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.The first three patterns are made of dots and follow a rule. How many dots will the fifth pattern have?[3]
Text description of the figure
Three dot patterns in a row. The first has one column of 2 dots with a single dot above it, making 3. The second has two columns of 2 dots with a single dot above, making 5. The third has three columns of 2 dots with a single dot above, making 7.
A9
B10
C11
D13
E14
2.A pattern of tiles repeats: black, black, white. What colour is the 100th tile?[3]
Ablack
Bwhite
Cit depends where you start counting
Dgrey, because the pattern breaks
Ethere is no 100th tile
3.A sequence begins 7, 11, 15, 19, and continues with the same constant step. What is the 30th term?[3]
A123
B127
C120
D119
E137
4.A sequence is defined by a(1) = 2 and a(n+1) = 2 a(n) - 1 for every n. What is a(6)?[3]
A33
B31
C64
D17
E63
5.Beads are threaded in the repeating order red, green, blue, yellow. What colour is the 30th bead?[4]
Ared
Bgreen
Cblue
Dyellow
Eit depends where you start
6.A sequence starts 4, 7, 10, 13 and continues in the same way. What is the 20th term?[4]
A57
B60
C61
D63
E64
7.Dots are arranged in triangles: 1 dot, then 3, then 6, then 10, and so on. How many dots does the tenth triangle have?[4]
A36
B45
C55
D66
E100
8.A staircase of blocks has 4 blocks in the first step, 7 in the second and 10 in the third. How many blocks are in the eighth step?[4]
A22
B24
C25
D28
E32
9.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?[4]
A64
B15
C36
D72
E81
10.A machine turns 3 into 7, 5 into 11 and 8 into 17. What does it turn 12 into?[5]
A19
B21
C24
D25
E29
Math Kangaroo Star · https://kangaroo-atlas.vercel.app · seed 2 · 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.C — 11KA-0008Continuing a visual pattern
AI continued the pattern to the fourth stage and stopped one stage early.
BI counted only the columns of two and forgot the single dot sitting on top of each pattern.
DI continued the pattern one stage too far and gave the sixth pattern instead of the fifth.
EI doubled the third pattern's count, assuming the pattern doubles rather than grows by a fixed amount.
2.A — blackKA-0108Repeating cycles and position mod n
BI got a remainder of 1 but read the last colour of the repeat rather than the first.
CI thought the pattern had no fixed first tile, even though tile one is given.
DI assumed a repeating pattern must eventually change.
EI assumed the pattern runs only for as many tiles as one repeat contains.
3.A — 123KA-0160Arithmetic sequences and the nth term
BI multiplied the step by 30 instead of by 29, forgetting that the first term needs no steps.
CI used 4 times 30 and forgot to add the starting value.
DI added 28 steps instead of 29, counting the gaps one short.
EI treated the first term as the step and used 7 times 30 minus something close.
4.A — 33KA-0171Recursive rules
BI used the rule 2a(n) - 1 but started the sequence at 1 instead of 2.
CI doubled six times and ignored the minus one entirely.
DI stopped at a(5), one term early.
EI computed 2^6 - 1, applying the minus one only once at the very end.
5.B — greenKA-0014Repeating cycles and position mod n
AI got a remainder of 2 but started counting the colours at zero, which shifted me back one bead.
CI counted the seven whole repeats and then counted three more beads instead of two.
DI divided 30 by 4, got 7 remainder 2, and used the last colour of a repeat as though the remainder were zero.
EI thought the repeating pattern had no fixed starting point, even though bead one is given.
6.C — 61KA-0030Arithmetic sequences and the nth term
AI added the step 18 times, counting the gaps between terms one too few.
BI multiplied the step of 3 by 20 and forgot that the first term is already in place.
DI used a first term of 3 instead of 4 while adding 20 steps.
EI added the step 20 times to the first term instead of 19 times.
7.C — 55KA-0107Growth patterns and figurate numbers
AI stopped at the eighth triangle, losing count while adding the rows.
BI gave the ninth triangle instead of the tenth, being one row short.
DI gave the eleventh triangle, adding one row too many.
EI squared the position number, which describes square patterns rather than triangular ones.
8.C — 25KA-0109Arithmetic sequences and the nth term
AI added the step of 3 six times instead of seven, stopping at the seventh step.
BI multiplied 3 by 8 without adding the first step's blocks.
DI multiplied the step of 3 by 8 and added 4, taking one step too many.
EI multiplied the first step's 4 blocks by the step number instead of following the pattern.
9.A — 64KA-0156Growth patterns and figurate numbers
BI gave the number of dots in the eighth ROW instead of the whole figure.
CI added the row numbers 1 through 8 instead of the odd numbers of dots.
DI multiplied 8 rows by 9, using a rough average row that is one too large.
EI counted the rows starting from zero and used the ninth square number.
10.D — 25KA-0106Inferring a rule from examples
AI used the rule add 4, which fits the first example but not the others.
BI found a rule from two examples only and never tested it against the third.
CI doubled the input and forgot the extra one that every example needs.
EI used double and add five, which fits none of the examples exactly.