Math
Mental math practice
Calculations, missing numbers, estimation and everyday problems, with worked methods and an optional timer.
10 untimed questions · 2- or 8-minute sprint
Try a practice
Math
Number properties
Explore factors, multiples and remainders with short whole-number questions.
6 questions · 3 levels · No time limit
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Percentages
Calculate percentages, changes and original values.
10 questions · 3 levels · Untimed
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Fractions and decimals
Calculate with fractions and decimals, or build targets with fraction pieces.
10 questions or a workshop · 3 levels
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Estimate and compare
Round to useful benchmarks and choose the closest of five answers.
8 questions · 3 levels · Untimed
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Compare quantities
Compare number quantities using arithmetic, fractions, percentages and powers.
9 questions · 3 levels · Untimed
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Ratios & averages
Divide amounts in a ratio and find averages across unequal groups.
8 questions · 3 modes · Untimed
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Speed & work rates
Convert time units, compare speeds and combine work rates.
8 questions · 3 modes · Untimed
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Number sequence puzzles
Find the next number, fill a grid, or untangle two sequences.
6 questions · Explanations · Optional 2-minute challenge
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Unit conversion
Convert between metric and imperial units, then check the result against an anchor.
6 questions · 3 levels · Untimed
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Find the missing number
Type the number that fills the blank in each equation.
10 items · 4 levels · A clock on each item
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Fast multiplication
Multiply two digit numbers by a method instead of long multiplication.
10 questions or a 3 minute sprint · 4 levels
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Quant interview arithmetic
Answer as many short questions as you can before the clock runs out.
10 kinds of question · Typed answers · Wrong answers cost a point
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Squares and roots
Type the square, the cube or the root from memory.
12 items · 4 levels · Untimed or a 2-minute sprint
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Times tables
Answer twenty multiplication facts, then see which ones are still slow.
20 facts · 15 sets · Optional 5 second clock
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Exam word problems
Salt water, speed, work rate and counting cases, in the shape aptitude tests ask them.
6 questions · 3 levels · Untimed
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Number bases
Read a number in one base and write it in another.
12 questions · 4 levels · Untimed or a 2-minute sprint
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Make 24
Merge four cards two at a time and make the last one 24. Fractions are allowed.
6 deals · 3 levels · Undo · Hint
Math
Number challenges
Solve number problems with hints and worked solutions. Extended rounds add digit constraints and missing digits in squares and cubes.
4 challenges · 3 levels · Worked solutions
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Algebra: Equations & inequalities
Solve equations and describe full solution sets, from linear steps to systems, quadratics and rational inequalities.
6 questions · 3 levels
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Algebraic expressions
Recognize equivalent expressions by collecting terms, factoring, using exponent rules and preserving domain restrictions.
6 questions · 3 levels
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Functions & graphs
Read graphs and reason through function composition, transformations, inverses and domains.
6 questions · 3 levels · Untimed
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Compare quantities: Variables
Prove an algebraic comparison or find allowed values that change the answer.
6 questions · 3 levels · Untimed
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Kakuro
Fill each run with different digits from 1 to 9 to make its clue total. Crossing runs share a digit.
1 puzzle · No time limit
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Shop within a budget
Compare pack sizes, quantities, and offers to build a basket that meets the brief.
3 levels · Guided practice
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Build a vector
Combine two arrows using positive, negative and fractional multipliers. Explore which targets are reachable.
3 levels · Guided practice
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Clock and calendar
Read clock faces, work out how long things take, and find days and dates on a calendar.
6 questions · 3 levels · Untimed
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Large-number arithmetic
Work through bigger calculations, one useful step at a time.
At your pace · Exact whole-number answers
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Prime or not?
Make a quick decision, then discover the factors behind each answer.
Yes or no · Every answer explained
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Reshape a calculation
Make the numbers easier while keeping the answer the same.
At your pace · Integer arithmetic
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Letter sums
Give each letter a digit and make every sum work.
3 puzzles · No timer
Learn a method
Browse lessonsPreserve the solution set
Undo operations, track signs and check restrictions when an equation becomes an inequality.
Goes with Algebra: Equations & inequalities
Simplify without losing restrictions
Choose the right identity, cancel complete factors and keep the original domain.
Goes with Algebraic expressions
Read functions and graphs
Connect inputs and outputs, combine graphs and compositions, and keep every restriction when finding a domain or inverse.
Goes with Functions & graphs
Prove a comparison or find a counterexample
Use real-solution constraints to prove a bound, then test whether equality or a counterexample changes the comparison.
Goes with Compare quantities: Variables
Use factors and remainders
See what is left after division, then find the numbers that divide exactly.
Goes with Number properties
Multiply in parts
Split a number into useful parts, then add the products.
Goes with Mental math practice
Multiply by 11 in your head
Move the two digits apart, then put their sum in the middle.
Goes with Mental math practice
Doubling and halving
Halve one factor and double the other to reach an easier pair.
Goes with Mental math practice
Find a percentage in your head
Find 10% first, then build the percentage you need from it.
Goes with Percentages
Read a number sequence from its gaps
Write the gaps between the terms, then find the rule in them.
Goes with Number sequence puzzles
Reverse a percentage change
Use the original value as 100% to work backwards from an increase or decrease.
Goes with Percentages
Make equivalent fractions
Change the number of equal parts without changing the amount.
Goes with Fractions and decimals
Convert fractions and decimals
Use decimal place value and division to keep the same exact value.
Goes with Fractions and decimals
Estimate with useful benchmarks
Use easy nearby numbers, then check which option is closest to the original value.
Goes with Estimate and compare
Compare two quantities
Write a fraction and a percentage in the same form, then compare their values.
Goes with Compare quantities
Divide in a ratio
Turn a ratio into equal parts, then find the value of one part.
Goes with Ratios & averages
Weight the average
Use group counts to combine averages without losing the totals.
Goes with Ratios & averages
Combine work rates
Add the work completed per hour to find a shared finishing time.
Goes with Speed & work rates
Convert with anchors
Keep two known pairs for each set of units, and use them to check every answer.
Goes with Unit conversion
Undo the operation
Find the missing number by doing the opposite operation to the result.
Goes with Find the missing number
Multiplication shortcuts
Split one number, multiply the parts, then add. Plus three shortcuts worth knowing.
Goes with Fast multiplication
Keep the pace
Skip what stalls you, learn the sign rules, anchor a decimal, and know the conversions by heart.
Goes with Quant interview arithmetic
Squares near round numbers
Square a number by working from the round number next to it, and estimate a root from the two nearest squares.
Goes with Squares and roots
Learn the tables
Many times-table facts repeat. Learn the patterns, then practice six useful facts.
Goes with Times tables
Set up the equation
Name the unknown, write the thing that does not change, and solve one equation.
Goes with Exam word problems
Read the places
A base is only place values. Read binary by adding the places, and read hex four binary digits at a time.
Goes with Number bases
Work back from 24
Start at 24 and ask what makes it. Try pairs of cards, then explore other groupings and fractions.
Goes with Make 24
Reconstruct from number clues
Use digit totals to find the digits, position weights to order them, and nearby powers to fill missing places.
Goes with Number challenges
Multiply around a base
Keep signed differences from 100 or 1000, multiply the base part, then add or subtract the correction.
Goes with Fast multiplication
Start where two runs cross
Learn the kakuro sums that allow only one set of digits, and how a crossing run picks the digit for the cell two runs share.
Goes with Kakuro
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