xponentials and
Logarithms
Twitter: @Owen134866
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Given that and , evaluate 3) Plot the following on a
these expressions without a scatter graph and draw a line of
calculator: best fit.
1 1.2 2.1 3.5 4 5.8
125 3 32
a) b) c) 5.8 7.4 9.4 10.3 12.8
d) e) Find the gradient of your line of
49 1 best fit, giving answers to 1dp.
2) Simplify each expression by
writing it as a single power:
𝑦 =1.5 𝑥+4.1
66 𝑦 21
a) b)
c) d)
2 6 𝑥4
,Teachings for
Exercise 14A
, Exponentials and Logarithms
y
Graphs of Exponential Functions
8
7
You need to be familiar with the
6
function;
x 5
y a where a 0 4
3
For example, y = 2 , y = 5 and so x x
2
on… 1
x
-3 -2 -1 1 2 3
1) Draw the graph of y = 2x
x -3 -2 -1 0 1 2 3 Any graph of y a x will be the same
basic shape
y 1
/8 1
/4 1
/2 1 2 4 8
It always passes through (0,1) as
1 anything to the power 0 is equal to 1
Remember: 2 3
23
14A
Logarithms
Twitter: @Owen134866
www.mathsfreeresourcelibrary.com
, Prior Knowledge Check
1) Given that and , evaluate 3) Plot the following on a
these expressions without a scatter graph and draw a line of
calculator: best fit.
1 1.2 2.1 3.5 4 5.8
125 3 32
a) b) c) 5.8 7.4 9.4 10.3 12.8
d) e) Find the gradient of your line of
49 1 best fit, giving answers to 1dp.
2) Simplify each expression by
writing it as a single power:
𝑦 =1.5 𝑥+4.1
66 𝑦 21
a) b)
c) d)
2 6 𝑥4
,Teachings for
Exercise 14A
, Exponentials and Logarithms
y
Graphs of Exponential Functions
8
7
You need to be familiar with the
6
function;
x 5
y a where a 0 4
3
For example, y = 2 , y = 5 and so x x
2
on… 1
x
-3 -2 -1 1 2 3
1) Draw the graph of y = 2x
x -3 -2 -1 0 1 2 3 Any graph of y a x will be the same
basic shape
y 1
/8 1
/4 1
/2 1 2 4 8
It always passes through (0,1) as
1 anything to the power 0 is equal to 1
Remember: 2 3
23
14A
