discriminants and four with the abc formula. Writing space under each question, and the first one worked in the key.

  • Trigonometry in right triangles

    Six questions per definition. An angle and a side are given and the side beside them is asked for, to one decimal. Calculator allowed.

  • Equation of a straight line

    Eight questions on the equation of a line, asking for x, y or the intercept, and eight on the slope between two points, sometimes asking for a coordinate.

  • Percentage change and multipliers

    Six questions on the multiplier, six on the change as a percentage and six where one change follows another. Calculator allowed.

  • Simple and compound interest

    Six questions on simple interest and six on compound interest. Sometimes the interest is asked for, sometimes the capital you started with. Calculator allowed.

  • Derivatives with the differentiation rules

    Ten questions with the power rule and six with the derivative of eˣ. Each asks for the derivative at a point, so the answer can be checked as a number.

  • Forces: Newton's second law, weight, friction and springs

    Seventeen questions on force: F = ma, weight, friction and Hooke's law.

  • Work, energy and power

    Sixteen questions on work, kinetic energy, potential energy and mechanical power.

  • Arithmetic and geometric sequences

    Ten questions on terms of arithmetic and geometric sequences and six on their sums.

  • Exponential growth and half-life

    Six questions on exponential growth, six on half-life and four exponential equations. Calculator allowed.

  • Sine and cosine rule

    Six questions with the sine rule, six with the cosine rule and four on the area of a triangle with sine. Calculator allowed.

  • Radians and sectors

    Ten questions on converting between degrees and radians, three on arc length and three on sector area. Calculator allowed.

  • Distance, midpoint and perpendicular lines

    Six questions on the distance between two points, six on the midpoint and four on the slopes of perpendicular lines.

  • Moments and levers

    Eight questions on the moment of a force and eight on moment equilibrium, where a force or a lever arm is asked for.

  • Thermal expansion

    Eight questions on how much a material expands when the temperature changes and four on converting between celsius and kelvin.

  • pH value

    Six questions on the relation between pH and pOH, six on the pH of a weak acid and four on buffers. Calculator allowed.

  • Sound level in decibels

    Six questions on sound level from intensity, six from sound pressure and four on intensity as power per area. Calculator allowed.

  • Frequency, period and wave speed

    Eight questions on frequency and period, six on wave speed and four on the period of a pendulum. The first one is worked as an example. Calculator allowed.

  • Angular velocity and circular motion

    Sixteen questions: angular velocity, angular velocity from frequency, speed along the circle and centripetal acceleration. The first one is worked as an example. Calculator allowed.

  • Concentration and amount of substance

    Six questions on concentration c = n/V, four on amount of substance, three on dilution and three on mass percent. The first one is worked. Calculator allowed.

  • Factorial and binomial distribution

    Eight questions on the factorial n!, four on the mean and four on the variance of a binomial distribution. The first one is worked. Calculator allowed.

  • Efficiency

    Eight questions with efficiency worked from useful and supplied energy, and eight from power. The first one is worked. Calculator allowed.

  • pKa, pKb and buffers

    Four questions on the relation between pKa and pKb, six on the pH of a weak acid and six on buffers. The first one is worked. Calculator allowed.

  • Vectors

    Sixteen questions on the length of a vector, addition, multiplication by a scalar and the dot product. The first one is worked. Calculator allowed.

  • Acceleration and free fall

    Sixteen questions on acceleration, v² = v₀² + 2as, distance at constant acceleration and free fall. The first one is worked. Calculator allowed.

  • Quadratic functions and parabolas

    Eight questions on the vertex form and eight on the vertex and axis of symmetry from the coefficients. No calculator. The first one is worked.

  • Unit circle and trigonometric identities

    Fifteen questions on the relations in the unit circle: sin(90° − v), cos(180° − v), sin(−v), tangent as a quotient and the Pythagorean identity. Exact values, no calculator. The first one is worked.

  • Momentum, impulse and collisions

    Four questions on momentum, four on impulse and eight on collisions where momentum is conserved. The first one is worked. Calculator allowed.

  • Cones and cylinders

    Sixteen questions on the surface area of the cylinder and the volume, lateral area and surface area of the cone. The first one is worked. Calculator allowed.

  • Differentiation rules

    Four questions on each: the sum rule, the product rule, the quotient rule and the chain rule. No calculator. The first one is worked.

  • Range and standard deviation

    Sixteen lists of numbers: four ranges, six variances and six standard deviations. Calculator allowed. The first one is worked.

Worksheets without a formula

Practice sheets for arithmetic, measures and number theory that are not built from a formula. Each comes with its answer key and can be answered on screen too.

Practise these formulas on screenAll formulas