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Either paper 3 marks
Owen thinks of a number, \(n\).
(a)Owen multiplies the number by 2 and then subtracts 12.
Write an expression, in terms of \(n\), for his answer.
(b)Owen then multiplies his answer by 2.
Write an expression, in terms of \(n\), for his new answer. Give your expression in its simplest form.
Show answer
(a) \(2n - 12\)
(b) \(4n - 24\)Multiplying \(n\) by 2 gives \(2n\). Taking 12 away gives
\(2n - 12\)
Multiply every term inside the bracket by 2:
\(2(2n - 12) = 4n - 24\)
- (b) M1each term multiplied by 2: \(4n\) or \(24\)
- (b) A1simplest form \(4n - 24\)
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Either paper 3 marks
Leo is \(x\) years old.
(a)Oscar is 7 years older than Leo.
Write an expression, in terms of \(x\), for Oscar's age.
(b)Write an expression, in terms of \(x\), for the total of Leo's age and Oscar's age.
Give your expression in its simplest form.
Show answer
(a) \(x + 7\)
(b) \(2x + 7\)Oscar is 7 years older than Leo, so Oscar is
\(x + 7\) years old.
Leo is \(x\) years old and Oscar is \(x + 7\) years old.
Total \(= x + (x + 7) = 2x + 7\)
- (b) M1adds the two ages \(x + (x + 7)\)
- (b) A1simplest form \(2x + 7\)
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Either paper 3 marks
A pen costs \(p\) pence.
(a)A pencil costs 10 pence less than a pen.
Write an expression, in terms of \(p\), for the cost of a pencil, in pence.
(b)Rosa buys 6 pens and 4 pencils.
Write an expression, in terms of \(p\), for the total amount she pays, in pence. Give your expression in its simplest form.
Show answer
(a) \(p - 10\)
(b) \(10p - 40\)A pencil is 10 pence cheaper than a pen, so it costs
\(p - 10\) pence.
The pens cost \(6p\) pence.
The pencils cost \(4(p - 10) = 4p - 40\) pence.
Collecting the \(p\) terms: \(6p + 4p - 40 = 10p - 40\)
- (b) M1cost of the pencils \(4(p - 10)\) or \(4p - 40\)
- (b) A1total in simplest form \(10p - 40\)
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Either paper 2 marks
Joel is a plumber. He charges £30 for each hour he works, plus a fixed call-out fee of £10.
Write an expression, in terms of \(h\), for the total charge, in pounds, for a job that lasts \(h\) hours.
Show answer
\(30h + 10\)\(h\) hours of work cost \(30 \times h = 30h\) pounds.
The call-out fee of 10 pounds is added once, whatever the length of the job:
\(30h + 10\)
- M1cost of the hours \(30h\)
- A1adds the fixed fee: \(30h + 10\)
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Either paper 1 mark\(m\) is double \(n\). Circle the correct formula.
\(m = 2n\) \(m = n - 2\) \(m = n + 2\) \(m = \frac{ n }{ 2 }\) Show answer
\(m = 2n\)"double" means m is 2 times as big as n, so n is multiplied by 2, which gives \(m = 2n\).
Adding 2 to n would give a value only 2 bigger, not 2 times as big, and dividing n by 2 makes it smaller.
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Either paper 1 mark
\(h\) is 8 smaller than \(g\).
Circle the correct equation.
\(g = 8h\) \(g = h - 8\) \(h = g - 8\) \(h = 8g\)
Show answer
\(h = g - 8\)\(h\) is the letter named first, so \(h\) is the one that stands on its own on the left.
"smaller than" means subtract 8 from \(g\): \(h = g - 8\)
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Either paper 3 marks
A rectangle has width \(w\) cm.
(a)The length of the rectangle is 7 cm more than its width.
Write an expression, in terms of \(w\), for the perimeter of the rectangle, in centimetres. Give your expression in its simplest form.
(b)Work out the perimeter of the rectangle when \(w = 12\) cm.
Show answer
(a) \(4w + 14\)
(b) \(62\ \text{cm}\)The length is \(w + 7\) cm.
