Sketching Curves (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Recognising, Sketching, and Interpreting Linear and Quadratic Graphs
Includes Full Worked Solutions (No graph drawing required)
Paper 1 – Non-Calculator Section
Q1.
Which of the following equations represents a straight line?
A) y = x² + 3
B) y = 2x – 4
C) y = x² – x
D) y = –x² + 6
Solution:
Only B is in the form y = ax + b (linear).
Answer: B
Q2.
For the linear equation y = –3x + 2, state:
a) The gradient
b) The y-intercept
Solution:
a) Gradient = –3
b) y-intercept = 2
Answer:
a) –3 b) 2
Q3.
The quadratic graph y = x² – 9 intersects the x-axis at which points?
Solution:
Set y = 0:
x² – 9 = 0 → x² = 9 → x = ±3
Answer: x = –3 and x = 3
Q4.
The graph of y = –x² + 4x is a curve.
a) Does it open upwards or downwards?
b) What is the y-intercept?
Solution:
a) a = –1 → opens downwards
b) y-intercept: x = 0 → y = –(0)² + 4(0) = 0
Answer:
a) Downwards
b) y = 0
Q5.
For the quadratic equation y = x² – 2x – 3, find:
a) The y-intercept
b) The line of symmetry
Solution:
a) x = 0 → y = 0² – 2×0 – 3 = –3
b) Line of symmetry = –b/2a = –(–2)/(2×1) = 1
Answer:
a) –3
b) x = 1
Paper 2 – Calculator Allowed Section
Q6.
A graph of the function y = 2x + 1 is drawn.
Find the x-intercept (where y = 0).
Solution:
0 = 2x + 1 → 2x = –1 → x = –0.5
Answer: x = –0.5
Q7.
The graph of y = x² – 6x + 8 is a parabola.
Find the coordinates of the x-intercepts (roots).
Solution:
Factor: x² – 6x + 8 = (x – 2)(x – 4)
Roots: x = 2 and x = 4
Answer: (2, 0) and (4, 0)
Q8.
The equation of a straight line is y = 0.5x – 2.
Find the value of y when x = 8.
Solution:
y = 0.5(8) – 2 = 4 – 2 = 2
Answer: y = 2
Q9.
The function y = –x² + 4 is sketched.
State:
a) The shape of the graph
b) The coordinates of the y-intercept
Solution:
a) a = –1 → ∩-shape (opens downwards)
b) x = 0 → y = –(0)² + 4 = 4 → (0, 4)
Answer:
a) ∩-shape
b) (0, 4)
Q10.
Which graph has line of symmetry x = 0?
A) y = x + 1
B) y = –x² + 2
C) y = x² – 4x + 3
D) y = 2x – 5
Solution:
Line of symmetry = –b/2a
Only B has b = 0 → x = –0/(2×–1) = 0
Answer: B
This exam tests all CORE-level objectives for recognising and interpreting linear and quadratic graphs using symmetry, roots, and intercepts — without needing to sketch.