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Math Kangaroo practice

Name: ______________________Date: ____________5 questions · 20 points

1.A sequence starts 4, 7, 10, 13 and continues in the same way. What is the 20th term?[4]
- A57
- B60
- C61
- D63
- E64
2.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
3.Each row of a grid starts 3 more than the row above. Each cell is 1 more than the one to its left. The top-left cell is 1. What is in row 4, column 3?[4]
Text description of the figure
A grid four rows by four columns. The first row reads 1, 2, 3, 4 and the second row reads 4, 5, 6, 7. The remaining rows are blank, and the cell in row 4, column 3 is shaded.
- A9
- B10
- C12
- D13
- E15
4.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
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.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.
2.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.
3.C — 12KA-0105Patterns in tables and grids
- AI stopped at row 3, taking two steps down from the top instead of three.
- BI found where row 4 starts but forgot to move across to the third column.
- DI moved three columns across instead of two, counting columns rather than steps between them.
- EI took four steps of 3 downwards instead of three, counting rows rather than the gaps between them.
4.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.
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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