KS4 Maths – Higher

 Year Long Term Objective: To Build upon the foundation laid in KS3 to prepare students for the rigours of the GCSE. Students should be stretched with challenging GCSE style questions routinely. Year Autumn 1 Autumn 2 Spring 1 Spring 2 Summer 1 Summer 2 10 Number Fractions, Ratio and Percentages Graphs Transformations and Constructions Probability Similarity and Congruence 11 Algebra Angles and Trigonometry Area and Volume Equations and Inequalities Multiplicative reasoning More Trigonometry

Number

Overview

– Place value and estimating

– HCF and LCM

– Calculating with powers (indices)

– Zero, negative and fractional indices

– Powers of 10 and standard form

– Surds

Example Key Words

Significant figure

The first non zero digits of a number

Factors

A number that divides exactly into another number

Multiple

A value in the number’s time table

Indices

Indices show how many times a number or letter has been multiplied by itself.

Standard Form

A way of writing very large and very small numbers using a power of 10

Surd

A surd is an expression that includes a square root and the value is an irrational number

Fractions, Ratio and Percentages

Overview

– Fractions

– Ratios

– Ratio and proportion

– Percentages

– Fractions, decimals and percentages

Example Key Words

Numerator

The top number of a fraction

Denominator

The bottom number of a fraction

Equivalent fraction

Fractions that are equal in size but are written differently

Simplest terms

A fraction in its simplest terms cannot be cancelled down

Percent

Out of one hundred

Percentages and fractions

Percentages are fractions with a denominator of 100

Graphs

Overview

– Linear graphs

– Graphing rates of change

– Real-life graphs (To include phone bills and taxi charges)

– Line segments

– Cubic and reciprocal graphs

Example Key Words

Linear graph

A straight line graph

The measure of the steepness of a curve.

Y intercept

The point where the line crosses the y axis

Distance- time graph

A graph that plots the distance traveled by an object on a vertical axis against the time taken

Involves an x2 and will be the shape of a parabola

Cubic and reciprocal

Involves an x3 (cubic) and 1/x (reciprocal)

Transformations and Constructions

Overview

– 3D solids

– Reflection and rotation

– Translation and enlargement (To include computer generated imagery and vectors)

– Combinations of transformations

– Bearings and scale drawings

– Constructions

– Loci

Example Key Words

Transformation

A change in the position, size or shape of a figure

Bearing

Measuring the angle from one postion to another. Written as a 3 digit number, measured from the north line, in a clockwise direction.

Scale Drawing

A drawing that shows a real object with accurate sizes in proportion to the reduced or enlarged by a certain amount (called the scale)

Construction

Turning a shape around a fixed point.

Loci

This changes the size of the shape – it can make it smaller.

Scale factor

A drawing which has been reduced or enlarged from its original size, to a specified scale

Probability

Overview

– Combined events

– Mutually exclusive events

– Experimental probability

– Independent events and tree diagrams

– Conditional probability

– Venn diagrams and set notation

Example Key Words

Probability

The likelihood or chance of a given event happening. Often expressed as a fraction, decimal or percentage.

Experimental probability

A calculation obtained from an experiment.

Venn diagram

A diagram that represents sets and shows where those sets intersect.

Probability tree diagram

A tree diagram is used to determine and visualise all the outcomes and probabilities of 2 or more events

Mutually exclusive

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes

Independent events

Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event.

Similarity and Congruence

Overview

– Congruence

– Geometric proof and congruence

– Similarity

– Similarity in 3D solids

Example Key Words

Congruent

Congruent shapes are shapes that are exactly the same. The corresponding sides are the same and the corresponding angles are the same.

Similar

Two shapes are said to be similar if they are exactly the same shape, but are different in size. All sides are in the same proportion defined by the scale factor.

Similarity in area and volume

If 2 shapes are similar and the scale factor of the lengths is x, then the scale factor of the area is x2 and the scale factor iof the volume is x3

Algebra

Overview

– Algebraic indices

– Expanding and factorising

– Equations

– Formulae

– Linear sequences

– Non-linear sequences

Example Key Words

Expanding brackets or multiplying out brackets

This involves mulitplying each term inside the bracket by the number/letter outside the bracket or inside a second bracket

Factorising

The opposite of multiplying out brackets, involves putting the expression into bracket(s)

Formula

An equation that expresses a mathematical relationship between two or more variables

Term of a sequence

A number in a sequence

Linear sequences

The term to term rule is a constant number and the nth term rule just involves “n”

Non- linear sequence

Generally a quadratic sequence where you need to find the 2nd difference and the nth term rule will involve “n2”

Angles and Trigonometry

Overview

– Angle properties of triangles, quadrilaterals and parallel lines

– Interior angles of a polygon

– Exterior angles of a polygon

– Pythagoras’ theorem

– Trigonometry

Example Key Words

Hypotenuse

The longest side of a triangle. It is also the side opposite the right angle.

Pythagoras' Theorem

A theorem stating that in a right triangle the area of the square on the hypotenuse is equal to the sum of the areas of the squares drawn on the other two sides.

The side opposite (opposite) and next to (adjacent) the angle you are dealing with in a triangle (not the right angle)

The Sine ratio

The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to that of the hypotenuse.

The Cosine ratio

The cosine of an angle in a right triangle is defined as the ratio of the length of the side adjacent to the angle to that of the hypotenuse.

The Tangent ratio

The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to that of the adjacent side.

Area and Volume

Overview

– Perimeter and area

– Units and accuracy

– Prisms

– Circles

– Sectors of circles

– Cylinders and spheres

– Pyramids, cones and spheres

Example Key Words

Surface area

The sum of the areas of all faces of a solid figure

Prism

A 3D shape that has the same cross sectional throughout the length of the shape.

Circumference of a circle

The perimeter of a circle.

Radius and Diameter of a circle

The radius is a straight line from the centre to the circumference. The diameter goes from one side of the circle to the other passing through the centre.

Segment of a circle

Equations and Inequalities

Overview

– Completing the square

– Solving simultaneous equations

– Solving linear and quadratic inequalities

Example Key Words

Variable

A symbol that stands for an unknown quantity

Equation

A mathematics statement that uses an equals sign to show that two expressions are equal.

Inequality

A relationship between two expressions that are not equal, often written with the symbols >, >, <, and

An expression or equation that includes an x²

Simultaneous equations

A set of two or more equations that contain two or more unknown quantities

Completing the square

A way of simplifying or solving a quadratic equation by adding an expression to both sides to make one part of the equation a perfect square.

Multiplicative reasoning

Overview

– Growth and decay (To include loan sharks and exponential growth in diseases)

– Compound measures

– Ratio and proportion

Example Key Words

Compound Interest

The amount of interest earned each year is added onto the original capital and included in the following year’s calculation

Simple interest

The total amount of interest is added on at the end the term

Depreciation

The reduction in value of an asset over time.

Growth and decay

Using a compound interest type formula to calculate the growth of a population or depeciation of an asset

Direct Proportion

A direct relationship between the increase or decrease of two variables.

Inverse proportion

The relationship between one variable is directly proportional to the reciprocal of another.

More Trigonometry

Overview

– Accuracy

– Graph of the sine and Cosine functions

– The tangent function

– Calculating areas of non right angled triangles

– Using the Sine and Cosine rules

– Solving problems in 3D

– Transforming trigonometric graphs

Example Key Words

Area = 1/2abSinC