Algebra and Equality

This page delves deeper into algebraic concepts, focusing on equations and the principle of equality.

Vocabulary: Equality refers to the state of being equal or equivalent.

The page provides examples of algebraic equations and demonstrates how to solve them using the concept of equality.

Example: In the equation 4x + 3x - 2x = 5x, like terms are combined to simplify the expression.

There are also practice problems that involve filling in missing numbers to maintain equality in equations.

Highlight: The page emphasizes the importance of grouping like terms in algebraic expressions and understanding the concept of equality in equations.

Shapes and Angles

This page focuses on geometric shapes and their properties, particularly squares, triangles, and quadrilaterals.

Definition: A square is a four-sided shape with all sides equal and all angles measuring 90 degrees.

Definition: A triangle is a three-sided shape with angles that add up to 180 degrees.

The page provides information on different types of triangles $equilateral, isosceles, and scalene$ and their properties.

Vocabulary: Perpendicular lines meet at a right angle $90 degrees$.

Highlight: The page emphasizes the importance of understanding the properties of different shapes and how angles relate to these properties.

Sequences

This page provides an in-depth look at sequences, offering numerous examples and practice problems.

Definition: A sequence is a series of numbers that follow a specific pattern or rule.

The page includes exercises where students are asked to identify and continue various sequences.

Example: In the sequence 3, 5, 7, 9, ..., students are asked to write down the 5th and 6th terms.

Highlight: The page emphasizes the importance of recognizing patterns in sequences and being able to continue them based on the identified rule.

Linear Sequences

This page focuses specifically on linear sequences, a key concept in GCSE Maths.

Definition: A linear sequence is a sequence that goes up or down by the same amount each time.

Highlight: Linear sequences give straight line graphs when plotted.

The page provides examples of how to create different linear sequences starting from the same number.

Example: Two different linear sequences starting with 20: 20, 25, 30, 35, ... and 20, 27, 34, 41, ...

Vocabulary: The term "linear" refers to the constant difference between consecutive terms in the sequence.

Geometric Sequences

This page introduces geometric sequences, another important concept in GCSE Maths.

Definition: A geometric sequence is a sequence where each term is found by multiplying or dividing the previous term by a constant.

The page provides several examples of geometric sequences.

Example: 2, 6, 18, 54, ... is a geometric sequence where each term is multiplied by 3 to get the next term.

Highlight: The page emphasizes the difference between linear sequences $which involve addition or subtraction$ and geometric sequences $which involve multiplication or division$.

Inverse Operations

This page focuses on inverse operations, a crucial concept in algebra and problem-solving.

Definition: Inverse operations are operations that undo each other.

The page illustrates how addition and subtraction are inverse operations, as are multiplication and division.

Example: If you add 5 to a number and then subtract 5, you end up with the original number.

Highlight: Understanding inverse operations is crucial for solving equations and manipulating algebraic expressions.

Function Machines

This page introduces the concept of function machines, a key topic in algebra sequences and function machines study guide PDF.

Definition: A function machine is a diagram that shows how a number $input$ is changed according to certain rules to produce a result $output$.

The page provides examples of function machines and how to use them.

Example: If the input is 4 and the function machine multiplies by 2 and then adds 6, the output would be 14.

Highlight: Function machines are a visual way to represent mathematical operations and can help in understanding more complex algebraic concepts.

Function Machines Practice

This page provides additional practice with function machines, reinforcing the concepts introduced in the previous page.

The page includes several examples of function machines with different operations.

Example: A function machine that multiplies the input by 3 and then adds 5.

Highlight: The page emphasizes the importance of understanding both the input and output of function machines, as well as the operations performed within the machine.

Multiplying Algebraic Expressions

This page focuses on multiplying algebraic expressions, an important skill in algebra.

Definition: When multiplying algebraic expressions, we multiply the coefficients and combine like terms.

The page provides examples of how to multiply algebraic expressions.

Example: 5x × 5x = 25x²

Vocabulary: Coefficients are the numerical factors of algebraic terms.

The page also introduces the concept of substitution in algebra.

Definition: Substitution in algebra involves replacing variables with specific values.

Example: If x = 5, then 3x + 2 would become 3$5$ + 2 = 17

Algebraic Substitution Practice

This page provides further practice with algebraic substitution, building on the concepts introduced in the previous page.

The page includes several examples where students are asked to substitute given values into algebraic expressions.

Example: If x = 10, what is the value of 3x + 2?

Highlight: The page emphasizes the importance of following the order of operations when performing substitutions.