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.What is the units digit of 7 multiplied by itself 2026 times, that is 7 to the power 2026?[5]
Ait cannot be found without a calculator
B1
C3
D7
E9
2.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
3.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
4.How many two-digit numbers have both of their digits odd?[5]
A10
B20
C25
D45
E50
5.What is the last digit of 3 multiplied by itself 2026 times, that is, of 3 to the power 2026?[5]
A3
B9
C7
D1
E6
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 1 · 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.E — 9KA-0037Last-digit behavior of products and powers
AI assumed a number this large has no reachable last digit and gave up on the cycle.
BI found the cycle 7, 9, 3, 1 but used a remainder of 0 when the remainder is actually 2.
CI found the cycle but counted its positions starting at zero, shifting my answer along by one.
DI assumed the units digit of any power of 7 is always 7.
2.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.
3.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.
4.C — 25KA-0135Digit-constraint puzzles
AI counted the odd numbers in one row of ten and treated that as the whole answer.
BI used four odd digits instead of five, forgetting that 9 is odd.
DI counted every two-digit number that is itself odd, which only fixes the last digit.
EI let the first digit be any of ten values rather than only the five odd ones.
5.B — 9KA-0158Last-digit behavior of products and powers
AI used the first entry of the cycle because 2026 is even, without working out where in the cycle it lands.
CI counted the cycle starting from zero, so a remainder of 2 put me one place too far along.
DI assumed a power that large must end in 1.
EI multiplied 3 by 2 and used the last digit of that.