Maths skills 2 (AQA GCSE Design and Technology): Revision Notes

Maths skills 2

This topic covers essential mathematical skills you'll need for calculations involving precision, large numbers, and proportional relationships. Understanding these concepts will help you tackle real-world problems with confidence.

Decimal and standard form

Understanding decimal places

When working with measurements and calculations, you don't always need extreme precision. Decimal places help you express numbers to an appropriate level of accuracy. The number of decimal places tells you how many digits appear after the decimal point.

For example, if you're measuring the volume of a cube and get 65.83756 cm³, you might only need this expressed to two decimal places as 65.84 cm³. This gives you the right level of precision without unnecessary detail.

Standard form notation

Standard form provides a neat way to write very large or very small numbers using powers of 10. This method makes calculations much easier and helps you avoid writing lots of zeros.

The pattern works like this:

• Large numbers: $1,000 = 10 \times 10 \times 10$ or $10^3$
• Even larger: $6,000,000 = 6 \times 10^6$
• Very large: $9,000,000,000 = 9 \times 10^9$
• Small numbers: $0.0071 = 7.1 \times 10^{-3}$

Significant figures and rounding

What are significant figures

Significant figures show the level of accuracy needed in your calculations. They represent the meaningful digits in a number that contribute to its precision.

For instance, when measuring a cylinder's volume as 345.3247 cm³, expressing this to four significant figures gives you 345.3 cm³. This provides appropriate accuracy without false precision.

Rounding with significant figures

Understanding when to round up or down is crucial for accurate calculations. The rule depends on the digit that comes after your desired precision:

When rounding to the nearest 10, 100, or 1000, look at the last digit. If it's 5, 6, 7, 8, or 9, round the number upward. For example, 47 becomes 50 when rounded to the nearest ten. However, if the last digit is 0, 1, 2, 3, or 4, round downward - so 43 becomes 40.

Working with ratios, scales, fractions and percentages

Understanding ratios

Ratios demonstrate how quantities relate to each other in proportional relationships. They're particularly useful when you need to divide something into specific parts or combine materials in precise amounts.

Consider a steel bar that's 10 cm long, divided in the ratio 2:3. This means the material splits into 5 total parts (2 + 3), with the sections measuring according to these proportions.

Using scales effectively

Scales enable you to represent large objects in smaller drawings while maintaining accurate proportions. When you see "Scale 2:1" on a technical drawing, this indicates the drawing is twice the actual size. Conversely, if something appears 5 cm long on the page, the real object measures 10 cm when built at full scale.

Any measurements you take from the scaled drawing will need converting to find the actual dimensions of the finished object.

Fractions as proportions

Fractions represent parts of a whole, helping you understand proportional relationships. A proper fraction like $\frac{1}{2}$ shows a portion less than the complete amount, while an improper fraction like $\frac{5}{2}$ represents more than one whole unit.

Percentage applications

Percentages express ratios or fractions as parts of 100, making them easy to understand and compare. When you see "50%", this equals one-half $\left(\frac{1}{2}\right)$ or the ratio 1:2.

Worked example with real applications

This example shows how mathematical skills connect in real-world situations, from basic ratio calculations to percentage conversions and appropriate rounding.

Practice makes perfect

Try working with different scenarios involving volumes, measurements, and proportional relationships. The more you practice these skills, the more confident you'll become at recognising which mathematical tools to use in different situations.

Remember that accuracy matters, but so does using appropriate precision for your specific context. A measurement doesn't need to be calculated to 10 decimal places if your situation only requires whole numbers!