Yr 11 maths methods

 To define and understand exponential functions.  To sketch graphs of the various types of exponential functions.  To understand the rules for manipulating exponential and logarithmic expressions.  To solve exponential equations.  To evaluate logarithmic expressions.  To solve equations using logarithmic methods.  To sketch graphs of functions of the form y = logax and simple transformations of this.  To understand and use a range of exponential models.  To sketch graphs of exponential functions.  To apply exponential functions to solving problems.

 Functions in which the independent variable is an index number are called indicial or exponential functions. For example:  f (x) = a x where a > 0 and a ≠ 1  quantities which increase or decrease by a constant percentage in a particular time can be modelled by an exponential function.  Exponential functions can be seen in everyday life for example in science and medicine (decay of radioactive material, or growth of bacteria like those shown in the photo), and finance ( compound interest and reducing balance loans).

a m × a n = a m + n  When multiplying two numbers in index form with the same base, add the indices.  For example, 2 3 × 2 4 = (2 × 2 × 2) × (2 × 2 × 2 × 2) = 2 7

a m ÷ a n = a m - n  When dividing two numbers in index form with the same base, subtract the indices.

(a m ) n = a m × n = a mn  To raise an indicial expression to a power, multiply the indices.

a 0 = 1, a ≠ 0  Any number raised to the power of zero is equal to one.

 Page 220 Questions 1 – 3

 Page 220 – Questions 4 – 10