Calculator and number skills Revision Notes for AQA GCSE Maths

Calculator and number skills

Essential calculator keys

Understanding your calculator's key functions is crucial for efficient mathematical calculations. These keys will help you perform complex operations quickly and accurately, saving time in exams and problem-solving situations.

Here are the most important keys you need to master:

Basic operation keys:

x² - Square a number (multiply a number by itself)
x³ - Cube a number (multiply a number by itself three times)
x⁻¹ - Find the reciprocal of a number (1 divided by the number)
√ - Find the square root of a number
∛ - Find the cube root of a number (you might need to press shift first)

Special function keys:

Ans - Use your previous answer in a new calculation
(-) - Enter a negative number (different from the subtraction key)
S↔D - Change between fraction and decimal format (not available on all calculators)

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Practice using these keys regularly to build muscle memory. The more familiar you become with their locations and functions, the faster and more accurately you'll be able to perform calculations during exams.

Order of operations

When performing calculations, you must follow the correct sequence of operations to get the right answer. This mathematical rule ensures consistency and accuracy in all calculations, whether done by hand or with a calculator.

Remember BIDMAS:

Brackets - Work out anything in brackets first
Indices - Calculate powers and roots next
Division - Then division operations
Multiplication - Then multiplication operations
Addition - Then addition operations
Subtraction - Finally subtraction operations

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Worked Example: Order of Operations

Calculate: $(10 - 7) + 4 \times 3^2$

Step 1: Brackets first - $(10 - 7) = 3$ Step 2: Indices next - $3^2 = 9$
Step 3: Multiplication - $4 \times 9 = 36$ Step 4: Addition - $3 + 36 = 39$

Therefore: $(10 - 7) + 4 \times 3^2 = 39$

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Always follow BIDMAS even when using a calculator. While modern calculators follow order of operations automatically, understanding the sequence helps you check your work and catch input errors.

Working with fractions on calculators

You can enter fractions directly on your calculator using the fraction key and arrow buttons. This feature is particularly useful when you need to calculate a fraction of a number, as it maintains precision and can display exact fractional answers.

Many students find it helpful to work with fractions rather than converting to decimals immediately, as this often leads to more accurate final answers.

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Worked Example: Calculating Fractions

To work out $\frac{3}{8}$ of 52:

Step 1: Enter 3 using the fraction key Step 2: Enter 8 in the denominator
Step 3: Multiply by 52 Step 4: Your calculator will show the result

The answer is $\frac{3 \times 52}{8} = \frac{156}{8} = 19.5$

To convert between fractions and decimals, use the S↔D key if your calculator has this function. This allows you to switch between exact fractional answers and decimal approximations as needed.

Understanding reciprocals

Reciprocals are an important mathematical concept that you can calculate manually or using your calculator. Understanding reciprocals is essential for solving equations and working with rates and ratios.

To find the reciprocal of a number, you write it as a fraction and then turn the fraction upside down:

The reciprocal of 7 is $\frac{1}{7}$ (since $7 = \frac{7}{1}$ , flipped = $\frac{1}{7}$ )
The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$ (flip the fraction)

You can use the x⁻¹ key on your calculator to find reciprocals quickly, which is particularly useful for complex calculations.

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Remember that multiplying a number by its reciprocal always equals 1. This property is useful for checking your work: $7 \times \frac{1}{7} = 1$ .

Worked examples

Here are some key calculation techniques that often appear in exams:

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Worked Example: Square Roots with Subtraction

When calculating $\sqrt{6} - 0.71$ , remember that the square root acts like a bracket, so you must work out everything under the square root sign first before subtracting.

Step 1: Calculate $\sqrt{6} = 2.449...$ Step 2: Subtract: $2.449... - 0.71 = 1.739...$

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Worked Example: Powers of Decimal Numbers

For calculations like $3.1^4$ , use the power key on your calculator.

Using calculator: $3.1^4 = 92.3521$

Write down all the digits shown on your calculator display for accuracy.

Practice techniques

When working without a calculator, always apply the correct order of operations (BIDMAS). This systematic approach prevents errors and ensures consistent results across different types of problems.

Double-check your work by ensuring you've followed the proper sequence and that your intermediate steps make logical sense.

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When using a calculator, remember that you might need to convert fraction answers to decimals using the S↔D key, depending on the question requirements. Always read the question carefully to determine the required format for your answer.

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Key Points to Remember:

Master the essential calculator keys: x², x³, x⁻¹, √, ∛, Ans, and S↔D
Always follow BIDMAS when calculating: Brackets, Indices, Division, Multiplication, Addition, Subtraction
The reciprocal of a number is 1 divided by that number, or the fraction turned upside down
Square roots act like brackets - calculate what's inside first
Use the S↔D key to convert between fractions and decimals when needed

Calculator and number skills (AQA GCSE Maths): Revision Notes