# Maths skills

## Percentage Change

You might be asked to calculate the percentage change from some given data. To do this you work out the difference between the two sets of data you are comparing and then divide by the intial value in your set of data. To convert to a percentage you then multiply by 100.

**Example question: **Use the graph below to calculate the percentage increase in the survival rate of people diagnosed with skin cancer in 1961 compared to 2001.

**Step 1:** Identify the survival rate for skin cancer in 1961 and 2001.

**Step 2: **Calculate the difference between the two values: Survival rate in 2001 - survival rate in 1961 = 89 - 48 = 41

**Step 3:** Calcualte the difference divdided by the initial survival rate and then multiply by 100 = (41/48) x 100 = **85.4%**

## Prefixes

You will be expected to know about prefixes and to be able to convert between them. Here is a list of prefixes you need to know:

**10 ^{12 }tera - T**

**10 ^{9 }giga - G**

**10 ^{6 }mega - M**

**10 ^{3 }kilo - k**

**10 ^{-1 }deci - d**

**10 ^{-2 }centi - c**

**10 ^{-3 }milli - m**

**10 ^{-6 }micro - μ **

**10 ^{-9 }nano - n**

**10 ^{-12 }pico - p**

A question about magnification will often expect you to be able to covert between different units. For example you might be given the image size in mm (millimeters) and the real size in micrometers. In order to work out the magnifcation, you need to ensure both are in the same unit.

**To convert from millimeters to micrometers: Times by 1000**

**To convert from micrometers to millimeters: Divide by 1000**

**Example:** 2mm = 2000μm, 5μm = 0.005mm

### Example question

An onion cell has a length of 200**μ**m. Calcualte the magnification if the image size is 20mm.

**Magnification = Image size / Real size**

Before calculating, ensure both numbers have the same prefix. 200**μ**m is equivalent to 0.2mm (divide by 1000)

**Magnification = 20 / 0.2 = 100**

## Calculating a mean value

You may be asked to calculate a mean value from a set of data, such as this one from the AQA Physics specimen paper 6

**To calculate a mean value, add up the data points and divide by the number of data points involved. **

In the table below, the mean reaction time for** Boy 1 **is found by adding the reaction time for each test and dividing by 3.

( 0.28 + 0.27 + 0.26 ) / 3 = 0.27

**Be careful to check for anomalous data.** For **Boy 2, Test 2** contains an anomaly and should not be included when calculating the mean value.

( 0.28 + 0.22 ) / 2 = 0.25