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LearnCambridge4024Current syllabusPaper 2 · CalculatorAlgebra

Paper 2 · Module

Algebra

8 subtopics≈ 255 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
Direct and inverse proportion
Proportion links two quantities by one constant $k$ . Direct: $y=kx^n$ , so $y$ grows with $x$ . Inverse: $y=\dfrac k{x^n}$ , so $y$ shrinks as $x$ grows. Write the equation, find $k$ from the given pair, then use it.
≈ 30 min
Functions
A function $f(x)$ is a rule turning an input into an output. A composite $fg(x)$ means "do $g$ , then $f$ ". The inverse $f^{-1}$ undoes $f$ : swap $x$ and $y$ and rearrange. Some inputs can't be used, such as values that make you divide by zero.
≈ 30 min