Mathematical Literacy Level 4 Module 12

Mathematical Literacy NQF 4 Downloaded from hlayiso.com Maths Lit NQF Level 4

Tables, graphs and formulae in the workplace Module 12 Downloaded from hlayiso.com Maths Lit NQF Level 4

Overview 12.1 Reading values off graphs 12.2 Plotting graphs of linear relationships 12.3 Graph of inverse proportion functions 12.4 The graph of constant ratio patterns 12.5 Using formulae to determine values of variables using substitution Downloaded from hlayiso.com Maths Lit NQF Level 4

Reading values off graphs Unit 12.1 Completing a table of values by Dependent variable reading values from a graph • A graph shows a number pattern by giving the input numbers on one axis and the output numbers on the other axis. • The shape of the graph shows how the numbers change in relation to each other. • We usually put the independent Vertical axis variable on the horizontal axis, and the dependent variable on the vertical axis. Independent variable Horizontal axis Downloaded from hlayiso.com Maths Lit NQF Level 4

Reading numbers from a graph Unit 12.1 Point A shows R900 for 5 • Look at the numbers on the hours worked. graph and the number of values in between each mark. • The vertical axis in this graph shows R150 between each mark. • Hold a ruler from each point vertically to read the input number on the axis at the bottom. • Hold a ruler horizontally from each point to read the output number on the axis on the left. R150 – 0 = R150 Point B shows R450 for 2½ hours worked. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.1 page 233 Unit 12.1 Look at the graph showing the entry fee for students on a trip to the zoo. a) Draw up a table of values showing the points plotted on this graph. b) What is the flat fee per group of students accompanied by their lecturer? Explain how you know this. c) What is the cost per student? Explain. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.1 page 233 Unit 12.1 d) Is this is a constant difference or a constant ratio pattern? Explain, e) Derive a formula for this relationship. Let n be the number of students and c be the cost. f) Is this relationship a direct proportion? Explain. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.1 page 233 Unit 12.1 a) Table of the pattern: Number of students n 0 20 40 60 80 100 Entry fee (R) 50 150 250 350 450 550 b) The flat fee is R50, because there is a charge of R50 for 0 students. c) The cost for 20 students is R150 – R50 = R100, so the cost per student is R100 ÷ 20 = R5. d) It is a constant difference or linear pattern, because the entry fee increases by R5 for each student that is added. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.1 page 233 Unit 12.1 e) The difference between the values where n increases by 1 is R5, so the formula will contain 5n. The flat fee or constant value is R50. So the formula is c = 50 + 5n. f) This is not a direct proportion, for example 40 student : 20 student is not equal to R250 : R150. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 12.1 Unit 12.1 Complete Exercise 12.1 on page 234 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

How to identify the kind of relationship Unit 12.1 in a graph You can see what kind of graph it is by looking at the shape of the graph. Linear Both graphs below are notgraph or straight line graph in proportion • A straight line can be increasing or decreasing Downloaded from hlayiso.com Maths Lit NQF Level 4

How to identify the kind of relationship Unit 12.1 in a graph Linear graph or straight line graph If a straight line graph starts at zero, it shows a direct proportion • A straight line • Always increasing • Both quantities increase in the same proportion. Downloaded from hlayiso.com Maths Lit NQF Level 4

How to identify the kind of relationship Unit 12.1 in a graph Linear graph or straight line graph An inverse proportion • A curve • Does not touch either of the axes. • As one quantity increases, the other one decreases. Downloaded from hlayiso.com Maths Lit NQF Level 4

How to identify the kind of relationship Unit 12.1 in a graph Linear graph or straight line graph Constant ratio • A curve • An increasing graph. • Touches the vertical axis. • The vertical quantity increases very quickly. • This is called an exponential graph. Downloaded from hlayiso.com Maths Lit NQF Level 4

Plotting graphs of linear relationships Unit 12.2 We can use a written description of a pattern to draw up a table of values, find the formula and draw a graph of the pattern. Choosing an appropriate scale Draw axes to fill the space on the page. This makes the graph more 1 accurate and easier to read. Then use the costs per unit area or per item to calculate the total 2 cost. The highest value on your axes must be higher than the highest 3 values of the variables, usually rounded up to a whole 10. Choose intervals between the marks on your axes that will work 4 well with the values you need to plot. Downloaded from hlayiso.com Maths Lit NQF Level 4

Plotting graphs of linear relationships Unit 12.2 Example • To plot values such as 142, 156 and 178, choose intervals of 10 units apart from 140 to 180. • Choose to increase in multiples of 5 or 10, even when the values to plot are not multiples of 10. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing a graph Petrol (litres) 0 2 4 6 Cost (R) Cost = litres × 15 Petrol (litres) 0 2 4 6 Cost (R) 0 30 60 90 Draw a table of values, unless one is given. Choose at least 4 input values and include 0, to show what the 1 graph does at this point. Fill in the values of the other variable, using the formula or the description.Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing graphs Graph of cost versus petrol Petrol 0 2 4 6 (litres) Cost (R) 0 30 60 90 2 Give your graph a title, usually stating the effect of one variable compared to another, e.g. “Graph of cost versus time”. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing graphs Graph of cost versus petrol Highest value rounded off: 6 90 Petrol 0 2 4 6 (litres) Cost (R) 0 30 60 90 0 6 Highest value rounded off: 90 Choose an appropriate scale to make your graph clear and easy to 3 read. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing graphs Graph of cost versus petrol 90 Petrol 0 2 4 6 Cost( R) (litres) 60 Cost (R) 0 30 60 90 30 0 2 4 6 Petrol (litres) Label both the axes and write the units in which the values are 4 measured. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing graphs Graph of cost versus petrol 90 Petrol 0 2 4 6 Cost (R) (litres) 60 Cost (R) 0 30 60 90 30 0 2 4 6 Petrol (litres) • Plot the points as ordered pairs from the table of values. 5 • Use the horizontal axis (the x-axis) for your independent variable. • The vertical axis (y-axis) takes the dependent variable. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing graphs Graph of cost versus petrol 90 Petrol 0 2 4 6 Cost (R) (litres) 60 Cost (R) 0 30 60 90 30 0 2 4 6 Petrol (litres) 6 Connect the points. Downloaded from hlayiso.com Maths Lit NQF Level 4

