Qm - Module 2 - Basic Mathematics

Front 1

Describe key points of Graphical Representation

Back 1

1. Any point in a graph is located by two co-ordinates.
2. First coordinate is (3,2) is the X-value (horizontal); the second is the Y value (vertical)

Front 2

What is the Origin in graphs?

Back 2

Fixed point on the graph representing the coordinates (0, 0)

Front 3

What is a quadrant?

Back 3

One of the 4 sections that a graph is split into. Each quadrant has different signs for the x and y values.

Front 4

Define a Linear function

Back 4

Function that results in a straight line. X and Y are not raised to powers. No exponents, logarithms, etc.

Front 5

Shape of Squared function.

Back 5

"U" shaped

Front 6

Shape of cubed function.

Back 6

"Z" on its side

Front 7

Describe parts of linear function:

y = mx + c.

Back 7

m - coefficient of x, also slope (gradient) of the line.
C is the y intercept

Front 8

Formula for slope

Back 8

(y1 - y2) / (x1 - x2)

Front 9

Three possibilities for m (slope).

Back 9

m is negative. Line leans in backward direction.
m is zero. then y - constant. Line is parallel to the x axis
x = constant, is parallel to the y axis. Slope is infinite.

Front 10

Equation of straight line can be determined if the values for m and c are known. Can determine if what info is available.

Back 10

1. Values of m and c
2. Value of m and 1 set of coordinates
3. Value of c and 1 set of coordinates
4. Coordinates of 2 points on line

Front 11

Explain solving of two linear equations in two variables.

Back 11

Finding a point which satisfies both equations. 1 of 3 outcomes:
1. One common point. Unique solution.
2. Infinite number of solutions. Same line.
3. No solution, equations are inconsistent. Runs parallel to each other.

Front 12

What are exponential functions important?

Back 12

The way they express growth or decay. Natural pattern of both.

Front 13

What is the difference between linear and exponential growth.

Back 13

Linear is growth by a constant increase
Exponential represents a constant percentage increase.

Front 14

Basic logarithmic equation

Back 14

if y = a to the xth , then x is said to be the logarithm of y to the base a.
log a y = x.

Front 15

What is a common logarithm?

Back 15

Logarithms to the base 10

Front 16

What is a binary logarithm?

Back 16

Logarithms to the base 2.

Front 17

What is a natural logarithm?

Back 17

Logarithms to the base e.
Written x = ln y means x = log e y.

Front 18

Rules for logarithms?

Back 18

1. Addition: log a x + log a y = log a xy.
2. Subtraction: log a x - log a y = log a x/y
3. Multiplication by a constant:
c log a y = log a y to the cth.

Front 19

General form of exponential function:

Back 19

y = ka to the cxth.

Front 20

Transformation

Back 20

by taking logarithms of both sides of a exponential function can be treated as a linear one.