Geometry questions show a shape being cut, fitted, reflected or drawn on a grid; sketch it, then find the property that settles it. For students entering Year 7 or 8, the cooperative test is on 27 February 2027.
A geometry question is about shape and space: lengths, angles, area, turns and reflections. In our ACER-style questions, the shape is doing something. A card is cut and rearranged, tiles fit around a point, a clock is seen in a mirror.
ACER describes its Mathematics test as aiming at mathematical ability rather than school achievement. In our geometry questions, the work is picturing what happens to a shape, then finding the one fact about it that settles the question.
A shape is cut into pieces and put back together differently
Area stays the same; perimeter can change
Fit at a point
Tiles or angles meet around a point
Angles around a point make a full turn
Reflect or turn
A shape or clock is seen in a mirror or rotated
Left and right swap; distances from the mirror stay the same
Shapes on a grid
Corners are given as points on a grid
Split the shape into pieces you can measure
How should your child work a geometry question?
The thread is the same as for every ACER question (read the situation, find the maths, check), and in geometry a sketch carries most of it.
Sketch the situation
Draw it roughly, even if a picture is given. Drawing the cut, the fit or the reflection is how your child sees what changed.
Mark what you know
Write every given length and angle on the sketch. Equal sides and right angles are worth marking too.
Find the property that fixes it
Ask which fact about angles, area or symmetry links what is known to what is asked.
Check against the sketch
Does the answer look about right on the drawing? A long thin strip should have a long perimeter.
Four worked examples
These geometry questions are our own, pitched at ACER's Level 1 Mathematics and set from easier to harder. None is an ACER item. Each one shows the answer and the working; make a rough sketch with your child as you read.
Worked explanation 1
A square card with sides of 12 cm is cut into three identical rectangles. The three rectangles are then placed end to end, short side against short side, to make one long strip. What is the perimeter of the strip?
AA.
48 cm
BB.
72 cm
CC.
76 cm
DD.
80 cm
Answer: D
Answer: D (80 cm)
Each rectangle is 12 cm long and 12 ÷ 3 = 4 cm wide. Placed end to end along the 4 cm sides, the strip is 3 × 12 = 36 cm long and 4 cm wide. Perimeter = 36 + 4 + 36 + 4 = 80 cm.
The trap: 48 cm tempts children who think cutting and rearranging keeps the perimeter the same. The area stays the same, but the perimeter changes.
Why the other options are wrong
A (48 cm): 48 cm is the perimeter of the original square; rearranging changes the perimeter.
B (72 cm): 72 cm counts the two long sides but forgets the two 4 cm ends.
C (76 cm): 76 cm forgets one of the 4 cm ends.
Worked explanation 2
A tiler covers a floor with two kinds of tiles. At every point where tiles meet, there are exactly three tiles: one square and two identical regular polygons (all sides equal and all angles equal). How many sides does each of the identical polygons have?
AA.
6
BB.
8
CC.
10
DD.
12
Answer: B
Answer: B (8)
The angles around a point make 360°. The square takes 90°, leaving 360 − 90 = 270° for the two identical polygons, so each corner angle is 135°. A regular polygon with 135° corners turns 180 − 135 = 45° at each corner, and 360 ÷ 45 = 8. Each polygon is an octagon with 8 sides.
The trap: 6 tempts children because hexagons are familiar floor tiles. A hexagon's corner is 120°, and 120 + 120 + 90 is only 330°, which leaves a gap.
Why the other options are wrong
A (6): Hexagon corners are 120°; two of them with a square make 330°, not 360°.
C (10): A 10-sided shape has 144° corners; two of them with a square make 378°, which overlaps.
D (12): A 12-sided shape has 150° corners; two with a square make 390°, which overlaps.
Worked explanation 3
Ellie looks at a wall clock in a mirror. The clock has only marks, no numbers, so in the mirror it looks like an ordinary clock showing 2:25. What is the real time?
AA.
2:35
BB.
9:25
CC.
9:35
DD.
10:35
Answer: C
Answer: C (9:35)
A mirror swaps left and right, so the minute hand on the 5 (25 minutes) is really on the 7, which is 35 minutes. The hour hand just past the 2 is really just before the 10, so the hour is 9. A quick check: the real time and the mirror time add to 12 hours, and 2:25 + 9:35 = 12:00. The real time is 9:35.
The trap: 10:35 tempts children who do 12:00 − 2:25 as 12 − 2 = 10 and 60 − 25 = 35, forgetting that borrowing the 60 minutes takes an hour away.
