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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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72 problemsClear all filters

KA-0066
4 points, difficulty 2 of 3Level 5–6not yet calibrated
The mean of four numbers is 9. Three of them are 5, 8 and 12. What is the fourth?
NUM-15Means, and working backwards from a meanalso LOG-08
KA-0068
4 points, difficulty 2 of 3Level 3–4not yet calibrated
A coin is tossed three times. In how many of the possible outcomes are there exactly two heads?
CNT-02Tree diagramsalso CNT-01, CNT-04
KA-0069
4 points, difficulty 2 of 3Level 5–6not yet calibrated
In a class of 30, 18 play football and 14 play chess. 6 play both. How many play neither?
CNT-10Inclusion–exclusion with two setsalso CNT-09
KA-0073
4 points, difficulty 2 of 3Level 5–6not yet calibrated
How many different four-letter arrangements can be made from the letters of the word MATH, using each letter once?
CNT-05Arrangements of a few objectsalso CNT-03
KA-0074
4 points, difficulty 2 of 3Level 5–6not yet calibrated
Two students are chosen from a group of six to represent the class. How many different pairs are possible?
CNT-06Selections of a few objectsalso CNT-08
KA-0076
4 points, difficulty 2 of 3Level 3–4not yet calibrated
In how many ways can 7 be written as the sum of two different whole numbers bigger than zero? Swapping the order does not make a new way.
CNT-04Caseworkalso CNT-01, NUM-03
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-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-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-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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