Tap a speaker to listen. Then try saying it yourself! Tap it again to stop.
Loading…
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.
This exact URL always produces this exact sheet — bookmark it and the answer key will still match next term. Print with your browser; the controls and the site navigation are left off the page.
1.A three-digit code uses only the digits 1, 2 and 3, and digits may repeat. How many such codes contain at least one 3?[5]
A8
B9
C12
D19
E27
2.On a 4 by 4 board, how many aligned squares of any size are there, counting 1 by 1, 2 by 2, 3 by 3 and 4 by 4?[5]
A16
B20
C26
D30
E36
3.The numbers 1 to 9 are placed in a row in some order. Can every neighbouring pair add up to an odd number?[5]
AYes, and many orders work
BYes, but only one order works
CNo, there are too many odd numbers
DNo, nine places is an odd number of places
EOnly if the row starts with an even number
4.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
5.A and B are different digits. The two-digit number AB added to the two-digit number BA gives 132. What is A + B?[5]
A3
B6
C11
D12
E13
6.Five beads of five different colours are threaded on a circular bracelet. Two bracelets count as the same if one can be turned or flipped into the other. How many different bracelets are there?[5]
A12
B20
C24
D60
E120
7.How many three-digit whole numbers contain at least one digit 7?[5]
A243
B252
C271
D280
E648
8.Ten different whole numbers, each bigger than zero, add up to 100. What is the largest that the biggest of them can be?[5]
A45
B50
C55
D91
E100
9.A drawer holds 12 red socks, 10 blue socks and 8 green socks, all mixed up. You take socks out one at a time in the dark. What is the smallest number of socks you must take to be certain of having three of the same colour?[5]
A4
B7
C9
D13
E3
10.How many diagonals does a convex polygon with 12 sides have? A diagonal joins two vertices that are not already joined by a side.[5]
A54
B66
C108
D120
E42
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 5 · 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.D — 19KA-0018Complementary counting
AI counted the codes that avoid 3 entirely and gave that as my answer without subtracting.
BI counted the codes with a 3 in the first position only and forgot the other two positions.
CI counted the codes with exactly one 3 and forgot the ones with two or three of them.
EI counted every possible code and forgot to remove the ones with no 3 at all.
2.D — 30KA-0047Counting by position (sliding window)
AI counted only the sixteen smallest squares and stopped there.
BI counted the small squares and the single big one, and forgot every size in between.
CI counted the 2 by 2 squares as four rather than nine, splitting the board into blocks.
EI used 4 by 4 positions for every size instead of shrinking the range as the square grows.
3.A — Yes, and many orders workKA-0049Parity of numbers (odd/even behavior)
BI found one arrangement that works and assumed a problem this fiddly could only have one answer.
CI saw five odd numbers against four even ones and called that a mismatch, when a row of nine needs exactly five of one and four of the other.
DI blamed the length of the row rather than checking how many odd and even numbers it has to hold.
EI decided the first number settles it without checking that starting even would need five even numbers, and only four exist.
4.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.
5.D — 12KA-0060Operation puzzles and cryptarithms
AI added the digits of 132 instead of working out what A and B must be.
BI found A + B correctly and then halved it, as if the question wanted one digit.
CI spotted the 11 in the working and gave that instead of the sum it multiplies.
EI found a pair of digits by trial and misadded them by one.
6.A — 12KA-0071Overcount, then correct
BI divided the 120 arrangements by 6 rather than by the 10 movements that leave a bracelet looking the same.
CI allowed for turning the bracelet but forgot it can also be flipped over.
DI halved the 120 for flipping but forgot that turning also gives the same bracelet.
EI counted every arrangement in a line, as if the bracelet had a fixed first bead.
7.B — 252KA-0075Complementary counting
AI counted the numbers made entirely of digits other than 7 in every position, including a leading zero.
CI counted the numbers with a 7 in each position separately and forgot that some were counted twice.
DI added three lots of 90 and one extra hundred, double counting the 700s.
EI counted the numbers with no 7 at all and gave that instead of subtracting it.
8.C — 55KA-0078Extremal / worst-case counting
AI found the smallest possible total of the other nine and gave that instead of what is left.
BI assumed the biggest number could be at most half the total.
DI made the other nine numbers all equal to 1, forgetting that they have to be different from each other.
EI ignored the other nine numbers entirely, as if the biggest could take the whole total.
9.B — 7KA-0157The pigeonhole principle
AI thought that one more than the number of colours must give three of a kind, which only guarantees a PAIR.
CI got to two of each colour, then added one more for each colour instead of one more in total.
DI assumed the worst case meant emptying the largest pile of 12 reds first.
EI answered with the number of socks I want rather than the number I must take to be sure of them.
10.A — 54KA-0177Overcount, then correct
BI counted every line joining two vertices and forgot to remove the 12 sides.
CI counted each diagonal from both of its endpoints and forgot to halve.
DI used 12 x 10 without halving, double counting every diagonal.
EI subtracted 24 rather than 12, removing each side twice.