Why the other options are wrong
A (2:35): 2:35 flips the minute hand but not the hour hand.
B (9:25): 9:25 flips the hour hand but not the minute hand.
D (10:35): 10:35 forgets that borrowing 60 minutes uses up an hour.
Worked explanation 4
A scientist marks out a square survey plot on a grid map where each small square is 1 m by 1 m. Two corners of the plot that are next to each other (joined by one side of the square) are at the points (1, 2) and (4, 6). What is the area of the plot?
AA.
12 m²
BB.
20 m²
CC.
24 m²
DD.
25 m²
Answer: D
Answer: D (25 m²)
From (1, 2) to (4, 6) is 3 across and 4 up, so the square is tilted. Draw the whole square: it fits exactly inside an upright square 3 + 4 = 7 m wide, with area 7 × 7 = 49 m². The four corner triangles are each half of a 3 by 4 rectangle, so 6 m² each and 24 m² altogether. 49 − 24 = 25 m².
The trap: 12 m² tempts children who multiply the 3 across by the 4 up, treating the side as if it were a rectangle's length and width.
Why the other options are wrong
A (12 m²): 12 m² multiplies 3 by 4, but those are not the sides of the square.
B (20 m²): 20 m² is the perimeter of the square (4 × 5 m), not its area.
C (24 m²): 24 m² is the area of the four corner triangles, not the square.
Which facts should your child know by heart?
Geometry questions move fast when a few facts come without thinking.
Angles on a straight line make a half turn; angles around a point make a full turn.
The angles of a triangle add to a half turn, so the angles of any shape can be found by splitting it into triangles.
A regular shape has equal sides and equal angles. The more sides, the bigger each angle. Shapes fit around a point only if their angles make a full turn, which is why just some regular shapes fit together.
Area and perimeter are different measures. Rearranging pieces keeps the area but can change the perimeter.
A mirror swaps left and right but not up and down.
These are tools, not answers. ACER-style questions ask your child to choose which one the situation needs.
Why can't your child just measure the picture?
ACER does not allow rulers, books or papers, calculators, watches or mobile phones on test day, so there is nothing to measure with. Even with a ruler, a picture may not be drawn exactly to size.
So a picture is a guide to the arrangement, not to the numbers. In the tiling and grid questions, the answer comes from the given lengths and the properties of the shape. Estimating by eye can lead to an option that looks right and isn't.
These slips match the wrong options in the tiling, mirror and grid questions. As you read each working, go back to the sketch together and find the property that wrong option skips.
Thinking rearranging keeps the perimeter. The area is unchanged, but the edges that were inside can end up outside.
Choosing the familiar shape. Hexagons are common floor tiles, but they don't fit the angle left beside a square.
Reflecting half the picture. In a mirror clock, both hands are reflected, not just the minute hand.
Borrowing time like ordinary numbers. Taking minutes from a full hour uses up an hour, which is easy to forget.
Treating a tilted side as a width. On a grid, the steps across and up are not the side of a tilted square.
How hard do ACER geometry questions get?
ACER describes its scholarship tests as designed to be challenging. In our geometry questions, the hardest ones need an extra construction: a line from the centre, a box drawn around a tilted shape, a triangle cut off a corner. Once that line is drawn, the arithmetic is short.
With 32–36 multiple-choice questions in 40 minutes, your child can't try every construction. A useful question to ask is "what shape do I know how to work with, and can I make one here?"
Use real things. Fold and cut paper, then predict the new shape's perimeter before measuring. Look at clocks and writing in a mirror.
Find tiles, pavers and honeycomb patterns, and talk about why those shapes fit together.
Keep grid paper at home. Drawing tilted squares and triangles on it, then boxing them in to find their area, builds the habit the hardest questions need.
Four examples show the method. Practice test 1 has a full Mathematics section on ACER's time, and its results by skill show whether geometry is costing marks.
The geometry lesson in the app has an Interactive version and Notes, and skill drills give more shapes to work. Geometry sits with the other kinds on the ACER Maths sample questions page. Lengths, area and angles also appear in measurement questions, and growing shapes are covered under patterns.
See where your child stands
Practice test 1 marks every answer and shows results by skill: what your child already does well and the three skills to work on next.
Sample
Practise for the real test
Practice test 1 is free. Then packs from A$109 for 12 months, or A$9 a week, per exam.
