Graphs and functions are essential parts of the Elementary Mathematics (E-Math) syllabus in Singapore, and they form a key foundation for understanding many real-life applications of math. Whether it’s reading graphs, solving equations, or understanding how changes affect outcomes, this topic is critical for students aiming to score well in the O-Level E-Math exam.
In this beginner-friendly guide, we’ll explore everything you need to know about graphs and functions in E-Math—what they are, how to master them, and how they’re tested in Singapore’s curriculum.
1. What Are Functions and Graphs in E-Math?
In E-Math, a function is a relationship between inputs (usually x-values) and outputs (y-values). A graph is a visual way to represent this relationship.
For example, the function y=2x+1y = 2x + 1 tells us how y changes when x changes. The corresponding graph is a straight line that slopes upward.
Students are expected to:
- Understand linear and quadratic functions
- Draw and interpret graphs
- Use graphs to solve equations and real-life problems
2. Why This Topic Matters in E-Math
Graphs and functions show up frequently in exams and real-world contexts. You’ll use them in:
- Solving algebraic equations
- Modelling real-life relationships (distance-time graphs, cost-revenue, etc.)
- Understanding rates of change
- Geometry and statistics applications
Plus, this topic helps build intuition for more complex math in A-Math, JC, and beyond.
3. Key Graph Types in the E-Math Syllabus
There are several types of graphs you must be familiar with for the O-Level E-Math exam:
Linear Graphs
- Equation form: y=mx+cy = mx + c
- m = gradient (slope), c = y-intercept
- Straight line, constant rate of change
- Example: Speed-time, cost models
Quadratic Graphs
- Equation form: y=ax2+bx+cy = ax^2 + bx + c
- U-shaped curve (called a parabola)
- Vertex is the maximum or minimum point
- Used to solve quadratic equations graphically
Distance-Time & Speed-Time Graphs
- Distance-time: gradient = speed
- Speed-time: area under graph = distance
- Must interpret changes in gradient or flat lines
Other Graphs
- Reciprocal: y=1xy = \frac{1}{x}
- Exponential growth and decay (e.g., interest, bacteria growth)
- Piecewise (multiple segments with different gradients)
4. Important Concepts to Understand
Before jumping into graphing, you must be confident in:
- Coordinates: (x, y) points on the Cartesian plane
- Gradient: Rise over run = ΔyΔx\frac{\Delta y}{\Delta x}
- Intercepts: Where the graph crosses axes (x-intercept when y = 0)
- Solving equations graphically: Intersection points = solution
- Tables of values: Plugging in x-values to get y-values
💡 Tip: Always label your axes clearly and plot your points neatly.
5. How to Plot a Graph Step-by-Step
Let’s say you’re asked to plot y=x2−4y = x^2 – 4.
Step 1: Create a Table of Values
Choose x-values from -3 to 3.
Calculate corresponding y-values.
| x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|---|---|
| y | 5 | 0 | -3 | -4 | -3 | 0 | 5 |
Step 2: Plot the Points
Plot each (x, y) point on the graph paper.
Step 3: Draw the Curve or Line
Use a smooth curve (for quadratics) or straight edge (for linear graphs).
Step 4: Label the Graph
Write the equation and mark the intercepts, turning point, and axis of symmetry if needed.
6. Common Graph Questions in the O-Level Exam
Expect these question formats:
| Question Type | Topic | Difficulty |
|---|---|---|
| Draw the graph of a function | Graph plotting | Easy |
| Find the gradient of a straight line | Linear graphs | Easy |
| Find the coordinates of the minimum point | Quadratic graph | Moderate |
| Use a graph to solve an equation (e.g. find x) | Graph solving | Moderate |
| Interpret real-life graphs (e.g. distance-time) | Application | Hard |
| Calculate area under speed-time graph | Integration (conceptual) | Moderate |
7. Real-World Applications in E-Math
Many graph questions are tied to real-life contexts, such as:
- A car’s journey over time (distance-time graph)
- Sales increasing over time (linear or exponential)
- Cooling of an object (exponential decay)
- Cost of items bought (linear relationship)
Understanding these helps you interpret graphs not just for exams—but in practical scenarios too.
8. Common Mistakes Students Make
Avoid these to protect your marks:
- Wrong scale on axes – makes graph inaccurate
- Plotting errors – misplacing even one point ruins curve
- Not labelling graph lines – unclear for markers
- Forgetting units – e.g., time in seconds or distance in km
- Using too few points – makes curve/line unreliable
- Ignoring context – e.g., speed can’t be negative
📝 Reminder: Always use graph paper and a pencil in exams. Rulers are essential!
9. How to Study Graphs and Functions Effectively
Here’s a proven strategy:
Start with Understanding Concepts
Don’t jump straight into plotting. First, understand what the function means and what the graph should look like.
Use Graph Sketching Apps or Tools
Try apps like Desmos, GeoGebra, or even Google Search (type a function like “y = 2x + 3”) to instantly visualise graphs.
Practise Drawing By Hand
Exams require hand-drawn graphs. Build accuracy and speed by drawing them manually.
Work on Past Year Papers
Practice from the Ten-Year Series (TYS) or your school’s prelim papers. Pay special attention to graph-related problem-solving.
Test Yourself
Give yourself 10 minutes to complete a graph question. Set a timer. Check accuracy after.
10. Helpful Formulas and Tips
- Gradient formula: m=y2−y1x2−x1m = \frac{y_2 – y_1}{x_2 – x_1}
- y-intercept: where x = 0
- To find x when y = 0, solve the equation y=mx+cy = mx + c for x
- Area under speed-time graph: use trapezium or rectangle formulas
- Turning point of a quadratic: can be estimated from the graph if not asked algebraically
Create a formula cheat sheet and review it before each test.
Conclusion: Graphs Are Visual, Scoring & Practical
Graphs and functions aren’t just theoretical—they’re real, visual, and often very scoring if done carefully. Once you get comfortable with identifying patterns, plotting accurately, and interpreting relationships, this topic can become a major asset in your O-Level preparation.
To recap:
- Learn the key graph types
- Practise plotting accurately
- Use graph paper and neat presentation
- Apply graph understanding to real-world scenarios
- Avoid common mistakes with consistent practice
With the right mindset and preparation, you can master graphs and functions in E-Math—and give your grades a significant boost!