Tips for drawing a graph Unit 12.2 Steps for drawing graphs Graph of cost versus petrol 90 Cost ) 60 30 0 2 4 6 Petrol (litres) Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 12.2 Unit 12.2 Complete Exercise 12.2 on page 236 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.2 Mbali is starting her career as a singer, but first she has to build up an audience. At her first show, the audience consisted of only 28 people. At the second show, the audience grew to 53. There were 78 people at the third show. a) Draw up a table to show the pattern if it continues. b) Write a formula to represent the pattern. c) If this pattern continues, how long will it take until there are 303 people at her show? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.2 a) Table of the pattern: Show number 1 2 3 4 5 6 7 Number of people 28 53 78 103 128 153 178 b) The difference between the terms is 25, so the pattern contains 25n. The first show is 25(1) + 3 The second show is 25(2) + 3 So the formula is p = 25n + 3, where p is the number of people and n is the show number. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.2 Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 12.3 Unit 12.2 Complete Exercise 12.3 on page 238 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Graph of inverse proportion functions Unit 12.3 • The graph of this function is known as the hyperbola. • To plot a hyperbola, draw up a table of values and plot enough points to reveal the shape of the graph. • The graph of an inverse proportion: • is a smooth curve with the shape shown here • the curve never touches the axes. Downloaded from hlayiso.com Maths Lit NQF Level 4

Graph of inverse proportion functions Unit 12.3 How to recognise an indirect proportion relationship In an inverse proportion: as one quantity decreases, the other increases OR as one quantity increases, the other decreases. the product of the quantities is always the same. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.3 page 240 Unit 12.3 Area = 32 square units • A piece of cardboard must have a fixed area ? of 32 square units, but it can have different values for the length l and breadth b. ? Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.3 page 240 Unit 12.3 a) Complete the following table of possible values for the length and breadth of the rectangle. Length 1 2 4 8 16 32 Breadth 32 b) Draw a graph to show all the possible values of the length and breadth. c) Is the graph continuous or discrete? Explain. d) Why does the curve not touch the axes Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.3 a) Length 1 2 4 8 16 32 Breadth 32 16 8 4 2 1 b) Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.3 c) The measurement values are continuous values, so the graph is continuous. d) Length and breadth cannot equal zero, so the graph does not touch either of the axes. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 12.4 Unit 12.3 Complete Exercise 12.4 on page 241 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

The graphs of constant rate and constant Unit 12.4 ratio Compare constant rate (Graph A) with constant ratio (Graph B): Graph A: Constant rate Graph A: Constant rate • constant rate of growth • the change is the same between each point of the graph • straight line graph • linear number pattern • constant difference is 20 Year 0 1 2 3 4 5 Value (R) 20 40 60 80 100 120 Downloaded from hlayiso.com Maths Lit NQF Level 4

The graphs of constant rate and constant Unit 12.4 ratio Graph B: Constant ratio Graph B: Constant ratio • Compound growth or exponential graph. • Big differences in the number of sheep from point to point. • The constant ratio is 2. Year 0 1 2 3 4 5 Value (R) 10 20 40 80 160 320 • Doubling is one example of compound growth. • Compound growth is also shown if you save an amount of money and it earns compound interest. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.4 page 243 Unit 12.4 Celeste invests R3 000 at compound interest. The interest is added every year at 10% of the money she has in the account. 1. Fill in the table to show how the money grows. Year 0 1 2 3 4 5 6 7 8 Amount of 1 000 10% of money (R) 1 000 = 1 100 The year that she starts is called year 0, because this is when she puts in the money. 2. Plot the graph of this relationship. Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.4 Note: The amount will be multiplied by 10% (or 0,1) each time to get the next number in the pattern. This is a constant ratio pattern. 1. Year 0 1 2 3 4 Amount of money (R) 1 000 1 100 1 210 1 331 1 464 Year 5 6 7 8 Amount of money (R) 1 610,5 1 771,6 1 948,7 2 143,6 Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 1.4 page 238 Unit 12.3 2. 2200 2000 1800 1600 1400 Money (R) 1200 1000 800 600 400 200 0 0 1 2 3 4 5 6 7 8 Years Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 12.5 Unit 12.4 Complete Exercise 12.5 on page 243 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Using formulae to determine values of variables using substitution Unit 12.5 • In formulae, letters such as x and y, or any letters, are used to represent values which are unknown. They can be used in equations or expressions to help solve problems. • The formulae we have been working with show the relationship between two variables. If we know the value of one variable in an equation, we can find the value of the other. • We can substitute the number for the letter. Substitution Putting a number in place of a letter in an equation. ” Downloaded from hlayiso.com Maths Lit NQF Level 4

Example 12.5 page 244 Unit 12.5 Thami needs to make a circle with an area of 40 cm2. What should the radius of the circle be? The formula for the area of a circle is A = πr2. Use the value of 3,14 for π. Downloaded from hlayiso.com Maths Lit NQF Level 4

Exercise 12.6 Unit 12.5 Complete Exercise 12.6 on page 244 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

Module assessment Module 12 Complete Module assessment on page 246 of your Student’s Book Downloaded from hlayiso.com Maths Lit NQF Level 4

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