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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 19 points

1.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
2.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
3.A sequence starts at 3. Each term after that is double the one before it, minus 1. What is the sixth term?[4]
- A17
- B33
- C65
- D96
- E129
4.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
5.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

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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.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.
2.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.
3.C — 65KA-0103Recursive rules
- AI stopped at the fourth term, counting the starting number as the first step rather than the first term.
- BI generated one term too few, giving the fifth term instead of the sixth.
- DI doubled six times and subtracted 1 only once at the end.
- EI generated one term too many, giving the seventh instead of the sixth.
4.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.
5.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.

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