Algebra, Year 7: formulae, sequences and coordinates

20 cm

HintDeal with the bracket before you double.

The why7 + 3 = 10, and 2 × 10 = 20. The answer is a length, so its unit is centimetres, not square centimetres.

15 cm²

HintMultiply the two lengths, then halve.

The why6 × 5 = 30, and half of 30 is 15. Two lengths have been multiplied, so the unit is square centimetres.

17

HintDo the multiplying before the adding.

The why2m means 2 × m, so 2 × 7 = 14, and 3 + 14 = 17. The 3 is a fixed charge that is paid once.

The length and the width

HintThey are the two different side measurements.

The whyA formula is a rule written with letters. Each letter stands for a quantity, and you can only use the formula if you know what each one means.

12 km/h

HintThe unit comes from the two units you divided.

The why36 ÷ 3 = 12. Kilometres divided by hours gives kilometres per hour, so the formula tells you the unit as well as the number.

31

HintReplace n with the position number.

The why3 × 10 + 1 = 31. A position rule lets you jump straight to any term without listing the ones before it.

7, 9, 11

HintUse n = 1, then 2, then 3.

The why2 × 1 + 5 = 7, 2 × 2 + 5 = 9 and 2 × 3 + 5 = 11. The terms go up in 2s because n is multiplied by 2.

Add 7

HintSubtract any term from the one after it.

The why11 − 4 = 7, 18 − 11 = 7 and 25 − 18 = 7. The same step each time makes it a simple adding sequence.

12

HintEach term is made by multiplying, not adding.

The why3 to 6 and 24 to 48 are both doublings, so the rule is 'multiply by 2' and the missing term is 6 × 2.

(−3, 2)

HintLeft gives a negative first number; the across number always comes first.

The whyThe x-coordinate (across) is written first and the y-coordinate (up) second. Left of the origin is negative x; above it is positive y.