Every card in Algebra, Year 7: formulae, sequences and coordinates
The whole deck, in order — so you can read it through before your child ever sees it.
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- Use P = 2(l + w) to find the perimeter of a rectangle with l = 7 cm and w = 3 cm.
20 cm
HintDeal with the bracket before you double.
Why7 + 3 = 10, and 2 × 10 = 20. The answer is a length, so its unit is centimetres, not square centimetres.
- The area of a triangle is A = ½bh. Find A when b = 6 cm and h = 5 cm.
15 cm²
HintMultiply the two lengths, then halve.
Why6 × 5 = 30, and half of 30 is 15. Two lengths have been multiplied, so the unit is square centimetres.
- A taxi fare in pounds is F = 3 + 2m, where m is the number of miles. What is the fare, in pounds, for 7 miles? (number only)
17
HintDo the multiplying before the adding.
Why2m means 2 × m, so 2 × 7 = 14, and 3 + 14 = 17. The 3 is a fixed charge that is paid once.
- In the formula P = 2(l + w) for a rectangle, what do l and w stand for?
The length and the width
HintThey are the two different side measurements.
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.
- Speed is found with s = d ÷ t. A cyclist travels d = 36 km in t = 3 hours. What is s, with its unit?
12 km/h
HintThe unit comes from the two units you divided.
Why36 ÷ 3 = 12. Kilometres divided by hours gives kilometres per hour, so the formula tells you the unit as well as the number.
- The nth term of a sequence is 3n + 1. What is the 10th term? (number only)
31
HintReplace n with the position number.
Why3 × 10 + 1 = 31. A position rule lets you jump straight to any term without listing the ones before it.
- A sequence has the position rule 2n + 5. What are its first three terms?
7, 9, 11
HintUse n = 1, then 2, then 3.
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.
- What is the term-to-term rule for the sequence 4, 11, 18, 25, …?
Add 7
HintSubtract any term from the one after it.
Why11 − 4 = 7, 18 − 11 = 7 and 25 − 18 = 7. The same step each time makes it a simple adding sequence.
- Find the missing term: 3, 6, __, 24, 48.
12
HintEach term is made by multiplying, not adding.
Why3 to 6 and 24 to 48 are both doublings, so the rule is 'multiply by 2' and the missing term is 6 × 2.
- A point is 3 units left of the origin and 2 units up. What are its coordinates?
(−3, 2)
HintLeft gives a negative first number; the across number always comes first.
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.
1★ KS3-MATH-ALG-0058
2★ KS3-MATH-ALG-0059
3★ KS3-MATH-ALG-0060
4★ KS3-MATH-ALG-0061
5★ KS3-MATH-ALG-0062
6★ KS3-MATH-ALG-0063
7★ KS3-MATH-ALG-0064
8★ KS3-MATH-ALG-0065
9★ KS3-MATH-ALG-0066
10★ KS3-MATH-ALG-0067
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