Discrete Functions Practice Test
Chapter
Chapter 6
Section
Discrete Functions Practice Test
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Solutions 45 Videos

Which is a recursion formula for the sequence shown?

A f(n) = f(n -1) + 4

B f(n) = 4n -2

C f(n) = 2 + (n -1)(4)

D f(1) = 2, f(n) = f(n-1) + 4

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Q1

Which expressions represent the missing terms in the binomial expansion shown?

\displaystyle (x + y)^7 = x^7 + 7x^6y + ... + 35x^4y^ + 35x^3 y^4 + 21x^2y^5+ ... + y^7

A 21y^5x^2, 7yx^6

B 21x^5y^2, 7xy^6

C -21x^5y^2, - 7xy^6

D x^5y^2, xy^6

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Q2

What is the formula for the general term of an arithmetic sequence with a = 8 and d=2?

A t_n = 2+ (n + 1)(8)

B 8 + (n -1)(2)

C 8 + (n + 1)(2)

D 2 + (n - 1)(8)

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Q3

What are the first three terms of a geometric sequence with a = 3 and r = 2?

A 3, 5, 7

B 2, 6, 18

C 3, 6, 12

D 2, 5, 8

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Q4

Which series is neither arithmetic nor geometric?

A 5+15+21+27+...

B 1+8+27+64+...

C 64-32+16+-8+...

D -3-2.7-2.4-2.1-...

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Q5

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

t_n = 9 - 5n

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0.27mins
Q6a

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

f(n) = 2n^2 + 3n -4

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1.56mins
Q6b

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

f(n) = \frac{1}{8}(4)^{n -1}

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0.48mins
Q6c

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

t_n = 0.2n + 0.8

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0.37mins
Q6d

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

t_n = \frac{n + 4}{2}

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0.52mins
Q6e

Determine the first five terms of the sequence. Determine if the sequence is arithmetic, geometric or neither.

f(n) = -3(2)^n

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0.46mins
Q6f

Write an explicit formula and recursive formula for the sequence.

64, 32, 16, 8, ...

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0.22mins
Q7a

Write an explicit formula and recursive formula for the sequence.

\displaystyle -20, -17, -14, -11, ...

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0.19mins
Q7b

Write an explicit formula and recursive formula for the sequence.

\displaystyle -4000, 1000, -250, 62.5, ...

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0.18mins
Q7c

Write an explicit formula and recursive formula for the sequence.

64, 32, 16, 8, ...

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0.27mins
Q7d

Write an explicit formula and recursive formula for the sequence.

\displaystyle -3, -6, -12, -24, ...

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0.19mins
Q7e

Write an explicit formula and recursive formula for the sequence.

\displaystyle -12\sqrt{2}, -10\sqrt{2}, -8\sqrt{2}, -6\sqrt{2}, ...

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0.42mins
Q7f

Write t_{11} for each sequence.

6, 10, 14, 18, ...

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0.26mins
Q8a

Write t_{11} for each sequence.

-3, -6, -12, -24, ...

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0.22mins
Q8b

Write t_{11} for each sequence.

5, -10, 20, -40, ...

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0.29mins
Q8c

Write t_{11} for each sequence.

-5, -10, -15, -20, ...

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0.32mins
Q8d

Given the explicit formula, write t_{15} for the sequence.

\displaystyle f(n) = 2(-3)^{n + 1}

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Q9a

Given the explicit formula, write t_{15} for the sequence.

\displaystyle t_n = 25n + 50

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0.12mins
Q9b

Given the explicit formula, write t_{15} for the sequence.

\displaystyle t_n = 25n + 50

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0.17mins
Q9c

Given the explicit formula, write t_{15} for the sequence.

\displaystyle f(n) = \frac{-3n}{4}

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0.17mins
Q9d

Determine the number of terms in each sequence.

5, 8, 11, ..., 62

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0.42mins
Q10a

Determine the number of terms in each sequence.

-4, 12, -36, ..., -19 131 876

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1.20mins
Q10b

A new lake is being excavated. One day, 1.6 t of material is removed from the lake bed. On each of 10 days after that, 5% more is removed.

(a) Write the first three excavation amounts as a sequence.

(b) Write a recursion formula to represent the amount removed each day. Use this to determine the amount removed on the fifth day.

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1.45mins
Q11

Determine the specified sum for the series.

S_{10} for 200 + 100 + 50 + ...

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1.03mins
Q12a

Determine the specified sum for the series.

S_{18} for 12+ 5 -2 + ...$`

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0.50mins
Q12b

Determine the specified sum for the series.

120 + 110 + 100+ ... - 250

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1.20mins
Q13a

Determine the specified sum for the series.

8 + 24 + 40 + ... + 280

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1.22mins
Q13b

Determine the sum of the geometric series.

\displaystyle \frac{2}{81} + \frac{4}{27} + \frac{8}{9}+ ... + 6912

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1.47mins
Q14a

Determine the sum of the geometric series.

\displaystyle 5 + 10 + 20 + ... + 2560

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0.56mins
Q14b

Use Pascal's triangle to help you expand the expression.

(b - 3)^5

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0.57mins
Q15a

Use Pascal's triangle to help you expand the expression.

(2x - 5y)^6

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1.10mins
Q15b

The sum of the first three terms of a series is 32. Determine the fourth term if the sum of the first four terms is 40

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0.49mins
Q16a

The sum of the first three terms of a series is 32. Determine the fourth term if the sum of the first four terms is 25

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0.19mins
Q16b

Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92.

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1.56mins
Q17

Which is greater, A or B? Explain your reasoning.

A = 50^2 - 49^2 + 48^2 - 47^2 + ... + 2^2 - 1^2 B = 50 +49 + 48+ 47+ ... + 2 + 1

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0.57mins
Q18

In the arrangement of letters shown, starting from the top, proceed to the row below by moving diagonally to the immediate right or left. Determine the number of different paths that will spell the name PASCAL.

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0.56mins
Q19

A new wood stain loses 6.5% of its colour every year in a city that experiences a lot of hot, sunny days. What percent of colour will a fence in this city have 6 years after being stained?

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1.08mins
Q20

In an arithmetic series, the 4th term is 62 and the 14th term is 122. Determine the sum of the first 30 terms.

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1.20mins
Q21

A sailboat worth $140 000 depreciates 18% in the first year and 10% every year after that. How much will it be worth 8 years after it is bought?

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1.02mins
Q22

A magic square is an arrangement of numbers in which all rows, columns, and diagonals have the same sum. Using the magic square shown, substitute each number with the corresponding term from the Fibonacci sequence.

Show that the sum of the products of the rows is equal to the sum of the products of the columns.

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1.20mins
Q23