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177 problems, every one written from scratch, every wrong answer carrying the mistake that produces it. 708 explanations in all.

Level

1–2
3–4
5–6
7–8
9–10
11–12

Point value

3 pt
4 pt
5 pt

Strand

NUMNumber & Arithmetic
CNTCounting
GEOGeometry & Visualization
LOGLogic & Deduction
PATPatterns & Sequences
MODModeling & Word Problems
CFTContest Craft

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34 problemsClear all filters

KA-0052
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
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?
GEO-04Area by subtraction (shaded regions)also GEO-03, GEO-07
KA-0079
3 points, difficulty 1 of 3Level 3–4not yet calibrated
Which of these is true of every rectangle?
GEO-06Properties of triangles and quadrilateralsalso GEO-08
KA-0080
4 points, difficulty 2 of 3Level 5–6not yet calibrated
An isosceles triangle has an angle of 100 degrees. How big is each of the other two angles?
GEO-06Properties of triangles and quadrilateralsalso GEO-05
KA-0081
4 points, difficulty 2 of 3Level 3–4has a figurenot yet calibrated
A solid is built from unit cubes. The two pictures show it from above and from the front. What is the smallest number of cubes it could be made of?
GEO-12Views of a solid: top, front, sidealso GEO-13, CNT-14
KA-0082
5 points, difficulty 3 of 3Level 5–6has a figurenot yet calibrated
A room is 8 m long, 4 m wide and 2 m high. An ant walks across the floor and the walls from one bottom corner to the far top corner. What is the shortest distance in metres?
GEO-17Shortest paths on and around shapesalso GEO-10, GEO-01
KA-0083
3 points, difficulty 1 of 3Level 3–4not yet calibrated
A rectangle has a perimeter of 20 cm. One of its sides is 6 cm. What is its area in square centimetres?
GEO-01Perimeter and area of rectilinear shapes
KA-0084
4 points, difficulty 2 of 3Level 5–6not yet calibrated
A square of side 6 cm is cut along a midline into two identical rectangles. What is the perimeter of one of them?
GEO-03Area by dissection and rearrangementalso GEO-01
KA-0085
4 points, difficulty 2 of 3Level 3–4not yet calibrated
How many lines of symmetry does a regular hexagon have?
GEO-08Line and rotational symmetryalso GEO-09
KA-0086
3 points, difficulty 1 of 3Level 3–4not yet calibrated
A floor measuring 6 by 4 units is covered exactly with tiles measuring 2 by 1, with no gaps and no overlaps. How many tiles are needed?
GEO-14Tiling and tessellationalso GEO-01
KA-0087
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Two similar triangles have areas of 9 and 25 square units. A side of the smaller one is 6 units. How long is the matching side of the larger one?
GEO-16Scaling and similar figuresalso NUM-11
KA-0088
3 points, difficulty 1 of 3Level 5–6not yet calibrated
Three angles of a quadrilateral are 80, 95 and 110 degrees. What is the fourth angle?
GEO-05Angles on lines, in triangles, in polygonsalso GEO-06
KA-0089
4 points, difficulty 2 of 3Level 3–4not yet calibrated
A cube 3 units on each side is built from unit cubes and painted all over the outside. How many of the small cubes have no paint on them at all?
GEO-13Building and counting with unit cubesalso CNT-14

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