Algebra, Year 7: formulae, sequences and coordinates

20 cm

提示Deal with the bracket before you double.

为什么7 + 3 = 10, and 2 × 10 = 20. The answer is a length, so its unit is centimetres, not square centimetres.

15 cm²

提示Multiply the two lengths, then halve.

为什么6 × 5 = 30, and half of 30 is 15. Two lengths have been multiplied, so the unit is square centimetres.

17

提示Do the multiplying before the adding.

为什么2m 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

提示They are the two different side measurements.

为什么A 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

提示The unit comes from the two units you divided.

为什么36 ÷ 3 = 12. Kilometres divided by hours gives kilometres per hour, so the formula tells you the unit as well as the number.

31

提示Replace n with the position number.

为什么3 × 10 + 1 = 31. A position rule lets you jump straight to any term without listing the ones before it.

7, 9, 11

提示Use n = 1, then 2, then 3.

为什么2 × 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

提示Subtract any term from the one after it.

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

12

提示Each term is made by multiplying, not adding.

为什么3 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)

提示Left gives a negative first number; the across number always comes first.

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