Mathematical Literacy Level 2 Module 14

Mathematical Literacy NQF 2 Downloaded from hlayiso.com Maths Lit NQF Level 2

Patterns, tables and graphs Module 14 Downloaded from hlayiso.com Maths Lit NQF Level 2

Overview 14.1 Completing tables of values from graphs and formulae 14.2 Drawing straight line graphs Downloaded from hlayiso.com Maths Lit NQF Level 2

Completing tables of values from graphs and formulae Unit 14.1 • We can show patterns using a: • list of numbers • table of values • formula • We can also use a graph. Graph A graph summarises how one quantity changes if another quantity that is related to it also changes. ” Downloaded from hlayiso.com Maths Lit NQF Level 2

Completing tables of values from graphs and formulae Unit 14.1 • A point on a graph shows two numbers, a number on the horizontal axis and a number on the vertical axis. • The two numbers at a point form an ordered pair. • The point shown here is (4; 3), 4 on the horizontal axis, 3 on the vertical axis. • The number on the horizontal axis is always written first. Downloaded from hlayiso.com Maths Lit NQF Level 2

Reading values off graphs Unit 14.1 Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 14.1 page 260 Unit 14.1 • A caterer supplies a certain number of cakes, depending on the number of people at an event. • The graph shows the relationship between the number of cakes and the number of people. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 14.1 page 260 continued ... Unit 14.1 • Read the values of each point off the graph. • Draw up a table of values and enter the values shown on the graph. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 14.1 page 260 continued ... Unit 14.1 Step 1: Write the labels from the graph into the table. Number of people Total number of Number of cakes people is independent. Put it in top row of table. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 14.1 page 260 continued ... Unit 14.1 Step 1: Write the labels from the graph into the table. Number of people Total number of Number of cakes cakes is dependent. Put into second row of table. Downloaded from hlayiso.com Maths Lit NQF Level 2

Example 14.1 page 260 continued ... Unit 14.1 Step 1: Write the labels from the graph into the table. Number of people Total number of Number of cakes cakes needed for the number of Step 2: Write the heading of the graph. people. (0; 0) (2; 1) (2; 4) Step 3: Read off the ordered pair for each point. Step 4: Write the values into the table. Number of people 0 1 2 Total number of 0 2 4 cakes Downloaded from hlayiso.com Maths Lit NQF Level 2

Using formulae to determine values of variables using substitution Unit 14.1 • In formulae, variables represent unknown values. • Variables are usually letters. • If you know the value of one unknown, you can find the other. • Substitute numbers for the variables. If a = 35b + 10 and b = 3, then a = 35(3) + 10 a = 105 + 10 = 115 Substitution Substitution means putting a number in place of a letter in an equation. Downloaded from hlayiso.com ” Maths Lit NQF Level 2

Exercise 14.1 Unit 14.1 Complete Exercise 14.1 on page 262 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Drawing straight line graphs Unit 14.2 • To draw a graph, you need to: • use a given table of values • work out a table of values from a formula • draw a system of axes with an appropriate scale for each axis • write labels for the graph and both axes • plot the points as ordered pairs from the table of values Downloaded from hlayiso.com Maths Lit NQF Level 2

The axis of the graph Unit 14.2 • An axis is a reference line, which is numbered and labelled. • The place where the two axes cross is called the origin. It is the point (0; 0). • Use the horizontal axis, or x- axis, for your independent variable. • The vertical axis (y-axis) shows the dependent variable. 'axes' is the plural of 'axis' Downloaded from hlayiso.com Maths Lit NQF Level 2

Plotting points Unit 14.2 To plot the point representing the coordinate pair (3; 2): 1. Start at the origin (0; 0). 2. Move along the horizontal axis until you reach 3. 3. Move upwards until you are in line with 2 on the vertical axis. 4. Make a mark with your pencil at that point. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 14.2 Unit 14.2 Complete Exercise 14.2 on page 271 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Graphs of direct proportion and inverse proportion relationships Unit 14.3 If two quantities are directly proportional, the graph to represent the quantities will form a straight line. • In this graph, you can calculate the cost of the trip for any distance travelled by multiplying the distance by the constant of proportionality, which is ½ (half). • If you double one variable, the other will be doubled. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 • If two quantities are in inverse proportion, one quantity increases while the other decreases in the same proportion. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 1 60 min • The more people are helping to complete a job, the shorter the time it will take. So the number of people and the time taken to complete the job can be inversely proportional to each other. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 2 30 min • The more people are helping to complete a job, the shorter the time it will take. So the number of people and the time taken to complete the job can be inversely proportional to each other. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 3 20 min • The more people are helping to complete a job, the shorter the time it will take. So the number of people and the time taken to complete the job can be inversely proportional to each other. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 4 15 min • The more people are helping to complete a job, the shorter the time it will take. So the number of people and the time taken to complete the job can be inversely proportional to each other. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 4 2× 15 min • Check if one variable halves when you double the other one. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 2 30 min • Check if one variable halves when you double the other one. Downloaded from hlayiso.com Maths Lit NQF Level 2

Inverse proportion Unit 14.3 1 2 3 4 × × × × 60 30 20 15 = 60 = 60 = 60 = 60 • If you multiply the two quantities together, their product always remains constant (the same). Downloaded from hlayiso.com Maths Lit NQF Level 2

Graph for inverse proportion Unit 14.3 • A graph of two variables that are inversely proportional to each other, always has the shape called a hyperbola. • In theory, a hyperbola can also have negative values for x and y. Downloaded from hlayiso.com Maths Lit NQF Level 2

Exercise 14.3 Unit 14.2 Complete Exercise 14.3 on page 274 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

Module assessment Module 14 Complete Module assessment on page 276 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 2

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