Expanding brackets and substitution – Year 7 maths worksheet with answers to download as PDF

Work out the value of each expression when x = 4, y = -2 and z = 5.

1. \(3x+7\)
2. \(2x-5y\)
3. \(x^{2}+z\)
4. \(xy+z\)
5. \(\dfrac{3x}{6}-y\)
6. \(2(x+y)\)

Expand each expression.

1. \(3(x+4)\)
2. \(5(2a-3)\)
3. \(-2(y+6)\)
4. \(x(x+7)\)
5. \(4a(2a-b)\)
6. \(-3(2m-5)\)

Expand the brackets and simplify.

1. \(3(x+2)+4(x+1)\)
2. \(5(a+3)+2(a-4)\)
3. \(2(3y-1)-3(y+2)\)
4. \(4(2p+1)-(p-5)\)
5. \(x(x+3)+2(x+3)\)

Factorise each expression fully by taking out the highest common factor.

1. \(6x+9\)
2. \(10a-15\)
3. \(4y^{2}+8y\)
4. \(12ab+18b\)
5. \(x^{2}-5x\)
6. \(15m^{2}n+10mn^{2}\)

Use each formula to work out the value required.

1. \(v=u+at\). Find v when u = 5, a = 3 and t = 4.
2. \(A=\dfrac{1}{2}bh\). Find A when b = 8 and h = 5.
3. \(P=2(l+w)\). Find P when l = 7.5 and w = 4.
4. \(s=ut+\dfrac{1}{2}at^{2}\). Find s when u = 2, t = 3 and a = 4.

Work out the value of each expression when a = 3 and b = -4. Take care with the order of operations.

1. \(2a+b^{2}\)
2. \((2a+b)^{2}\)
3. \(ab-b\)
4. \(a^{2}-b^{2}\)
5. \(3(a-b)\)

A phone company uses the formula C = 15 + 0.04m to work out the monthly cost, C pounds, for using m minutes of calls beyond a free allowance.

1. Work out the cost when m = 200.
2. Work out the cost when m = 0. What does this number tell you?
3. One month Amira pays £27. How many minutes did she use? Rearrange the formula or use trial and improvement.
4. Sofia uses 350 minutes. Her mum says that it costs more than £30. Is she right?

A taxi firm in Leeds charges £3.20 for pick-up plus £1.80 for every mile. The formula for the cost is C = 3.2 + 1.8m.

1. Work out the cost of a 5 mile journey.
2. Work out the cost of a 12.5 mile journey.
3. A passenger pays £21.20. How far did the taxi travel?
4. A different firm charges £2 for pick-up and £2 per mile. Write a formula for its cost and decide which is cheaper for 10 miles.

A rectangular lawn is x metres long and (x - 2) metres wide. A path of width 1 metre goes round the outside, so the large rectangle is (x + 2) metres long and x metres wide.

1. Write an expression for the area of the lawn and expand it.
2. Write an expression for the area of the large rectangle (lawn and path) and expand it.
3. Find an expression for the area of the path and simplify.
4. Work out the area of the path when x = 8.

Year 7 pupils pay £x each for a trip plus £5 for lunch. A group of 30 pupils goes on the trip. The teacher writes the expression 30(x + 5) for the total money collected.

1. Expand the expression.
2. Work out the total when x = 12.
3. The total collected is £630. Find x.
4. The teacher wants to check: he works out 30x + 5 instead of 30(x + 5). What is the difference between the two when x = 12? Why is it wrong?

The maths club plays a game. "Think of a number n. Add 4. Multiply the result by 3. Subtract 12. Divide by 3."

1. Write an expression for the final answer in terms of n and simplify it.
2. What happens when you start with n = 9?
3. Use algebra to show that this game always gives back the number you started with.
4. Make up your own number puzzle where the answer is always double your starting number.

A recipe book gives the formula F = 1.8C + 32 to convert from degrees Celsius (C) to degrees Fahrenheit (F).

1. Convert 180 °C into Fahrenheit.
2. Convert 20 °C and 100 °C into Fahrenheit.
3. An oven is set to 392 °F. What is the temperature in Celsius?
4. Is there a temperature that is the same in both scales? Try -40.

The nth pattern in a sequence of block towers uses 4n + 3 blocks. A teacher builds the first few towers and records them in a table.

1. Complete the table.
2. How many blocks are needed for tower 25?
3. Which tower uses 83 blocks?
4. Alfie says that tower 6 uses 28 blocks. Is he right? Show your working.

The cinema sells a family pack. A family of 2 adults and 3 children pay £(2a + 3c), where a is the adult price and c is the child price. A group deal costs 4(a + c) − 5.

1. Expand and simplify the group deal formula.
2. Adult tickets cost £9 and child tickets cost £6. Work out the cost of the family pack.
3. Work out the cost using the group deal formula.
4. How much do 4 adults and 4 children pay without the deal, and how much does the deal save?

A rectangle has length (2x + 3) cm and width (x + 1) cm.

1. Write an expression for the perimeter and simplify.
2. Expand to find an expression for the area.
3. Work out the perimeter and area when x = 4.
4. The perimeter is 50 cm. Find x and the dimensions of the rectangle.

Two phone companies advertise these plans. Plan A costs £8 plus £0.10 per minute. Plan B costs £2 plus £0.15 per minute.

1. Write a formula for each plan with m minutes.
2. Complete the table.
3. For how many minutes do the two plans cost the same?
4. Maya uses about 100 minutes a month. Which plan is better for her? By how much?

Four pupils each made one mistake. Find the mistake and write the correct answer.

1. Ali: \(3(x+5)=3x+5\)
2. Beth: \(-2(x-4)=-2x-8\)
3. Carl: \((x+3)^{2}=x^{2}+9\)
4. Dina: \(x^{2}\text{ when }x=-3\text{ is }-9\)

A farmer has a field in the shape of a rectangle with sides x and x + 10 metres. He wants to put a fence round it. The fence costs £6.50 per metre. He also puts a gate that costs £75.

1. Write and simplify an expression for the length of fencing needed.
2. Write a formula for the total cost T of the fence and gate.
3. Work out the cost when x = 40.
4. The farmer has £1 000. Find the greatest whole value of x for which the cost does not exceed £1 000.

At the school fete, the Year 7 stall sells n cups of hot chocolate. Each cup costs the school 35p to make and is sold for £1.20. The stall also has a fixed cost of £15 for the table and decorations.

1. Write a formula for the profit P pounds in terms of n.
2. Complete the table.
3. How many cups must be sold to make a profit of £100? Give your answer to the nearest whole cup, rounded up.
4. The teacher says that selling 18 cups will cover the costs. Check by substituting n = 18.

Zara notices a pattern: 5 x 5 = 25, 4 x 6 = 24, 6 x 6 = 36, 5 x 7 = 35.

1. Complete: 10 × 10 = ..., 9 × 11 = ... What do you notice?
2. Let the middle number be n. Write 9 × 11 in the form (n − 1)(n + 1) and expand.
3. Use algebra to prove that (n − 1)(n + 1) is always one less than n².
4. Use this to work out 49 × 51 quickly.