Paper Together: sit a paper in a room with your friends.See how it works
This page sets out the method for writing an expression in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Writing an expression topic page.
When you see 'I think of a number…' or a description in words, translate each phrase in order.
When you see a shape with sides given in terms of , write every side then add for the perimeter.
n can be the number of tickets.
The expression is the rule. It is not the answer until n is known.
“4 more than n” is n + 4.
“4 times n” is 4n. “4 less than n” is n − 4.
£3 per ticket for n tickets is 3n.
Then a £2 booking fee makes 3n + 2.
If n = 5, 3n + 2 = 17.
Write the expression first, then replace the letter if a value is given.
An expression has no equals sign.
3n + 2 is an expression. 3n + 2 = 17 is an equation.
Try n = 1 in the story and in the expression.
They should give the same cost.
Say what the letter means before you write it, if you are choosing it yourself. "Let n be the number" takes one line and stops you mixing two unknowns up. Then translate one operation at a time. "Multiply by 4, then subtract 7" is 4n-7. "Subtract 7, then multiply by 4" is 4(n-7). Those are not equal. The bracket holds the operation that has to happen first.
Watch the small words. "Sum" and "total" mean add. "Difference" and "less than" mean subtract. "Product" and "of" often mean multiply, as in "half of n", which is n/2. "Quotient" and "shared between" mean divide. "Twice n" is 2n. "3 more than twice n" is 2n+3, not 3-2n and not 2(n+3).
Method: 1. Name your own letter in a short sentence before you use it. 2. A line such as “let n be the number” stops two unknowns being mixed up. 3. Translate the sentence one operation at a time.
If one item costs p pounds, then three of them cost 3p. Adding p+3 would mean one item plus an extra £3, which is a different story. Write the quantity first as a multiplier. A family ticket might be "2 adults at £a each and 3 children at £4 less than an adult". The child price is a-4, so three children cost 3(a-4). The total expression is 2a+3(a-4), which simplifies to 5a-12.
Ages work the same way. If Mia is y years old, then her brother who is 4 years older is y+4, and in 5 years Mia will be y+5. "Twice as old as Mia was 3 years ago" is 2(y-3). Substitute a simple age, such as y=10, into both the sentence and the expression. Both should give the same number. That check catches a reversed subtraction.
Method: 1. Three items at p pounds each cost 3p. 2. Write p+3 only when the story adds an extra £3 to a single item. 3. Put how many items there are in front of the letter.
A perimeter is the distance around the outside, so every side is included once. A rectangle has two lengths and two widths. If the length is 2x+1 and the width is x, the perimeter is (2x+1)+x+(2x+1)+x, which simplifies to 6x+2. Forgetting a pair of sides is the usual miss. An equilateral triangle with side 2x+1 uses that side three times: 3(2x+1)=6x+3.
A formula is what you get when the story names the total. "The perimeter is P" gives P=6x+2. The expression on its own is still 6x+2, with no equals sign. If a question says "write an expression", do not invent =. If it says "write a formula for P in terms of x", the equals sign is required. Simplify either way. An unsimplified string of four sides can lose the final mark even when the sides were right.
Method: 1. Add every side once, because the perimeter is the distance around the outside. 2. A rectangle contributes two lengths and two widths. 3. Add (2x+1) and x twice, then collect to 6x+2.
Real exam questions describe a letter in words and ask for an expression. The key is to translate each phrase into one operation. "More than" and "greater than" add, "less than" and "younger than" subtract, "times as many" and "twice" multiply and "shared between" divides. So "r is 8 more than w" is r=w+8, and "q is 3 less than w" is q=w-3.
Watch the order for "less than". "3 less than w" means start at w and take away 3, so it is w-3, never 3-w. Phrases with two steps need brackets. "Twice the sum of n and 4" is 2(n+4) because the doubling applies to the whole sum. "Twice n, then add 4" is 2n+4. Say the phrase aloud in order and write one piece at a time.
Method: 1. Underline the letter and the number in the phrase. 2. Decide which operation each key word means. 3. Write the expression in the order the words describe, using brackets if a sum is multiplied. 4. Test with an easy number, for example let w=10 and check the sentence is true.
Tip: Brackets are needed when the words say twice or three times something that is itself a sum or a difference.
A very common exam context is a shop or a café. If a T-shirt costs £9 and there are t of them, the cost is 9t. If caps cost £7 and there are c of them, the cost is 7c. The total is the sum, 9t+7c. The number of items and the price each both stay in the term, and you never write 9+t for a cost.
You can put numbers in afterwards. When t=4 and c=3 the total is 9×4+7×3=36+21=57 pounds. Keep to one unit. If prices are in pence and the question wants pounds, change them first or at the end. A question that mentions "boxes" and "packets" is the same idea: 3 boxes of x sweets and 2 packets of y sweets give 3x+2y sweets in total.
Method: 1. Write the cost of each type of item as number of items times price each. 2. Add the separate costs for a total, or subtract from the money given for change. 3. Keep the unit the same in every term. 4. If asked, substitute the given values into the finished expression and work out the number.
Perimeter means the total distance around a shape, so you add every side. A rectangle with length (2x+5) cm and width (x-1) cm has two lengths and two widths: (2x+5)+(2x+5)+(x-1)+(x-1). Collect like terms to get 6x+8. Putting brackets around each side before you add is a safe habit because it stops sign slips.
The words "give your answer in its simplest form" mean you must collect like terms and leave nothing that can be combined. Triangles are the same: add the three sides. The sides (2x+3), (x+5) and (3x-2) give 6x+6. A good check is to pick a small value of x, such as x=4, work out each side as a number and add them.
Method: 1. Write down every side of the shape, using the same expression for equal sides. 2. Add them all, with brackets around each expression. 3. Remove the brackets and collect the x terms and the numbers. 4. Check with a small value of x.
Tip: A rectangle has two of each side. Writing only one length and one width is the usual lost mark.
Many charges have two parts: a fixed amount you pay once and a rate for each unit. A plumber might charge a call-out fee of £20 plus £15 for each hour. For h hours the cost in pounds is C=20+15h. The fixed part has no letter and the rate part is multiplied by the letter.
When a question asks for a formula you must write the left-hand side too, for example C=20+15h, and not just 20+15h. To find a cost, substitute the number of hours. For h=6 the cost is 20+15×6=20+90=110 pounds. Remember to do the multiplication before the addition, and check the answer is sensible: six hours should cost more than the call-out fee alone.
Method: 1. Spot the fixed charge and the rate for each unit. 2. Write C= fixed charge + rate × letter. 3. Substitute the number, doing the multiplication first. 4. State the unit in the answer, for example pounds.
AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.