Maths

Quantitative aptitude from arithmetic through to data interpretation, worked step by step.

1Number System: Place Value, Divisibility, Unit Digits and RemaindersLearn the place value of a digit and the family of numbers it belongs to, the divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 11, how to find the smallest number to add or subtract to make a number divisible, how to read the unit digit of a large power from its cycle, how to find a remainder for a big power or a shared divisor, and how to count the multiples in a range, through six worked examples and a revision block.
2HCF and LCM: Prime Factors, the Product Rule and Lining Numbers UpLearn to find the HCF and LCM of numbers by prime factorisation, use the rule that HCF times LCM equals the product of two numbers, count how many pairs share a given HCF and product, handle numbers given as a ratio, find the smallest number that leaves a fixed remainder, and work out when repeating events next happen together, through six worked examples and a revision table.
3Fractions, Decimals and Percentages: Convert and CompareLearn to change a fraction into a decimal or a percentage and back, turn a recurring decimal into a fraction, compare fractions quickly, and add, subtract, multiply and divide fractions and mixed numbers, through six worked examples and a revision table.
4Simplification: A Lesson on BODMAS, 'of' and Fast ApproximationLearn to simplify a long numerical expression in the right order using BODMAS, handle 'of' and brackets correctly, combine fractions and percentages, and use approximation to answer "find the approximate value" questions quickly. Worked step by step in the exam's simplification and approximation styles, with the squares and roots worth memorising and the mistakes to avoid.
5Percentage: Find, Compare, Increase, Decrease and Work BackwardsLearn to find a percentage of a number, write one amount as a percentage of another, work out a percentage increase or decrease from the right starting value, combine two changes in a row, and find the original value after a change, through six worked examples and a revision block.
6Ratio and Proportion: Simplify, Share, Join Ratios and Find a Missing TermLearn what a ratio such as 2 : 3 means, write a ratio in its simplest form even with fractions, decimals or different units, share an amount in a given ratio, join two ratios into one, find a fourth, third or mean proportional, and solve questions where a ratio changes, through six worked examples and a revision block.
7Average: Find It, Work Backwards, and Combine Groups the Right WayLearn that the average is the total divided by how many, find the total back from the average, use the first-plus-last shortcut for evenly spaced numbers, see how adding, removing or replacing a value shifts the average, correct a wrongly recorded number, and combine two groups with the weighted average instead of the plain mean, through six worked examples and a revision block.
8Profit, Loss and Discount: Cost Price, Selling Price and Marked PriceLearn to work out a profit or loss as a percentage of the cost price, find the selling price from the cost price and the cost price from the selling price, use a marked price with one or more discounts, combine a markup with a discount, and handle two sales together, through six worked examples and a revision block.
9Simple and Compound Interest: Find the Interest, Amount, Rate and TimeLearn what principal, rate, time, interest and amount mean, find simple interest and rearrange the formula to get the rate, time or principal, work out compound interest year by year and with the formula, handle interest compounded half-yearly, use the shortcut for the gap between compound and simple interest, and solve an everyday loan question, through six worked examples and a revision block.
10Partnership: A Lesson on Sharing Profit by Capital and TimeLearn how partners share a profit — in the ratio of each person's capital when they invest for the same time, and in the ratio of capital multiplied by time when the periods differ. Covers simple and compound partnership, three partners, and a working partner's salary, worked step by step in the exam's profit-sharing style, with the mistakes to avoid.
11Time and Work: Working Together, the LCM Units Method and Men-DaysLearn to turn "finishes in n days" into a daily share of the work, add the shares when people work together, find one person's time from the pair, use the quicker LCM units method, solve men-days questions where the number of workers or hours changes, handle work that starts and stops partway, and fill a tank with an inlet and an outlet, through six worked examples and a revision block.
12Time, Speed and Distance: Trains, Average Speed and Boats in StreamsLearn the one relation speed = distance ÷ time and its three forms, change km/h to m/s and back with the ×5/18 and ×18/5 factors, use relative speed for trains and walkers, add a train's own length when it crosses a platform, find the right average speed over equal distances (not the plain mean), and handle boats going downstream and upstream, through six worked examples and a revision block.
13Algebra: The Standard Identities, Factorising and Solving EquationsLearn the square identities for (a + b)² and (a − b)², the difference of two squares, the cubes and the sum and difference of cubes, the a + 1/a family that turns one given value into a² + 1/a² and a³ + 1/a³, how to factorise and simplify, how to evaluate an expression by substitution or by spotting an identity, and how to solve a linear equation, a pair of equations and a quadratic, through six worked examples and a revision block.
14Geometry: A Lesson on Triangles, Circles and Their Angle RulesLearn the geometry the exam actually tests — the angle rules of a triangle, the Pythagoras theorem and its common triples, similar triangles and the basic proportionality theorem, the centroid's two-to-one split, and the circle theorems for angles, semicircles, cyclic quadrilaterals and tangents. Worked step by step with the figures the exam reuses and the mistakes to avoid.
15Mensuration: Area, Perimeter, Surface Area and VolumeLearn the perimeter and area of the rectangle, square, triangle, parallelogram, rhombus, trapezium and circle, how to work backwards from a perimeter, diagonal or area, the surface area and volume of the cube, cuboid, cylinder, cone, sphere and hemisphere, and how to answer a cutting-up or cost word problem, through six worked examples and a revision block.
16Trigonometry: A Lesson on Ratios, the Standard Table and IdentitiesLearn the six trigonometric ratios, the standard-angle table for 0, 30, 45, 60 and 90 degrees, the three Pythagorean identities, the complementary-angle rule, and how to use the tangent ratio in height-and-distance questions. Worked step by step with the values the exam expects on sight and the mistakes to avoid.
17Mixture and Alligation: A Lesson on the Rule and ReplacementLearn the rule of alligation — the ratio in which two things at different prices or strengths are mixed to reach a given mean is (dearer minus mean) to (mean minus cheaper) — and the repeated-replacement formula for a quantity removed and topped up with water. Worked step by step in the exam's mixture style, with milk-and-water problems and the mistakes to avoid.
18Data Interpretation: Reading Tables and Answering FastLearn to read a value straight off a data table, add up row and column totals, find a row or column average, write one cell as a percentage of its total, work out a percentage change on the right base, say by what percent one cell is more or less than another, and reduce the ratio of two cells, through fully worked tables and a revision block.
19Statistics and Probability: Mean, Median, Mode and Basic ChanceLearn the three measures of central tendency — the mean, the median and the mode — for both raw and grouped data, the range, the empirical relation between them, and the basics of probability as favourable outcomes over total outcomes for coins, dice and cards. Worked step by step with the exam's data sets and the mistakes to avoid.