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LearnAQA8300First teaching 2015Papers 1–3 · Foundation tierAlgebra

Papers 1–3 · Module

Algebra

9 subtopics≈ 290 min in total

Start the module: Expanding and factorising Open graphing calculator

Expanding and factorising
Expanding removes brackets; factorising puts them back. They are the same skill in reverse: every term in one bracket multiplies every term in the other, and factorising finds the brackets that would multiply out to give the expression.
≈ 30 min
Algebraic fractions and formulae
Algebraic fractions follow exactly the same rules as number fractions: factorise, cancel whole brackets, and use a common denominator to add. Changing the subject of a formula means undoing operations in reverse order, doing the same to both sides.
≈ 35 min
Linear and simultaneous equations
An equation is a balance: whatever you do to one side, do to the other. Linear equations take a few balancing steps. Simultaneous equations have two unknowns, so you eliminate one of them first, then substitute back.
≈ 35 min
Quadratic equations
Rearrange to $ax^2+bx+c=0$ . If it factorises, each bracket gives a solution. Otherwise use the quadratic formula, or complete the square, which also gives the turning point of the graph. In context, reject solutions that make no sense.
≈ 35 min
Inequalities and regions
Inequalities are solved almost like equations, with one trap: multiplying or dividing by a negative flips the sign. On a graph, an inequality in $x$ and $y$ is a region on one side of a line: solid line if included, dashed if not.
≈ 30 min
Sequences
A sequence follows a rule. Linear sequences go up by a constant difference, so their nth term is $dn+c$ . Quadratic sequences have a constant second difference; geometric sequences multiply by the same number each time; Fibonacci-type sequences add the previous two terms.
≈ 30 min
Gradients and straight lines
Two points fix a straight line. From them you can find how steep it is (gradient), how long the segment is (Pythagoras), its middle (average the coordinates), and its equation $y=mx+c$ .
≈ 30 min
Parallel and perpendicular lines
Parallel lines have equal gradients. Perpendicular lines have gradients that multiply to $-1$ : flip the fraction and change the sign. With these two facts, plus one point, you can write down any related line.
≈ 30 min
Travel graphs and curves
On a distance–time graph the gradient is the speed. On a speed–time graph the gradient is the acceleration and the area underneath is the distance. Learn the shapes of quadratic, cubic, reciprocal and exponential graphs so you can recognise them at a glance.
≈ 35 min