Geometry
Graphical representation — the nature and uses of graphs, and graphs of equations and functions.
Geometry (Cat A) — summary notes
- A graph shows the relationship between two quantities — how one changes as the other changes — far faster than a table of numbers.
- Points are plotted on two axes: the horizontal x-axis and the vertical y-axis, written as a coordinate pair (x, y).
- A straight-line graph has the form y = mx + c, where m is the gradient (steepness) and c is the y-intercept (where the line crosses the y-axis).
- The gradient tells you the rate of change — a steeper line means y changes faster for the same change in x.
- In maintenance, graphs appear constantly: calibration curves, temperature-versus-pressure charts and performance data are all read this way.
- Straight line
- y = mx + c
- Gradient
- m = change in y ÷ change in x
A line passes through (0, 3) and has a gradient of 2. Write its equation and find y when x = 4.
It crosses the y-axis at 3, so c = 3 and the equation is y = 2x + 3. At x = 4: y = 2(4) + 3 = 11.
What is the gradient of a line rising from (1, 2) to (5, 10)?
m = (10 − 2) ÷ (5 − 1) = 8 ÷ 4 = 2.
Geometry concept map
Geometry (Cat A)
Geometry quiz
Geometry (Cat A)
1. The horizontal axis on a graph is called the:
2. The vertical axis on a graph is called the:
3. The point where the two axes cross is called the:
4. The coordinates of the origin are:
5. In the coordinate (3, 5), the x-value is:
6. In the coordinate (3, 5), the y-value is:
7. A point with coordinates (4, 0) lies on the:
8. A point with coordinates (0, 6) lies on the:
9. Coordinates are always written in the order:
10. Moving right along the x-axis, the values:
11. To plot the point (2, 3) you go:
12. The point (−2, 1) lies to the:
13. The point (5, −3) lies:
14. Plotting several points and joining them produces a:
15. On graph paper, each small square represents: