Graphs of Functions (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Graphs of Functions – Linear, Quadratic, Reciprocal & Graphical Solutions
Includes Full Worked Solutions
(No graph plotting required – exam-style interpretation and calculation questions only)
Paper 1 – Non-Calculator Section
Q1.
Complete the table for the function y = 2x – 1 for x = –2, –1, 0, 1, 2
| x | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y = 2x – 1 |
Solution:
- x = –2 → y = 2(–2) – 1 = –4 – 1 = –5
- x = –1 → y = 2(–1) – 1 = –2 – 1 = –3
- x = 0 → y = 2(0) – 1 = –1
- x = 1 → y = 2(1) – 1 = 1
- x = 2 → y = 2(2) – 1 = 4 – 1 = 3
Answer:
| x | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| y | –5 | –3 | –1 | 1 | 3 |
Q2.
The graph of y = x² – 4 intersects the x-axis at two points.
Find the x-values of these points.
Solution:
Set y = 0:
x² – 4 = 0 → x² = 4 → x = ±2
Answer: x = –2 and x = 2
Q3.
Which of the following is the graph of a reciprocal function?
A) y = x² + 1
B) y = 3x – 2
C) y = 1/x
D) y = x³ – 4x
Solution:
C is the reciprocal form
Answer: C) y = 1/x
Q4.
State the gradient and y-intercept of the line: y = –3x + 5
Solution:
Gradient = –3, y-intercept = 5
Answer: Gradient = –3, y-intercept = 5
Paper 2 – Calculator Allowed Section
Q5.
A graph of y = x² – 2x – 3 is drawn.
a) Find the roots of the equation x² – 2x – 3 = 0 using the graph.
b) Estimate the value of x when y = 2.
Solution:
a) Roots = where graph crosses x-axis → Factorise:
x² – 2x – 3 = (x – 3)(x + 1)
→ Roots at x = –1 and x = 3
b) From table or graph: when y = 2, estimate x-values.
Try x = 0: y = 0 – 0 – 3 = –3
x = 1: y = 1 – 2 – 3 = –4
x = 2: y = 4 – 4 – 3 = –3
Keep checking. When y = 2, approx x = –2 and x = 4 (based on parabola shape)
Answer:
a) x = –1 and x = 3
b) x ≈ –2 and x ≈ 4
Q6.
Complete the table for y = 1/x for x = –2, –1, –0.5, 0.5, 1, 2
| x | –2 | –1 | –0.5 | 0.5 | 1 | 2 |
|---|---|---|---|---|---|---|
| y |
Solution:
- y = 1/x
- x = –2 → y = –0.5
- x = –1 → y = –1
- x = –0.5 → y = –2
- x = 0.5 → y = 2
- x = 1 → y = 1
- x = 2 → y = 0.5
Answer:
| x | –2 | –1 | –0.5 | 0.5 | 1 | 2 |
|---|---|---|---|---|---|---|
| y | –0.5 | –1 | –2 | 2 | 1 | 0.5 |
Q7.
Two functions are drawn:
- Curve: y = x² – 1
- Line: y = x + 1
Find the x-values where the graphs intersect.
Solution:
Solve:
x² – 1 = x + 1 → x² – x – 2 = 0
Factor: (x – 2)(x + 1)
Answer: x = –1 and x = 2
Q8.
The straight line y = 2x – 3 intersects the curve y = x².
Find the coordinates of the points of intersection.
Solution:
Set equal:
2x – 3 = x² → x² – 2x + 3 = 0
This has no real solutions (discriminant < 0)
Answer: No points of intersection
Q9.
A function is given by y = –x² + 4x – 3
a) Is the graph a U-shape or ∩-shape?
b) Find the x-coordinate of the turning point.
Solution:
a) Coefficient of x² is negative → ∩-shape
b) Turning point at x = –b/2a
a = –1, b = 4 → x = –4 / (2×–1) = 2
Answer:
a) ∩-shape
b) x = 2
Q10.
The table below shows values for y = x² + 2x – 3. Complete the missing value.
| x | –3 | –2 | –1 | 0 | 1 | 2 |
|---|---|---|---|---|---|---|
| y | ? | –3 | –4 | –3 | 0 | 5 |
Solution:
x = –3 → y = (–3)² + 2(–3) – 3 = 9 – 6 – 3 = 0
Answer: 0
This practice exam covers all CORE-level content: completing tables of values, interpreting roots and intersections graphically, and understanding linear, quadratic, and reciprocal functions.