Pre Algebra Units and Topics
Number Theory Unit
1. Divisibility
 Divisibility Laws for numbers from1 to 10
 Factors and multiples of algebraic terms (review numeric terms)
 Prime numbers, prime factors, relatively prime numbers
 Prime factorisation of algebraic terms (review numeric terms)
 GCF, LCM of numeric and algebraic terms using prime factorisation
 Application of LCM and HCF eg word problems using HCF and LCM)
2. Square and Square Roots
 Review squares of numbers from -20 to 20 and 25, perfect squares, use of the radical sign,
squares and square roots of multiples of ten, decimal fractions
 Estimating the square root of any number
 Generalising and using the rules for squaring or finding the square root of a product or a
fraction
 Solving equations with squares and square roots
 Representing and using numbers in rational forms (surds)
 Cubes of numbers from1 to5.
3.
Exponents
 Review operation rules for numbers and algebraic terms with exponents
 Write numbers and algebraic terms as positive and negative powers
 Multiply and divide algebraic terms with positive and negative exponents
 Problem Solving using exponents
4.
Scientific Notation
 Review writing large numbers and decimals in scientific notation form
 Multiplying, dividing, adding and subtracting numbers and algebraic terms written in
scientific notation
5.
Rational and irrational numbers
 Defining and recognising different sets of numbers
 Recognising and differentiating between rational and irrational numbers
 Proofing that a number is rational or irrational number.
Algebra
Simplification of expressions
 Adding and subtracting like terms with powers e.g. 9xy2 + 2x2y – 12xy2 + x2y
 Using the distributive property e.g. 2a2b – 4a(ab + 3ab2) – 4(ab)2+ 1/a(4a3b +a2b2)
 Multiplying and dividing algebraic terms e.g. 7ab x 2a3b2

 Simplifying algebraic fractions
 Multiplying algebraic fractions e.g. 2x3b . 15a5b
5a
2x2b3
 Adding and subtracting algebraic fractions e.g.2ab + 9b
x
a
 Dividing fractions e.g. 2x3b  12x5b
5a
25a2
 Factorization
Solving Equations and Inequalities
 Solving simple two step equations e.g. 4x + 19 = -7
 Solving equations with simplification first sometimes using the
distributive property e.g. 1 – 2(x + 6) – 9x = 24
 Solving equations with the unknown on both sides e.g. x – 6 = -4x + 13
 Solving inequalities including with the unknown on both sides of the inequality e.g. 7x – 2(x
+12) > -4x +8
 Solving inequalities with negative coefficient of the variable -4x + 7 < 34
 Representing the solution of an inequality on a number line and on a graph
 Solving word problems for equations and inequalities.
 Solving for a variable (subject of the formula) e.g. T = r2l (l)
 Solving for a variable in word problems
Solving simultaneous equations
 By elimination
 By substitution
Substitution
 In expressions
 In formulae
 In word problems
Relations and Functions
 Introduction to relations and functions
 Representing relations and functions as ordered pairs, on mapping diagram, graphs
 domain and range
 Function notation
Coordinate Geometry




Graphing on the coordinate plane
Linear function
Symmetry and reflection
The Square Function
Geometry


Definition of one, two and three dimensions
Review of units


Angles relationship with algebra variables including between parallel lines
Constructing and bisecting angles












Naming polygons
Types of polygons – regular, irregular, convex, concave
Sum of the interior and exterior angles of a convex polygon
Properties of different types of triangles and quadrilaterals
Types of triangles
Unknown angles in a triangle
Pythagorean Theorem
Congruent and Similar Triangles
Constructing Triangles
Angle- Side relationship in Triangles
Relationship between the sides of a triangle
Angle relationships in various quadrilaterals

Parts of a circle


Perimeter of compound shapes
Using perimeter to solve problems with unknown lengths and arcs






Area of triangles
Using area of triangles to find unknown lengths and quantities
Area of quadrilaterals
Using area of quadrilaterals to find unknown lengths and quantities
Using area of a circle to find unknown lengths and arc length
Area of compound shapes

Properties of polyhedrons (right and oblique), cylinders, cones and spheres
Angles
Polygons
Circles
Perimeter
Area
Solids
Surface area of solids
 Determine the surface area of prisms, pyramids, cylinder, cones and spheres (face or net)
 Using surface area to find unknown lengths and arcs
Volume of solids
 Determine the volume of prisms, pyramids, cylinder, cones and spheres
 Using volume to find unknown lengths and arcs
Statistics



Organizing data - frequency, tables, line plot, stem and leaf
Representing data in graphical form- Bar Graphs, Histograms, Pie Chart, Scatter
Plots, Line Graphs, Box and Whiskers
Interpreting data – Central tendencies, quartiles, percentiles, interpreting
information from different graphs, appropriate use of different types of graph,
misrepresentation of graphs, predicting trends from graphs, making decisions
based on an statistical data