Discrete Functions Practice Test
Chapter
Chapter 6
Section
Discrete Functions Practice Test
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

0.22mins
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

1.03mins
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)

0.27mins
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

0.19mins
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-...

0.57mins
Q5

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

t_n = 9 - 5n

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

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}

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

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}

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

0.46mins
Q6f

Write an explicit formula and recursive formula for the sequence.

64, 32, 16, 8, ...

0.22mins
Q7a

Write an explicit formula and recursive formula for the sequence.

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

0.19mins
Q7b

Write an explicit formula and recursive formula for the sequence.

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

0.18mins
Q7c

Write an explicit formula and recursive formula for the sequence.

64, 32, 16, 8, ...

0.27mins
Q7d

Write an explicit formula and recursive formula for the sequence.

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

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}, ...

0.42mins
Q7f

Write t_{11} for each sequence.

6, 10, 14, 18, ...

0.26mins
Q8a

Write t_{11} for each sequence.

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

0.22mins
Q8b

Write t_{11} for each sequence.

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

0.29mins
Q8c

Write t_{11} for each sequence.

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

0.32mins
Q8d

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

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

0.20mins
Q9a

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

\displaystyle t_n = 25n + 50

0.12mins
Q9b

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

\displaystyle t_n = 25n + 50

0.17mins
Q9c

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

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

0.17mins
Q9d

Determine the number of terms in each sequence.

5, 8, 11, ..., 62

0.42mins
Q10a

Determine the number of terms in each sequence.

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

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.

1.45mins
Q11

Determine the specified sum for the series.

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

1.03mins
Q12a

Determine the specified sum for the series.

S_{18} for 12+ 5 -2 + ...$ Buy to View 0.50mins Q12b Determine the specified sum for the series. 120 + 110 + 100+ ... - 250 Buy to View 1.20mins Q13a Determine the specified sum for the series. 8 + 24 + 40 + ... + 280 Buy to View 1.22mins Q13b Determine the sum of the geometric series. \displaystyle \frac{2}{81} + \frac{4}{27} + \frac{8}{9}+ ... + 6912 Buy to View 1.47mins Q14a Determine the sum of the geometric series. \displaystyle 5 + 10 + 20 + ... + 2560 Buy to View 0.56mins Q14b Use Pascal's triangle to help you expand the expression. (b - 3)^5 Buy to View 0.57mins Q15a Use Pascal's triangle to help you expand the expression. (2x - 5y)^6 Buy to View 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 Buy to View 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 Buy to View 0.19mins Q16b Determine the sum of the first 15 terms of an arithmetic series if the middle term is 92. Buy to View 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` Buy to View 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. Buy to View 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? Buy to View 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. Buy to View 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?