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Worksheet generator
Pick what you want, print the page. The answer key comes with it, on its own sheet, and it tells you the mistake behind every wrong choice — not just which letter is right.
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1.In a triangle, one angle is 90 degrees and another is 35 degrees. What is the third angle?[3]
A35 degrees
B45 degrees
C55 degrees
D65 degrees
E145 degrees
2.What is the angle between the hands of a clock at exactly 3 o'clock?[3]
Text description of the figure
A clock face with the hour hand pointing at 3 and the minute hand pointing at 12, with the angle between them marked.
A30 degrees
B45 degrees
C90 degrees
D120 degrees
E180 degrees
3.Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?[3]
A65
B75
C85
D95
E105
4.A counter sits at the point (3, 5) on a grid. It moves 4 squares right and 2 squares down. Where is it now?[3]
A(1, 3)
B(1, 7)
C(5, 3)
D(7, 7)
E(7, 3)
5.A flag shape is rotated a quarter turn clockwise about its bottom-left corner. Which of the descriptions matches the result?[4]
Text description of the figure
A flag shape drawn as an upright pole with a small triangle attached to the top right of the pole, standing on a marked corner point at the bottom of the pole.
Athe pole points right and the triangle is below it
Bthe pole points right and the triangle is above it
Cthe pole points left and the triangle is above it
Dthe pole points down and the triangle is to the left
Ethe pole points up and the triangle is on the left
6.A photograph is enlarged so that each side becomes 3 times as long. How many times bigger is its area?[4]
A3 times
B6 times
C9 times
D12 times
E27 times
7.A square of side 6 cm is cut along a midline into two identical rectangles. What is the perimeter of one of them?[4]
A12
B15
C18
D24
E36
8.Two circles touch on the outside. One has a radius of 3 cm and the other a radius of 5 cm. How many centimetres apart are their centres?[4]
A2
B4
C8
D15
E16
9.What is the smaller angle between the hands of a clock at exactly 4 o'clock?[4]
A30
B60
C90
D120
E240
10.A circle of radius 5 is drawn inside a square of side 10, touching all four sides. What fraction of the square is outside the circle, to the nearest tenth?[5]
Text description of the figure
A square with a circle drawn inside it, the circle touching the midpoint of each of the four sides. The region inside the square but outside the circle is shaded.
A0.1
B0.2
C0.3
D0.5
E0.8
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 9 · CC BY-NC-SA 4.0 · Independent project, not affiliated with Math Kangaroo in USA, NFP.
Answer key — Math Kangaroo practice
Each wrong choice carries the thinking that produces it. When a student picks C, this is what they were doing.
1.C — 55 degreesKA-0022Angles on lines, in triangles, in polygons
AI assumed the triangle was isosceles because it had a right angle, so I repeated the 35.
BI assumed a right-angled triangle always has two 45 degree angles.
DI subtracted 35 from 100 instead of from 90, mixing the angle sum up with a round number.
EI subtracted only the 35 from 180 and forgot to take off the right angle as well.
2.C — 90 degreesKA-0032Clock geometry: hands, angles, times
AI gave the angle for one hour mark instead of the three hour marks between the hands.
BI divided the right angle in half, as if a quarter of the clock were 45 degrees.
DI used a third of the clock face rather than a quarter of it.
EI read 3 o'clock as the hands pointing in opposite directions.
3.B — 75KA-0088Angles on lines, in triangles, in polygons
AI added the three angles wrongly, getting 295 instead of 285.
CI used an angle sum of 370, mis-remembering the total for a quadrilateral.
DI repeated one of the given angles instead of computing the missing one.
EI used the triangle's 180 degrees and then adjusted, rather than the quadrilateral's 360.
4.E — (7, 3)KA-0145Grid coordinates and lattice reasoning
AI moved left instead of right, subtracting the 4 rather than adding it.
BI moved left and up, reversing both directions.
CI swapped the two coordinates round before moving.
DI moved up instead of down, adding the 2 rather than subtracting it.
5.A — the pole points right and the triangle is below itKA-0039Reflections, rotations, translations
BI turned the pole the right way but kept the triangle on the side it started on.
CI turned the shape anticlockwise instead of clockwise.
DI turned the shape half a turn instead of a quarter turn.
EI reflected the shape in a vertical line instead of rotating it.
6.C — 9 timesKA-0042Scaling and similar figures
AI applied the length scale factor straight to the area.
BI doubled the scale factor because area involves two dimensions, instead of squaring it.
DI multiplied the scale factor by four, as though area scaled with the number of sides.
EI cubed the scale factor, which is the rule for volume rather than area.
7.C — 18KA-0084Area by dissection and rearrangement
AI added the two different side lengths without doubling for the opposite pair.
BI halved the square's perimeter of 24 and adjusted by three, treating the cut as if it removed length.
DI gave the perimeter of the whole square instead of one of the pieces.
EI gave the area of the square rather than the perimeter of a piece.
8.C — 8KA-0147Circles: radius, diameter, and touching circles
AI subtracted the radii, which is the answer when one circle sits inside the other.
BI averaged the two radii instead of adding them.
DI multiplied the radii together rather than adding them.
EI added the two diameters instead of the two radii.
9.D — 120KA-0148Clock geometry: hands, angles, times
AI gave the angle for a single hour mark rather than the four marks between the hands.
BI counted two hour marks instead of four.
CI assumed any gap of a few hours is a right angle, as it is at three o'clock.
EI measured the angle the long way round the clock face instead of the smaller one.
10.B — 0.2KA-0052Area by subtraction (shaded regions)
AI estimated by eye from the four corner pieces without comparing them to the whole square.
CI used a diameter of 5 instead of a radius of 5 when working out the circle's area.
DI assumed the circle covers half the square because it touches all four sides.
EI found the fraction covered by the circle and gave that instead of the fraction outside it.