Mental maths tips

Apogee rewards speed, so a few habits make a real difference. These are the methods that help most for the five levels of the game.

Adding and subtracting

Break numbers into tens and units. To work out 67 + 38, add the tens first (60 + 30 = 90), then the units (7 + 8 = 15), then combine: 105. For subtraction, round up and adjust. 82 − 39 is the same as 82 − 40 + 1 = 43.

Multiplying

Split one number and use what you know. 14 × 6 is 10 × 6 plus 4 × 6, which is 60 + 24 = 84. For ×9, multiply by 10 and take one lot away. For ×5, halve the number then multiply by 10. For ×11 of a two-digit number, put the digits' sum in the middle: 34 × 11 = 3 (3+4) 4 = 374.

Dividing

Think of division as a missing multiplication. 91 ÷ 7 asks what times 7 makes 91. Knowing that 7 × 13 = 91 gets you there in a moment. Learn the tables up to 12 × 12 until they are automatic.

Finding x

An equation is a balance: whatever you do to one side, do to the other. For x + 7 = 19, take 7 from both sides: x = 12. For 4x = 28, divide both sides by 4: x = 7. For x ÷ 3 = 6, multiply both sides by 3: x = 18.

Two steps

Undo the adding or subtracting first, then undo the multiplying. For 3x + 5 = 29: take 5 from both sides to get 3x = 24, then divide by 3 to get x = 8. Check by putting 8 back in: 3 × 8 + 5 = 29.

x on both sides

Collect the x terms on one side first. For 3x + 2 = x + 14, take x from both sides to get 2x + 2 = 14, then take 2 to get 2x = 12, so x = 6. With brackets, multiply them out first: 3(x + 2) = x + 14 becomes 3x + 6 = x + 14.

Speed and accuracy

A wrong guess costs 3 seconds, so a quick check in your head usually beats a rushed second try. Start each question by deciding on the method, not by typing. Practice mode is a good place to build speed before the daily flight.