Introduction to Formulas
A formula is a maths rule that links two variables, like y = 2x + 3. Whichever value you pick for x, the rule gives one matching y. To find it, substitute your value in place of x and work it out: if x = 1, then y = 2 × 1 + 3, so y = 5.
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What Is a Formula?
- A formula is a mathematical rule that links two quantities.
- You substitute x values into a formula to find the corresponding y values.
How to Visualise a Formula?
- Use the formula to make a table of x and y values.
- Then plot these values on a graph to see the pattern.
Using Formulas to Solve Problems
- A formula can represent real-life situations like saving money.
- You substitute values to solve specific problems.
Practice Questions
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If , what is y when ?
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Substitute into the formula: .
The formula for the distance travelled by a car is , where y is the distance in miles and x is the number of hours driven. How far will it travel after 3 hours?
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Substitute into the formula: . The car will travel 300 miles after 3 hours.
If , what is x when ?
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Substitute into the formula: . Simplify: , so .
A company’s total revenue y is represented by , where x is the number of products sold. How many products must be sold to reach a revenue of £4800?
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Substitute into the formula: . Simplify: , so .
The total cost of a gym membership is calculated by , where x is the number of months and y is the total cost in pounds. If the total cost is £200, how many months did the member sign up for?
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Substitute into the formula: . Simplify: , so .
A company charges a £200 setup fee and £50 for printing each book. If you print more than 10 books, you get a discount on the total cost. How many books can be printed for £720?
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For , a discount applies. The discounted formula becomes . Substitute : . Simplify: . Solve: , so .
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Introduction to Formulas frequently asked questions
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A formula in maths uses an equation to show how two quantities are linked. If you know one value, the formula works out the other. For example, y = 2x + 3 links x and y. When x is 1, y is 5. Formulas turn one quantity into another.
A mapping shows the relationship between two quantities, often using an arrow. A formula shows that same relationship as a mathematical equation. So every formula is a mapping, but written with maths symbols. For example, y = 2x + 3 is a formula that maps each x to its matching y.
A simple example of a formula is y = 2x + 3. It links the two variables x and y. Whenever you choose a value for x, the formula tells you y. When x is 2, y is 2 times 2 plus 3, which is 7.
To use a formula, substitute a value you know into it. Then work out the calculation to find the other value. For y = 2x + 3, put x = 1 into the formula. This gives 2 times 1 plus 3, so y equals 5.
You show a formula on a graph by plotting its values as points. Work out pairs of x and y, then mark each pair on the grid. For y = 2x + 3, the points all fall on a straight line when you join them.
Formulas are useful because they help you solve real-life problems more easily. You can turn a situation into an equation, then work out the answer. For example, a savings formula like y = 20 + 12x tells you how many weeks it takes to reach a total.