Part A — Cartesian plane, transformations & angles
The Cartesian plane is two number lines crossing at zero (the origin). A coordinate pair (x, y) gives a position: x across first, then y up or down. The axes divide the plane into four quadrants.
Plotting points (four quadrants)
Q1. Write the coordinates of each plotted point on the diagram: the red, green, blue and purple dots.
Q2. Plot and label these on your own grid: A(2, 4), B(−3, 1), C(−2, −4), D(5, −2). Which quadrant is each in?
Q3. A point is reflected across the y-axis. If it started at (3, 2), where does it land?
Transformations
Q4. Describe the transformation: a shape slides 4 right and 2 down. (translation / reflection / rotation?)
Q5. A triangle is rotated 90° clockwise about a point. Does its size change? Does its orientation change?
Angles
Q6. Two angles sit on a straight line. One is 115°. Find the other.
Q7. Find the angle vertically opposite a 47° angle. Explain your reasoning.
Part B — Metric conversion & area
Part B — Metric conversion & area
Metric units connect to the decimal system: each step (mm → cm → m → km) is a multiple of 10, 100 or 1000. The area of a rectangle is found by multiplying length × width, giving an answer in square units.
Converting metric units (length, mass, capacity)
Q1. Convert: (a) 3 m = cm (b) 2500 mL = L (c) 1.5 kg = g (d) 450 cm = m
Q2. A jug holds 1.2 L. How many 200 mL cups can be filled?
Area of rectangles
Q3. Find the area: (a) a rectangle 6 cm × 4 cm (b) a square of side 9 m
Q4. Describe the sequence of steps you used to find a rectangle's area (test it on a 7 cm × 3 cm rectangle).
Q5. A garden bed is 5 m long and 2 m wide. What is its area? If turf costs $8 per square metre, what is the total cost?
Reasoning
Q6. Sam converts 3 m to 30 cm. Explain his mistake and give the correct value.