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SATs practice · Year 6Chapter 7 · Algebra and sequences
Year 6 Maths reasoning (SATs) · Algebra and sequences · Lesson 7.3

Year 6 Maths reasoning (SATs): Formulae in words and letters

Part of the Year 6 Maths reasoning (SATs) algebra and sequences chapter. Chapter overview · whole chapter on one page

7.3

Formulae in words and letters

Year 6
Use simple formulae written in words and in letters, and substitute values into them (Year 5-6)
Story. A trip to the science museum costs a fixed amount for the coach, plus a fixed price for each ticket. The teacher writes a formula so that she can work out the total for any number of pupils.

Rule

A formula shows how one amount depends on others. Put the value in place of each letter, then calculate.

Multiply before you add: 3n + 2 with n = 4 is 3 x 4 + 2 = 14.

Key ideas

  • Replace each letter with its value.
  • Follow the order of operations: multiply, then add.
  • The letter n usually stands for a number of things.
Worked example 7.3.1
A cost is worked out using the formula T = 4n + 10, where n is the number of tickets. Find T when n = 6.

Method. Replace n with the number, then multiply before you add.

  1. Write the formula. Total = 4 x n + 10.
    T = 4n + 10
  2. Substitute the value. Put n = 6 into the formula.
    4 x 6 + 10
  3. Work out. Multiply first, then add.
    24 + 10 = 34
  4. Write the answer.
    34

Check. 24 + 10 = 34. ✓

Watch out. Multiply before you add. 3n + 2 with n = 4 is 14, not 20.

Worked example 7.3.2
The perimeter P of a rectangle is found by P = 2l + 2w. Find P when l = 7 and w = 4.

Method. Substitute l = 7 and w = 4.

  1. Substitute. P = 2 x 7 + 2 x 4.
    2 x 7 + 2 x 4
  2. Work out. 14 + 8 = 22.
    22
  3. Write the answer.
    22

Check. 2 x 7 = 14 and 2 x 4 = 8. ✓

Worked example 7.3.3
The area of a triangle is A = bh / 2. Find A when b = 10 and h = 7.

Method. Substitute b = 10 and h = 7, then divide by 2.

  1. Substitute. A = 10 x 7 / 2.
    10 x 7 / 2
  2. Work out. 70 / 2 = 35.
    35
  3. Write the answer.
    35

Check. 35 x 2 = 70. ✓

Watch out

Watch out. 2n means 2 x n. If n = 5, then 2n = 10, not 25.

Exam tip

Practice guide. Write the formula with the numbers in place of the letters before you calculate.

Exercise 7C  Practice: formulae

Non-calculator
1
FA cost is worked out using the formula T = 2n + 5, where n is the number of tickets. Find T when n = 9.
2
FA cost is worked out using the formula T = 6n + 3, where n is the number of tickets. Find T when n = 7.
3
FA cost is worked out using the formula T = 7n + 0, where n is the number of tickets. Find T when n = 6.
4
FA cost is worked out using the formula T = 4n + 12, where n is the number of tickets. Find T when n = 10.
5
FWhich is the value of 3a + 2 when a = 5? Choose one: 17, 21 or 13.
6
PSThe formula for the total seats in a hall is S = 6r + 2, where r is the number of rows. Find S when r = 9.
7
PSThe cost of a day trip is C = 5n + 12 pounds, where n is the number of pupils. How much does a trip cost for 8 pupils?
8
FA rectangle has length 9 cm and width 5 cm. Use P = 2l + 2w to find P.
9
RExplain why 2n + 3 with n = 4 is 11, not 14.
10
PSThe cost of hiring a bike is C = 3h + 4 pounds, where h is the number of hours. Maya pays 22 pounds. How many hours did she hire the bike?
11
PSA cost is worked out using the formula T = 9n + 1, where n is the number of tickets. Find T when n = 3.
12
RWrite the formula in words for the total cost: a bus costs 4 pounds for each child plus 10 pounds for the driver.

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