Skip to main content

Atlas
Problems
Diagnostic
Mock
Papers
About

The whole Atlas

Number & Arithmetic15
Counting18
Geometry & Visualization18
Logic & Deduction11
Patterns & Sequences7
Modeling & Word Problems10
Contest Craft12

Loading…

About
Sign in
Worksheets
Privacy
Terms
License
Contact
GitHub

Code is MIT. Problems, skills, and explanations are CC BY-NC-SA 4.0. Practice never requires an account and nothing here is paywalled.

Independent project. Not affiliated with or endorsed by Math Kangaroo in USA, NFP.

Home
Atlas
Problems
Papers

Browse the problems

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

Sort

Id
Hardest first
Newest

72 problemsClear all filters

KA-0148
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is the smaller angle between the hands of a clock at exactly 4 o'clock?
GEO-18Clock geometry: hands, angles, timesalso GEO-05, NUM-11
KA-0149
4 points, difficulty 2 of 3Level 5–6not yet calibrated
What is the units digit of 3 multiplied by itself 100 times, that is 3 to the power 100?
NUM-07Last-digit behavior of products and powersalso NUM-06, PAT-03
KA-0150
4 points, difficulty 2 of 3Level 3–4not yet calibrated
A diagonal joins two corners of a shape that are not next to each other. How many diagonals does a hexagon have?
CFT-03Try small cases firstalso CNT-08, GEO-06
KA-0154
4 points, difficulty 2 of 3Level 7–8not yet calibrated
In a class of 30 students, 18 play football and 15 play chess. Exactly 7 students do both. How many students play neither?
CNT-10Inclusion–exclusion with two setsalso CNT-09, CFT-01
KA-0155
4 points, difficulty 2 of 3Level 7–8not yet calibrated
A photograph measures 8 cm by 12 cm. It is enlarged so that the shorter side becomes 20 cm, and the shape is not distorted. How long is the longer side of the enlargement?
GEO-16Scaling and similar figuresalso NUM-11, CFT-11
KA-0156
4 points, difficulty 2 of 3Level 7–8not yet calibrated
A pattern is built in rows. The first figure has 1 row, the second has 2 rows, and so on. In every figure, the first row has 1 dot, the second has 3 dots, the third has 5 dots, and each row after has 2 more dots than the one above it. How many dots are in the eighth figure?
PAT-04Growth patterns and figurate numbersalso CFT-03, PAT-02
KA-0163
4 points, difficulty 2 of 3Level 9–10not yet calibrated
A club has 8 members. In how many ways can a group of 3 be chosen to attend a conference, if the three places are all the same?
CNT-06Selections of a few objectsalso CNT-16, CFT-01
KA-0164
4 points, difficulty 2 of 3Level 9–10not yet calibrated
Two triangles are similar. The sides of the smaller are 3/5 as long as the matching sides of the larger. The smaller triangle has area 18 square cm. What is the area of the larger triangle?
GEO-16Scaling and similar figuresalso NUM-11, CFT-11
KA-0165
4 points, difficulty 2 of 3Level 9–10not yet calibrated
Four litres of a solution that is 25 percent acid are mixed with six litres of a solution that is 50 percent acid. What percentage of the mixture is acid?
MOD-08Mixtures and weighted averagesalso NUM-10, CFT-10
KA-0172
4 points, difficulty 2 of 3Level 11–12not yet calibrated
A committee of 4 must be formed from 5 boys and 4 girls, and it must contain exactly 2 boys and 2 girls. How many different committees are possible?
CNT-06Selections of a few objectsalso CNT-04, CNT-16
KA-0173
4 points, difficulty 2 of 3Level 11–12not yet calibrated
Each of the four edges of a square is painted either black or white. Two paintings count as the same if one can be rotated onto the other. How many genuinely different paintings are there?
CNT-15Counting up to symmetryalso CNT-04, LOG-11
KA-0174
4 points, difficulty 2 of 3Level 11–12not yet calibrated
A driver travels from one town to another at an average of 60 km/h and returns along the same road at an average of 40 km/h. What is the average speed for the whole journey?
MOD-03Rate, time, distancealso MOD-08, CFT-11

1
5
6

Showing 61–72 of 72

Browse the problems — Kangaroo Atlas