## Grade Descriptors

## Examples

## TERM 1

**Higher**

Factorise a quadratic expression in the form ax^2 + bx + c

Solving quadratic equations by factorising

Solve quadratic equations by completing the square

Using the quadratic formula to solve quadratic equations

Solve simultaneous two linear equations

Solve quadratic and linear simultaneous equations

Solving inequalities

Solve graphical inequalities

Solve quadratic inequalities

Recognise and explain how triangles are congruent

Understand similarity and congruency

Finding the length of similar shapes

Calculate areas and volumes of similar objects

Prove results in geometry using congruent triangles

Recognise and sketch the graphs of sin, cos and tan

Solve trigonometric equations

Translating graphs i.e. y=f(x)+a & y=f(x+a)

Reflect graphs i.e. y=-f(x) & y=f(-x)

Stretches of graphs i.e. y=af(x) & y=f(ax)

Combinations of transformations of graphs

Area of a triangle

The Sine Rule

The Cosine Rule

Sketch a quadratic graph by completing the square

Use the discriminant to decide how many solutions a quadratic equation has

Expand the product of more than 2 linear expressions

Sketching cubic graphs

Solve problems using chord and tangent problems

Use circle theorems and circular problems to solve problems

Use the alternate segment theorem to find missing angles and solve problems

Draw circles x^2 + y^2 = r^2

Write down the equation of a circle, centre (a,b) and radius r

Find the equation of a tangent to a circle at a given point

Simplify algebraic fractions

Multiply and divide algebraic fractions

Add and subtract algebraic fractions

Solve equations involving algebraic fractions

Changing the subject of more complicated formulae

Proof using algebra

Understand and use function notation

Add, subtract & multiply functions f(x)±g(x), af(x), f(ax) etc.

Find inverse functions

Composite functions i.e. gf(x)

**Foundation**

Convert between metric speed measures

Convert between density and pressure measures

Solve problems using kinematic formulae

Reverse percentages

Using isometric paper to draw 3D objects

Symmetry in 3D objects

Drawing plans and elevations of a 3D object

Using plans and elevations of a 3D shape

Constructing triangles

Drawing polygons

Construct the perpendicular at a point on a line

Constructing the perpendicular at a point on a line

Bisecting a line

Bisecting an angle

Loci

Measure, draw and apply bearings

Expand double brackets

Factorise a quadratic expression using difference of two squares

Factorise a quadratic expression in the form x^2 + bx + c

Solving quadratic equations by factorising

Solving quadratic equations by rearranging

Draw quadratic graphs

Identify lines of symmetry of quadratic graphs

Real life use of quadratic graphs

Use a graph to solve quadratic equations

Find the circumference and area of a circle

Find the perimeter and area of shapes involving parts of circles

Find sector area and arc lengths

Find the volume and surface area of a cylinder

Calculate the volume and surface area of a pyramid

Calculate the volume and surface area of a cone

Calculate the volume and surface area of a sphere

Use the laws of indices to multiply and divide numbers in index notation

Powers of Powers and fractional powers

Write large and small numbers in standard form

Carry out calculations with numbers written in standard form

Changing the subject of a formula

Prove results from geometry

Proof using algebra

Graphs of cubic functions

Graphs of reciprocal functions

Solve simultaneous equations

## TERM 2

**Higher**

Know the difference between a vector and a scaler

Adding and subtracting vectors

Calculating the magnitude and direction of a vector

Solve geormetric problems using vector methods

Estimate area under quadratic graphs by dividing into trapezia

Write and solve an equation for proportion problems

Write and solve an equation for inverse proportion problems

**Foundation**

Recognise and explain how triangles are congruent

Understand similarity and congruency

Finding the length of similar shapes

Calculate areas and volumes of similar objects

Know the difference between a vector and a scalar

Adding and subtracting vectors

Calculating the size and direction of a vector

Solve geometric problems using vector methods

## TERM 3

Exam Practice.