Exponential Functions - Progression Points

Dimension

Level

Progression Point

Structure

4.75

• Selection of a type of function (linear, exponential, quadratic) to match a set of data

5.0 Standard

… Students use exponent laws for multiplication and division of power terms (for example 23 × 25 = 28, 20 = 1, 23 ÷ 25 = 2−2, (52)3 = 56 and (3 × 4)2 = 32 × 42).

5.25

• Identification of linear, quadratic and exponential functions by table, rule and graph in the first quadrant

5.5

• Representation of numbers in a geometric sequence (constant multiple, constant percentage change) as an exponential function

5.75

• Testing of sequences by calculating first difference, second difference or ratio between consecutive terms to determine existence of linear, quadratic and exponential functions

6.0 Standard

… Students apply the algebraic properties (closure, associative, commutative, identity, inverse and distributive) to computation with number, to rearrange formulas, rearrange and simplify algebraic expressions involving real variables.

They verify the equivalence or otherwise of algebraic expressions (linear, square, cube, exponent, and reciprocal).

Students identify and represent linear, quadratic and exponential functions by table, rule and graph (all four quadrants of the Cartesian coordinate system) with consideration of independent and dependent variables, domain and range.

They distinguish between these types of functions by testing for constant first difference, constant second difference or constant ratio between consecutive terms.

Number

4.0 Standard

… Students evaluate natural numbers and simple fractions given in base-exponent form (for example, 54 = 625 and (2/3)2 = 4/9).