Mathematical Equations

How Mathematical Equations works

Each item is a small system of equations written with letters. Every letter stands for a whole number from 1 to 20 and there is exactly one solution. You work out the value of each letter yourself; there are no options to choose from, so guessing does not help.

Mathematical Equations is one of the three Core Module subtests of the digital TestAS: 20 items in 25 minutes. Easier items have two letters, harder ones three or four.

What the systems look like

• One letter given directly. Sometimes one equation contains a single letter, such as A + 3 = 11. Start there.
• Letters defined through each other. Equations like B = A + 4 or C = 2A let you write everything in terms of one letter.
• A linking equation. One equation combines all letters, such as A + B + C = 26. This is where you substitute.
• The 1 to 20 limit. Because every value lies between 1 and 20, you can rule out answers quickly, for example when 2A must stay below 20.

A method that works

1. Find the equation with only one letter, or the letter every other one is defined through.
2. Write the other letters in terms of that one.
3. Substitute into the equation that links them all and solve.
4. Work back to the remaining letters.
5. Check quickly: every value a whole number from 1 to 20 and every equation true.

Timing

25 minutes for 20 systems is 75 seconds each. Mental arithmetic speed matters: practise substitution until you can do two-letter systems in under 40 seconds and save time for the four-letter ones.

Common mistakes

• Sign errors when a letter is subtracted in the linking equation.
• Solving by trial and error instead of substituting.
• Not checking the 1 to 20 limit, which often catches a slip at once.
• Spending too long on one four-letter system early in the subtest.

Questions

Keep practising

• Figure Sequences
• Numerical Series
• Latin Squares
• The digital TestAS explained
• TestAS score calculator