What you'll learn
- โฆExplain why pi and root 2 are irrational, and place a surd on a number line
- โฆSimplify an expression using the laws of exponents for real numbers, including a negative or fractional power
- โฆFind the zeros of a polynomial, and use the remainder and factor theorems to factorise it
- โฆPlot points on the Cartesian plane and solve a pair of linear equations, graphically and algebraically
- โฆSolve a quadratic equation by factorisation or the formula, and use the discriminant to count its real roots
- โฆFind the nth term and sum of an arithmetic progression, and use it to plan a real saving pattern
- โฆUse similar triangles and the Pythagoras theorem to find an unknown length, and calculate trigonometric ratios for a right triangle
- โฆFind a tangent's length, a circle or trapezium's area, and a solid's surface area and volume. Then calculate the mean, median, mode and a simple probability from grouped data
Certification projects
Build 3 projects to earn your certificate
Hands-on work that proves you can apply what you learned โ part of the certificate requirements.
Syllabus
Module 1 ยท 24m
Number Systems Free
What you'll be able to do
- Can tell a rational number from an irrational one by looking at its decimal expansion
- Can prove a simple surd is irrational and place it on a number line
- Can simplify an expression using the laws of exponents for real numbers
Module 2 ยท 24m
Polynomials Locked
What you'll be able to do
- Can identify a polynomial's degree and evaluate it at a given value of x
- Can find a polynomial's zero and use the remainder theorem to find a remainder without dividing
- Can use the factor theorem to factorise a quadratic or cubic polynomial
Module 3 ยท 24m
Linear Equations and Coordinate Geometry Locked
What you'll be able to do
- Can plot and read a point's coordinates on the Cartesian plane
- Can find solutions of a linear equation in two variables and solve a pair of such equations algebraically
- Can graph a linear equation and read off the solution of a pair of linear equations from their graphs
Module 4 ยท 24m
Quadratic Equations and Progressions Locked
What you'll be able to do
- Can use the discriminant to say how many real roots a quadratic equation has
- Can solve a quadratic equation by factorisation and by the quadratic formula
- Can find the nth term and the sum of an arithmetic progression
Module 5 ยท 24m
Triangles, Trigonometry and Circles Locked
What you'll be able to do
- Can use similar triangles and the Pythagoras theorem to find an unknown length
- Can calculate sin, cos and tan for a right triangle and use a basic trigonometric identity
- Can find the length of a tangent from an external point to a circle
Module 6 ยท 24m
Mensuration, Statistics and Probability Locked
What you'll be able to do
- Can calculate the area of a circle, a sector and a trapezium
- Can calculate the surface area and volume of a solid, including one made of two combined solids
- Can find the mean, median and mode of grouped data and calculate a simple probability