Every card in Algebra essentials, Year 7: more practice
The whole deck, in order — so you can read it through before your child ever sees it.
- How is the expression n² read aloud, and what does it mean?
"n squared": n multiplied by itself
HintThe little raised 2 tells you how many times n appears in the multiplication.
Whyn² means n × n. It is not 2 × n, which is written 2n.
- Can 3a + 2b be simplified to a single term? Say why.
No — a and b are different letters, so the terms are unlike
HintAsk whether a and b stand for the same number.
WhyOnly like terms, with the same letter part, can be added. 3a + 2b has to stay as it is, but 3a + 2a = 5a.
- What is the inverse of "divide by 4"?
Multiply by 4
HintThink of what would undo it and give you the number you started with.
WhyMultiplying by 4 undoes dividing by 4: (20 ÷ 4) × 4 = 20. Addition and subtraction undo each other in the same way.
- Find the value of 2a + 3b when a = 4 and b = 5. (number only)
23
HintReplace each letter with its number, then multiply before you add.
Why2a + 3b = 2 × 4 + 3 × 5 = 8 + 15 = 23. Each term is a multiplication, so it is done before the addition.
- Write an expression for "a number n multiplied by 3, then 4 taken away".
3n − 4
HintWork through the words in order, one operation at a time.
WhyMultiplying n by 3 gives 3n, and taking away 4 gives 3n − 4. Writing 3(n − 4) would mean subtracting 4 first.
- A point has a negative x-coordinate and a positive y-coordinate. Which part of the grid is it in?
The top left (the second quadrant)
HintNegative x means west of the vertical axis; positive y means above the horizontal axis.
WhyThe four quadrants are numbered anticlockwise from the top right. A point such as (−3, 2) is 3 left and 2 up, so it sits in the top left.
- Expand 5(2y − 3).
10y − 15
HintThe 5 multiplies every term inside the bracket, including the one with the minus sign.
Why5 × 2y = 10y and 5 × (−3) = −15. Check with y = 2: 5(4 − 3) = 5 and 10 × 2 − 15 = 5.
- Is 4x + 7 an expression or an equation?
An expression — it has no equals sign
HintCheck whether there is a symbol joining two sides.
WhyAn equation states that two things are equal, such as 4x + 7 = 19. An expression like 4x + 7 only describes a value, so you simplify or evaluate it, not solve it.
- The perimeter of a square is P = 4s. Find P when s = 6.5 cm.
26 cm
HintSubstitute 6.5 for s and multiply; the answer is a length, so it needs units.
WhyP = 4 × 6.5 = 26 cm. The 4 and s are multiplied because no sign is written between them.
- The nth term of a sequence is 5n − 2. What is the 8th term? (number only)
38
HintReplace n with 8, multiplying before subtracting.
Why5 × 8 − 2 = 40 − 2 = 38. Only the position number is substituted: you do not need the first seven terms.
1★ KS3-MATH-ALG-0087
2★ KS3-MATH-ALG-0088
3★ KS3-MATH-ALG-0089
4★ KS3-MATH-ALG-0090
5★ KS3-MATH-ALG-0091
6★ KS3-MATH-ALG-0092
7★ KS3-MATH-ALG-0093
8★ KS3-MATH-ALG-0094
9★ KS3-MATH-ALG-0095
10★ KS3-MATH-ALG-0096
Keep what you learn
Here, nothing is saved. In your child’s own sky every card is scheduled — it comes back just before they’d forget it — and the professor who wrote it is one tap away.