Stp Mathematics 2a Answers 12
Tabatha Pasqua
STP Mathematics 2A Answers 12
STP Mathematics 2A is a textbook for students who are studying mathematics at Level 5 of the National Curriculum in the UK. It covers topics such as fractions, decimals, percentages, ratio, proportion, algebra, geometry, statistics, and probability. The book contains exercises and investigations for students to practice and apply their skills, as well as revision tests and summary questions at the end of each chapter.
The book also provides answers to some of the exercises and investigations in the back of the book. However, not all of the answers are given, and some of the answers may be incomplete or incorrect. Therefore, students may need to check their work with other sources or consult their teachers for guidance.
In this article, we will provide some of the answers to the exercises and investigations in Chapter 12 of STP Mathematics 2A. Chapter 12 is about statistics and probability, and it covers topics such as collecting and displaying data, finding averages and ranges, calculating probabilities, and using tree diagrams. The answers we provide are based on the second edition of the book, which was published in 2014 by Oxford University Press. We will also explain how we obtained the answers and provide some tips and tricks for solving similar problems.
Exercise 12A: Collecting and displaying data
This exercise is about collecting data from surveys or experiments and displaying them in tables, charts, or graphs. The exercise has four parts: A1 to A4.
A1: Frequency tables
This part is about making frequency tables from raw data. A frequency table shows how often each value or category occurs in a data set. To make a frequency table, we need to:
- Identify the values or categories that are possible in the data set.
- Count how many times each value or category appears in the data set.
- Write the values or categories in one column and their frequencies in another column.
- Label the columns appropriately.
For example, here is a frequency table for the number of pets owned by 20 students:
The first column shows the possible values for the number of pets, and the second column shows how many students have that number of pets. The labels indicate what the columns represent.
Here are some of the answers to A1:
A2: Bar charts
This part is about drawing bar charts from frequency tables. A bar chart is a type of graph that uses rectangular bars to show the frequencies of different values or categories in a data set. To draw a bar chart, we need to:
- Draw two axes: a horizontal axis (x-axis) and a vertical axis (y-axis).
- Label the axes with the names of the variables or categories that are being compared.
- Mark equal intervals along each axis to represent the possible values or categories.
- Draw a bar for each value or category with a height equal to its frequency.
- Make sure the bars are evenly spaced and do not touch each other.
For example, here is a bar chart for the number of pets owned by 20 students:
The x-axis shows the number of pets, and the y-axis shows the frequency. The bars have heights of 4, 7, 5, 3, and 1, corresponding to the frequencies in the table. The bars are separated by gaps to show that the number of pets is a discrete variable.
Here are some of the answers to A2:
A3: Pie charts
This part is about drawing pie charts from frequency tables. A pie chart is a type of graph that uses sectors of a circle to show the relative frequencies of different values or categories in a data set. To draw a pie chart, we need to:
- Calculate the angle of each sector by multiplying the frequency of each value or category by 360 and dividing by the total frequency.
- Draw a circle and mark the centre.
- Choose a starting point on the circle and draw a radius.
- Measure the angle of each sector from the starting point using a protractor and draw another radius.
- Shade or colour each sector to distinguish it from the others.
- Label each sector with the value or category and its frequency or percentage.
For example, here is a pie chart for the number of pets owned by 20 students:
The angle of each sector is calculated by multiplying the frequency by 360 and dividing by 20. For example, the angle for 0 pets is (4/20) x 360 = 72 degrees. The sectors are shaded with different colours and labelled with the number of pets and the percentage. The percentages are calculated by dividing the frequency by 20 and multiplying by 100. For example, the percentage for 0 pets is (4/20) x 100 = 20%.
Here are some of the answers to A3:
A4: Line graphs
This part is about drawing line graphs from tables of data. A line graph is a type of graph that uses points and lines to show how a variable changes over time or in relation to another variable. To draw a line graph, we need to:
- Draw two axes: a horizontal axis (x-axis) and a vertical axis (y-axis).
- Label the axes with the names and units of the variables that are being compared.
- Mark equal intervals along each axis to represent the values of the variables.
- Plot the points for each pair of values using a pencil and a ruler.
- Join the points with straight lines or smooth curves, depending on the type of data.
- Add a title to describe what the graph shows.
For example, here is a line graph for the temperature changes in London over 24 hours:
The x-axis shows the time in hours, and the y-axis shows the temperature in degrees Celsius. The points are plotted using the data from the table, and the lines are drawn using a ruler. The title indicates what the graph shows.
Here are some of the answers to A4:
Exercise 12B: Finding averages and ranges
This exercise is about finding the mean, median, mode, and range of a data set. These are measures of central tendency and dispersion that describe the characteristics of a data set. To find these measures, we need to:
- Sort the data in ascending or descending order.
- Find the mean by adding up all the data values and dividing by the number of data values.
- Find the median by locating the middle value of the data set. If there are an even number of data values, find the average of the middle two values.
- Find the mode by identifying the most frequent value or values in the data set. There may be more than one mode or no mode at all.
- Find the range by subtracting the smallest value from the largest value in the data set.
For example, here are the measures of central tendency and dispersion for the number of pets owned by 20 students:
The mean is calculated by adding up all the numbers of pets and dividing by 20: (0 + 0 + 0 + 0 + 1 + ... + 4) / 20 = 1.6. The median is found by arranging the numbers in order and locating the middle value: 0, 0, 0, 0, 1, 1, 1, ..., 4. Since there are an even number of values, the median is the average of the middle two values: (1 + 1) / 2 = 1.5. The mode is the most frequent value in the data set: 1. The range is found by subtracting the smallest value from the largest value: 4 - 0 = 4.
Here are some of the answers to B1:
Exercise 12C: Calculating probabilities
This exercise is about finding the probability of an event occurring in a random experiment. Probability is a measure of how likely an event is to happen, and it can be expressed as a fraction, a decimal, or a percentage. To find the probability of an event, we need to:
- Identify the possible outcomes of the experiment and how many of them are favourable to the event.
- Divide the number of favourable outcomes by the total number of possible outcomes.
- Simplify the fraction if possible, or convert it to a decimal or a percentage.
For example, here is the probability of getting a head when tossing a fair coin:
The possible outcomes of tossing a coin are head or tail, and only one of them is favourable to getting a head. The probability is calculated by dividing 1 by 2: 1/2. This fraction can be converted to a decimal by dividing the numerator by the denominator: 0.5. It can also be converted to a percentage by multiplying the decimal by 100: 50%.
Here are some of the answers to C1: