Writing an expression Quiz (Grade 2)

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Score: 0 / 10

Writing an expression — Notes & Worked Examples Show / Hide

Explanation:

An algebraic expression uses letters to stand for unknown numbers (and has no equals sign). Translate key words into algebra: “4 more than x” is x + 4, “5 less than x” is x − 5, “3 times x” is 3x, and “half of x” is x2.

If you are unsure which operation to use with a letter, test it with a simple number first to see what calculation you do, then replace the number with the letter. Always check that money or length units match before forming the expression.

Example 1: Ben is x years old. Alice is 4 years older than Ben. Dan is 3 times as old as Ben. Write a simplified expression for the sum of all three ages.

Solution:

• Ben: x • Alice: x + 4 • Dan: 3x

• Add all three ages together:

x + (x + 4) + 3x

• Collect like terms → Answer: 5x + 4

Example 2: A tea costs t pence, a coffee costs c pence, and a cake costs £2.50. Write an expression in pence for the total cost of 3 teas, 2 coffees, and 1 cake.

Solution:

• Convert £2.50 into pence first: £2.50 = 250p

• 3 teas = 3t pence; 2 coffees = 2c pence

• Add the items together in pence:

Answer: 3t + 2c + 250

One Page Guide (PDF) Writing an expression Worksheets

Question 1

[2 marks]

Cups are sold in packs and in boxes.
There are 12 cups in each pack.
There are 18 cups in each box.
Alison buys p packs of cups and b boxes of cups.
Write down an expression, in terms of p and b, for the total number of cups Alison buys.

Worked Solution & Answer

12 × p + 18 × b = 12p + 18b M1 A1

Answer: 12p + 18b

Question Paper (PDF) • Mark Scheme (PDF)

Question 2

[2 marks]

Work out
A shop sells apples and oranges.
There are 6 apples in each pack of apples.
There are 7 oranges in each bag of oranges.
The shop sells x packs of apples and y bags of oranges.
Write an expression, in terms of x and y, for the total number of apples and oranges the
shop sells.

Worked Solution & Answer

6 × x + 7 × y = 6x + 7y M1 A1

Answer: 6x + 7y

Question Paper (PDF) • Mark Scheme (PDF)

Question 3

[3 marks]

Naomi has b bags of apples and c crates of apples.
There are 5 apples in each bag.
There are 28 apples in each crate.
Naomi has a total of T apples.
Write a formula for T in terms of b and c.

T =

Worked Solution & Answer

Use + for more/older, - for less/fewer/younger, and multiply/divide for rates. M1
e.g. 4 less than m is m - 4 M1
3 times m is 3m
Answer: T = 5b + 28c A1

Answer: T = T = 5b + 28c

Question Paper (PDF) • Mark Scheme (PDF)

Question 4 AQA Jun 2022 2F Q14

[3 marks]

Match each expression on the left with one on the right.
One has been done for you.

State the match for:
a + 3 × 2
a × 3 × 2
a × 3 + 2

Answer

Worked Solution & Answer

a + 3 × 2 = a + 6 M1
a × 3 × 2 = 6a M1
a × 3 + 2 = 3a + 2. A1

Answer: Answer a + 3 × 2 = a + 6; a × 3 × 2 = 6a; a × 3 + 2 = 3a + 2

Question Paper (PDF) • Mark Scheme (PDF)

Question 5 AQA Nov 2024 3F Q17

[3 marks]

Match the algebra to the correct description.
One has been done for you.

