This topic is mainly about manipulating rational, exponential, and logarithmic algebraic expressions into various forms in order to solve problems. This will involve forming, visualizing and using linear and quadratic equations to answer problems from both a mathematical as well as a real life context.
There are a lot of quite abstract ideas in this topic but if you can take each topic one step at a time you will soon find that you can put your skills together to answer exam questions correctly!
#0.5 Algebra Rules
Ground work: get familiar with some rules of algebra! They are very handy and useful!!
Watch this video from Nancy Pi and then answer the questions on this slideshow.
Or do sections 1.1 & 1.2 of the 2.6 Algebra section of Education Perfect !
Exponent Laws
The videos on the left explain two simple exponent laws.
You can practice these on Education Perfect under 4.1 review of Exponent Laws
Add and Subtract algebraic fractions: this video explains how to add and subtract algebraic fractions
Multiply and Divide algebraic fractions: this video explains how to multiply and divide (multiply the reciprocal) algebraic fractions. However, for the most of cases, we could simply before we multiply and divide.
# 5 Solve quadratic equations
What is the relationship between the vertex and roots in quadratics? How do we know there are two roots, or one root, or no real roots?
This video demonstrates how to form a quadratic equation to solve a word problem.
This video shows the graphical representation of a quadratic inequality and how to find the possible solutions.
This slide dec k demonstrates the properties of logarithms and how to solve logarithmic equations - taking logs on the both sides of equations to solve exponential equations.
This video provides some examples of how to apply logarithm rules (properties).
2022 Prelim with schedule doc underneath
2019 Prelim with answer at the end
2018 Prelim with answer at the end
2017 Prelim with Schedule doc underneath