Coordinates (Copy)
IGCSE Mathematics 0580 – CORE Practice Exam
Topic: Cartesian Coordinates (Two Dimensions)
Includes Full Worked Solutions
Paper 1 – Non-Calculator Section
Q1.
Plot the following points on a coordinate grid:
A(2, 3), B(–4, 1), C(–2, –5), D(3, –2)
Which quadrant is each point in?
Solution:
- A(2, 3) → Quadrant I (both positive)
- B(–4, 1) → Quadrant II (x negative, y positive)
- C(–2, –5) → Quadrant III (both negative)
- D(3, –2) → Quadrant IV (x positive, y negative)
Answer:
A → Quadrant I
B → Quadrant II
C → Quadrant III
D → Quadrant IV
Q2.
State the coordinates of the point that is:
a) 4 units to the right and 2 units up from the origin.
b) 3 units to the left and 5 units down from the origin.
Solution:
a) Right = positive x → x = 4, Up = positive y → y = 2
Coordinates: (4, 2)
b) Left = negative x → x = –3, Down = negative y → y = –5
Coordinates: (–3, –5)
Answer:
a) (4, 2)
b) (–3, –5)
Q3.
Write down the coordinates of the midpoint between P(2, 6) and Q(6, 2).
Solution:
Midpoint = (2+62,6+22)left( frac{2+6}{2}, frac{6+2}{2} right)
= (4, 4)
Answer: (4, 4)
Q4.
A point E has coordinates (0, 5).
a) Is it on the x-axis, y-axis, or neither?
b) Which quadrant is it in?
Solution:
a) x = 0 → It is on the y-axis.
b) Not in any quadrant since it’s on the axis.
Answer:
a) y-axis
b) No quadrant (on axis)
Paper 2 – Calculator Allowed Section
Q5.
Find the distance between the points F(1, 2) and G(1, 7) by counting squares.
Solution:
- x-values are the same (both 1), so vertical distance.
- y changes from 2 to 7 → Difference = 7 – 2 = 5 units
Answer: 5 units
Q6.
Point H is (–2, 4).
After moving 5 units right and 3 units down, what are the new coordinates?
Solution:
- 5 units right → add 5 to x: –2 + 5 = 3
- 3 units down → subtract 3 from y: 4 – 3 = 1
New coordinates: (3, 1)
Answer: (3, 1)
Q7.
Find the midpoint between points J(–5, 3) and K(1, –1).
Solution:
Midpoint = (–5+12,3+(−1)2)left( frac{–5+1}{2}, frac{3+(-1)}{2} right)
= (–42,22)left( frac{–4}{2}, frac{2}{2} right)
= (–2, 1)
Answer: (–2, 1)
Q8.
The coordinates of point M are (x, y).
If x is positive and y is negative, in which quadrant is M?
Solution:
Positive x and negative y → Quadrant IV.
Answer: Quadrant IV
Q9.
What are the coordinates of a point that is located exactly halfway between (0, 0) and (8, –4)?
Solution:
Midpoint = (0+82,0+(−4)2)left( frac{0+8}{2}, frac{0+(-4)}{2} right)
= (4, –2)
Answer: (4, –2)
Q10.
Identify the point among the following that lies on the x-axis:
A(3, 0), B(0, 3), C(–4, 2), D(1, –1)
Solution:
Point on x-axis has y = 0.
Only A(3, 0) satisfies this.
Answer: A(3, 0)
This practice exam covers all CORE-level skills related to Cartesian coordinates, including plotting, interpreting quadrants, midpoints, and simple translations.