Match the algebra to the correct description (Identity, Equation, Inequality, Formula, Expression). [3 marks]

Worked Solution & Answer

An equation has an = sign to solve for an unknown M1
an identity has ≡ and holds for all values M1
an expression has no = or inequality sign
an inequality has <, >, ≤, ≥. A1

Answer: 5x + 10 = 2x + 4 -> Equation; 3(b + 2c) ≡ 3b + 6c -> Identity; 3L + 8M -> Expression; 20 < 7y + 13 -> Inequality

Question Paper (PDF) • Mark Scheme (PDF)

Question 6

[3 marks]

Work out
(a) Simplify m × m × m × m (1)
In a competition, a player gets 5 points for each win, 2 points for each draw, 0 points for each loss. Amy wins x games and draws y games.
(b) Write down an expression, in terms of x and y, for the total number of points Amy gets. (2)

(a) Simplify m × m × m × m [1 mark]

(b) Write down an expression, in terms of x and y, for the total number of points
Amy gets. [2 marks]

Worked Solution & Answer

(a)

m⁴ B1

Answer (a): m⁴

(b)

5 × x + 2 × y = 5x + 2y M1 A1

Answer (b): 5x + 2y

Question Paper (PDF) • Mark Scheme (PDF)

Question 7

[3 marks]

Greg is x years old.
Greg is 5 years older than Katy.

(a) Write down an expression, in terms of x, for Katy’s age. [1 mark]

(b) Write down an expression, in terms of x, for Carl’s age. [1 mark]

y =

Worked Solution & Answer

(a)

x – 5

Answer (a): x - 5

(b)

Answer (b): 2x

(c)

y = 12 ÷ 4 = 3 B1

Answer (c): y = 3

Question Paper (PDF) • Mark Scheme (PDF)

Question 8 AQA Jun 2025 2F Q14

[4 marks]

Match each description to the correct expression.
One has been done for you.

Match descriptions to expressions: 2 more than n, n doubled (done), n multiplied by itself, half of n, 2 less than n. [4 marks]

Worked Solution & Answer

2 more than n is n + 2. M1
n multiplied by itself is n × n = n² M1
Half of n is n / 2. M1
2 less than n is n – 2. A1

Answer: 2 more than n -> n+2; n multiplied by itself -> n²; half of n -> n/2; 2 less than n -> n–2

Question Paper (PDF) • Mark Scheme (PDF)

Question 9

[4 marks]

Ben is n years old.
Chloe is twice as old as Ben.
Dan is five years younger than Ben.
The total of Ben's age, Chloe's age and Dan's age is T years.

(a) Find a formula for T in terms of n. [3 marks]

T =

(b) In the table below, put a tick (✓) in the box next to the identity. [1 mark]

Worked Solution & Answer

(a)

T = n + 2n + (n – 5) = 4n – 5 M2 A1

Answer (a): T = T = 4n - 5

(b)

5m – 3m = 2m is true for all values of m B1

Answer (b): 5m – 3m = 2m ticked

Question Paper (PDF) • Mark Scheme (PDF)

Question 10 Specimen Set 1 1F Q13

[5 marks]

Here is a sequence of patterns made with grey square tiles and white square tiles.

(a) In the space below, draw pattern number 4 [1 mark]

(b) Find the total number of tiles in pattern number 20 [2 marks]

Worked Solution & Answer

(a)

Column of 6 grey tiles on the left and 4 white tiles on the right

Answer (a): Column of 6 grey tiles on the left and 4 white tiles on the right

(b)

Total tiles in pattern n = (n + 2) + n = 2n + 2 M1
⇒ 2(20) + 2 = 42 A1

Answer (b): 42

(c)

Grey tiles: 3, 4, 5, ... = n + 2 M1 A1

Answer (c): n + 2

Question Paper (PDF) • Mark Scheme (PDF)

Score: 0 / 10 (0 / 32 marks)

Writing an expression Worksheets Next: Function machines →

Grade 2 Quizzes

19 Topics

2A - Calculation problems	2B - Using a calculator
2C - Systematic listing	2D - Fraction of an amount
2E - FDP	2F - Simplifying algebra
2G - Writing an expression	2H - Function machines
2J - Solving one step equations	2K - Angles
2L - Area and perimeter	2M - Reading scales
2N - Probability & Probability Scale	2P - Frequency polygons
2Q - Unitary method	2R - Bar charts
2S - Pie charts	2T - Averages
2U - Stem and leaf diagrams