Relationships Between Quantities

Direct Proportion, Inverse Proportion, Fixed vs Variable, and Independent vs Dependent Variables

CAPS Grade 10 Mathematical Literacy

This document explores the essential relationships between quantities as outlined in the Grade 10 Mathematical Literacy CAPS curriculum. It delves into direct proportion, inverse proportion, fixed versus variable relationships, and independent versus dependent variables.

1. Direct Proportion Relationships

Key Concept

If one quantity doubles, the other also doubles.

Example: Petrol cost - 1L = R22, 2L = R44

Graph Representation

Straight line starting from origin (0,0)

Line passes through (0,0)

Direct Proportion

3 Questions
1 3 apples cost R15. Cost for 6 apples?
R20
R25
R30
R35
2 Car travels 60 km in 1 hour. Distance in 3 hours?
120 km
150 km
180 km
200 km
3 Which graph represents direct proportion?
Line through (0,0)
Curve
Horizontal line
Vertical line
0/3

2. Inverse Proportion Relationships

Key Concept

If one quantity doubles, the other halves.

Example: More workers = fewer days

Graph Representation

Descending curve that never touches axes

Curve approaches axes but never touches

Inverse Proportion

3 Questions
1 2 builders take 12 days. Time for 4 builders?
3 days
6 days
12 days
24 days
2 At 60 km/h, trip takes 4 hours. Time at 120 km/h?
1 hour
2 hours
4 hours
8 hours
3 Which graph represents inverse proportion?
Line through (0,0)
Descending curve
Horizontal line
Vertical line
0/3

3. Fixed vs. Variable Relationships

Fixed Quantity

Cost that remains constant regardless of usage.

Examples: Monthly line rental, base fare

Variable Quantity

Cost that changes based on usage.

Examples: R2 per minute, R15 per km

Formula

Total Cost = Fixed Cost + (Variable Rate × Usage)

Fixed vs Variable Challenge

Taxi: R20 base + R15/km. Cost for 8 km?
Hint: Total = Fixed + (Rate × Usage)

4. Independent vs. Dependent Variables

Variable Type Definition Example Axis
Independent (IV) Variable you can change/control Hours worked x-axis
Dependent (DV) Variable that depends on IV Money earned y-axis

Example

"How does study time affect test scores?"
IV = Study time | DV = Test scores

Independent vs Dependent

3 Questions
1 In "distance depends on time", independent variable is:
Distance
Time
Speed
Both
2 Which variable is plotted on the y-axis?
Independent
Dependent
Both
Neither
3 "Cost depends on litres bought." Dependent variable is:
Litres
Cost
Price per litre
None
0/3

Exam Tip: When describing relationships, avoid vague statements like "it goes up." Use specific terminology: "There is a direct proportion between items bought and total cost."

Final Assessment

8 Questions
1 5 kg potatoes cost R45. Cost for 8 kg?
R60
R72
R80
R90
2 3 workers take 8 hours. Time for 6 workers?
2 hours
4 hours
8 hours
16 hours
3 Phone: R100 monthly + R1.50/min. Cost for 200 min?
R200
R300
R400
R500
4 "Test scores improve with study time." Dependent variable?
Study time
Test scores
Both
Neither
5 Line through (0,0) represents?
Direct proportion
Inverse proportion
Fixed
Variable
6 Taxi: R25 base + R12/km. Fixed cost?
R25
R12
Both
Neither
7 Double speed = half time. This is:
Direct
Inverse
Fixed
No relationship
8 Gym: R300 monthly + R50/session. Cost for 6 sessions?
R300
R500
R600
R900
0/8

Conclusion

Understanding relationships between quantities is fundamental in Mathematical Literacy. By grasping direct and inverse proportions, fixed vs variable relationships, and independent vs dependent variables, students can enhance their mathematical reasoning and apply these principles to real-world situations.