Perimeter \(= w + (w + 7) + w + (w + 7) = 4w + 14\)
\(4 \times 12 + 14 = 62\)
- (a) M1adds the four sides \(w + (w + 7) + w + (w + 7)\)
- (a) A1simplest form \(4w + 14\)
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Either paper 3 marks
Ben has \(n\) stickers.
(a)He shares the stickers equally between 7 pupils.
Write an expression, in terms of \(n\), for the number of stickers each pupil gets.
(b)The next day Ben has \(n\) stickers again, but 12 of them are torn and he throws those away.
He shares the rest equally between the 7 pupils.
Write an expression, in terms of \(n\), for the number of stickers each pupil gets now.
Show answer
(a) \(\frac{ n }{ 7 }\)
(b) \(\frac{ n - 12 }{ 7 }\)Sharing equally between 7 pupils means dividing by 7:
\(\frac{ n }{ 7 }\)
Throwing 12 away leaves \(n - 12\) stickers.
That is what gets shared between the 7 pupils, so divide the whole of it by 7:
\(\frac{ n - 12 }{ 7 }\)
The whole of \(n - 12\) goes above the line. \(\frac{ n }{ 7 } - 12\) would mean something else — sharing all \(n\) out first and then taking 12 away from each pupil's share.
- (b) M112 taken away: \(n - 12\)
- (b) A1whole of it shared by 7: \(\frac{ n - 12 }{ 7 }\)
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Either paper 3 marks
A shop has 90 chopping boards in stock.
\(x\) of them are wooden and the rest are plastic.
(a)Find an expression, in terms of \(x\), for the number of plastic chopping boards in stock.
(b)The shop sells every plastic chopping board for £7.
Find an expression, in terms of \(x\), for the amount the shop takes for the plastic chopping boards, in pounds.
Show answer
(a) \(90 - x\)
(b) \(7(90 - x)\)Every chopping board is either wooden or plastic, and \(x\) of the 90 are wooden. Taking those away leaves
\(90 - x\)
There are \(90 - x\) plastic chopping boards, and each one brings in £7, so multiply the whole of the expression by 7:
\(7(90 - x)\)
Multiplied out that is \(630 - 7x\), which is the same expression written a different way.
- (b) M1multiplies \(90 - x\) by 7
- (b) A1\(7(90 - x)\)
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Either paper 4 marksIn each description, \(n\) is a number. Match each description to the correct expression. One has been done for you.
Description 3 has been matched to expression E. Match each of the other four descriptions to its expression. Give your answer as pairs, for example 2 to A.Description Expression 1 half of the sum of \(n\) and 6 A \(n - 6\) 2 subtract 6 from \(n\) B \(2n\) 3 \(n\) multiplied by 6 C \(\frac{ n }{ 2 } + 6\) 4 double \(n\) D \(\frac{ n + 6 }{ 2 }\) 5 \(n\) divided by 6 E \(6n\) F \(\frac{ n }{ 6 }\) G \(\frac{ 6 }{ n }\) Show answer
1 to D; 2 to A; 4 to B; 5 to FWrite each description as an expression, then find that expression in the list.
Description 1: half of the sum of \(n\) and 6 is \(\frac{ n + 6 }{ 2 }\), so it matches D.
Description 2: subtract 6 from \(n\) is \(n - 6\), so it matches A.
Description 4: double \(n\) is \(2n\), so it matches B.
Description 5: \(n\) divided by 6 is \(\frac{ n }{ 6 }\), so it matches F.
Description 3 to E was done for you, so the four pairs are 1 to D; 2 to A; 4 to B; 5 to F.
Expressions C and G are the spare ones. They look like the expressions above but say something different, such as the order of a subtraction or a division, or what is halved.
- B1reads description 1 as \(\frac{ n + 6 }{ 2 }\) and matches 1 to D
- B1reads description 2 as \(n - 6\) and matches 2 to A
- B1reads description 4 as \(2n\) and matches 4 to B
- B1reads description 5 as \(\frac{ n }{ 6 }\) and matches 5 to F