Algebra 1

Unit 1 Review

A basic tree fractal is shown.

Stage 0 Stage 1 Stage 2

Complete the table.

Stage 3

Write a recursive rule to describe the pattern of branches added.

Stage # of branches added

0 1

1 2

2

3

4

Algebra 1 – Unit 1 Review

ANSWERA basic tree fractal is shown.

Stage 0 Stage 1 Stage 2

Complete the table.

Stage 3

Stage # of branches added

0 1

1 2

2 4

3 8

4 16

Write a recursive rule to describe the pattern of branches added.

Start with 1, then double for each successive stage.

Algebra 1 – Unit 1 Review

A basic tree fractal is shown.

Stage 0 Stage 1 Stage 2

Is this pattern arithmetic or geometric?

Stage 3

Write an explicit rule for the number of branches, b, added in each stage, n.

Stage # of branches

added

0 1

1 2

2 4

3 8

4 16

Algebra 1 – Unit 1 Review

ANSWERA basic tree fractal is shown.

Stage 0 Stage 1 Stage 2

Is this pattern arithmetic or geometric?

Stage 3

Write an explicit rule for the number of branches, b, added in each stage, n.

Stage # of branches

added

0 1

1 2

2 4

3 8

4 16

geometric

b = 2n

Algebra 1 – Unit 1 Review

Algebra 1 – Unit 1 Review

Bob the biologist counted the fish population over a period of time in two different ponds.

Complete each table.Write a recursive rule for each population.

Apricot PondYear 0 1 2 3 4 5

# of fish 100 400 700

Great Grape PondYear 0 1 2 3 4 5

# of fish 20 60 180

ANSWERAlgebra 1 – Unit 1 Review

Bob the biologist counted the fish population over a period of time in two different ponds.

Complete each table.Write a recursive rule for each population.

Apricot PondYear 0 1 2 3 4 5

# of fish 100 400 700 1000 1300 1600

Great Grape PondYear 0 1 2 3 4 5

# of fish 20 60 180 540 1620 4860

Apricot Pond: start at 100, then add 300 for the next year.Great Grape Pond: start at 20, then triple for the next year.

Owen sells ornamental owls. He ships all sizes of his carefully crafted birds of prey. The cost to ship one depends on its weight. His shipping company charges him a base fee of $5.00, then an additional $0.50 for each additional pound.

Using c for cost and w for weight, write an explicit rule for the total cost.

How much would it cost to ship a 25 lb owl?

Algebra 1 – Unit 1 Review

ANSWERAlgebra 1 – Unit 1 Review

Owen sells ornamental owls. He ships all sizes of his carefully crafted birds of prey. The cost to ship one depends on its weight. His shipping company charges him a base fee of $5.00, then an additional $0.50 for each additional pound.

Using c for cost and w for weight, write an explicit rule for the total cost.

How much would it cost to ship a 25 lb owl?

c = 5 + 0.5w

c = 5 + 0.5(25) = $17.50

Katee is decorating her math binder with stickers. She starts with a center square, then adds stickers around all the edges.

Stage 1 Stage 2 Stage 3 Stage 4Stage # of

stickers added

# of total stickers

1 4 4

2

3

4

Is the number of stickers added an arithmetic sequence, geometric sequence, or neither?

Is the number of total stickers an arithmetic sequence, geometric sequence, or neither?

Algebra 1 – Unit 1 Review

ANSWERKatee is decorating her math binder with stickers. She starts with a center square, then adds stickers around all the edges.

Stage 1 Stage 2 Stage 3 Stage 4Stage # of

stickers added

# of total stickers

1 4 4

2 12 16

3 20 36

4 28 64

Is the number of stickers added an arithmetic sequence, geometric sequence, or neither?

Is the number of total stickers an arithmetic sequence, geometric sequence, or neither?

Algebra 1 – Unit 1 Review