Algebra Answers

Follow the instructions Below to create your own pattern:

A, draw the first three terms of a simple ascending geometrical pattern with a constant difference.
B, describe the pattern in words.
C, write down the rule of the pattern.
D,using the rule, extend the pattern to the fourth and the tenth term.
E, describe the pattern in a flow diagram (spider diagram)
F, describe the pattern in a table.
G, describe your pattern in a graph.
H, reflect on the ease of the activity.

Set up one example question(also provide solutions) which falls ubder the following:
Level 1 : mathematical knowledge
Level 2 : Routin procedure( in a real life context)
Level 3 : complex procedure ( in real life context)
Level 4 : problem solving ( in real life context)

Find the general term Tn for the following sequences;
a) 9; 14; 19
b) 3; 7; 11
c) 8; 15; 22
d) 4; 11; 18

State the first term, and write the next four terms of the sequences;
a) 9; 14; 19
b) 3; 7; 11
c) 8;15; 22
d) 4; 11; 18

1.draw the first three terms of a simple ascending geometrical pattern with a constant difference.
2.what is the pattern?
3.write down the rule of the pattern.
4.using the rule, extend the pattern to the fourth and the tenth term.
5.describe the pattern in a flow diagram (spider diagram).
6.describe pattern in a table.
7.describe your pattern in a table.
8.reflect on the ease of the activity.

The product of two even integers is 2020.Find their sum.

x⁴+x²y²+y⁴ = 133
x²+xy+y² = 19

Solve for x and y

The income tax a person pays depends on the person's total income.
The number of years of experience on a job has a direct bearing on the salary recieved.
The amount by which your savings will grow in a year depends on the interest offered by the bank.
The area of a circle depends on the raduis of the circle.
The distance traveled in a car at a certain rate depends on the time travelled.

a) Express each situation in functional words. For ecample, the income tax is a function of the total income.
b) For each situation, indicate the dependent and independent variable.
c) write the two variables as an ordered pair, and write the function using the notation y=(x)
d) Explain the meaning of a function in your own words, Illustrate with your own specific example.

What happens if we graph both f and f^{-1} on the same set of axes, using the x-axis for the input to both f and f^{-1} ?

[Suggestion: go to www.desmos.com/calculator and type y=x^3 {-2 < x < 2}, y=x^{1/3} {–2 < x < 2}, and y = x {–2 < x < 2}, and describe the relationship between the three curves.] Then post your own example discussing the difficulty of graph both f and f^{-1} on the same set of axes.

Suppose f:R \rightarrow R is a function from the set of real numbers to the same set with f(x)=x+1. We write f^{2} to represent f \circ f and f^{n+1}=f^n \circ f. Is it true that f^2 \circ f = f \circ f^2? Why? Is the set {g:R \rightarrow R l g \circ f=f \circ g} infinite? Why?