Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
15 questions · official format, shuffled order
1 Three corners of a rectangle are at (2, 3), (9, 3) and (9, 7). Where is the fourth corner?
Show worked solution
It sits above (2, 3) and level with (9, 7): (2, 7).
2 A point is 4 units to the right of (5, 6) and 3 units up from it. What are its coordinates?
Show worked solution
(5 + 4, 6 + 3) = (9, 9).
3 The marked cell is B3. Which cell is two columns to the right and one row up?
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Two columns right of B is D; one row up from 3 is 2: D2.
4 From the school, the library is 3 km north. From the library, the pool is 4 km east. From the pool, the park is 3 km south. How far, and in which direction, is the park from the school?
Show worked solution
North 3 then south 3 returns to the school's line; only the 4 km east remains: 4 km east.
5 On a map, 2 cm stands for 1 km. Two towns are 7.5 cm apart on the map. How far apart are they really?
Show worked solution
7.5 ÷ 2 = 3.75 km.
6 Four points are plotted: (1, 1), (5, 1), (5, 4) and (1, 4).1 Joined in order, they make a rectangle.
2 The perimeter of that rectangle is 14 units.
3 Its area is 20 square units.
Which statements are correct?
2 The perimeter of that rectangle is 14 units.
3 Its area is 20 square units.
Which statements are correct?
Show worked solution
Width 4, height 3: a rectangle (1 ✓). Perimeter 2 × (4 + 3) = 14 (2 ✓). Area 4 × 3 = 12, not 20 (3 ✗). 1 and 2.
7 The point (−3, 2) is reflected in the x-axis. Where is its image?
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Same x, opposite y: (−3, −2).
8 The point (4, 1) is turned a quarter turn clockwise about the origin (0, 0). Where does it land?
Show worked solution
Clockwise by 90°, (x, y) becomes (y, −x): (1, −4).
9 Start at (2, 2). Move 3 right, 4 up, 5 left and 1 down. Where do you finish?
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Across: 2 + 3 − 5 = 0. Up: 2 + 4 − 1 = 5. (0, 5).
10 Lee faces north-west and turns 135° clockwise. Which direction is Lee facing now?
Show worked solution
Three 45° steps clockwise from north-west: north, north-east, east.
11 The cell marked X is C2. What is the grid reference of the cell marked Y?
Show worked solution
Y is two columns right of C (so E) and two rows below 2 (so 4): E4.
12 A path goes from (1, 2) straight to (7, 2), then straight to (7, 10). How long is the path?
Show worked solution
6 across + 8 up = 14 units.
13 A floor plan uses the scale 1 cm for 2 m. A room measures 4.5 cm by 3 cm on the plan. What is the real area of the room?
Show worked solution
9 m by 6 m. 9 × 6 = 54 m².
14 Look at the point (−2, −5).
1 It is in the third quadrant.
2 It is 5 units below the x-axis.
3 Its reflection in the y-axis is (−2, 5).
Which statements are correct?
1 It is in the third quadrant.
2 It is 5 units below the x-axis.
3 Its reflection in the y-axis is (−2, 5).
Which statements are correct?
Show worked solution
Both coordinates negative: third quadrant (1 ✓). y = −5 is 5 below the axis (2 ✓). The y-axis reflection is (2, −5), not (−2, 5) (3 ✗). 1 and 2.
15 From the gate, Ava walks 50 m north, then 30 m west, then 20 m south, then 30 m east. Where is she now, measured from the gate?
Show worked solution
North 50 then south 20 leaves 30 m north. West 30 then east 30 cancels. 30 m north.