Page 2: Triangle Measurements

This page continues with right-angled triangle problems, featuring a triangle with sides of 9m and 2m.

Example: Using Pythagoras' theorem: x² = 9² + 2² x² = 81 + 4 x² = 85 x = √85 = 9.2

Highlight: The answer is rounded to one decimal place as specified in the question.

Page 3: Number Properties

This page explores different types of numbers and their properties, using a set of numbers: 3, 5, 12, 10, 9, 26, 24.

Vocabulary:

• Odd numbers: Numbers that cannot be divided evenly by 2
• Multiple: A number that can be divided evenly by another number
• Square number: The result of multiplying a number by itself
• Prime number: A number with exactly two factors - 1 and itself

Example: From the given set:

• Odd number: 3
• Multiple of 12: 24
• Square number: 9
• Prime numbers: 3, 5

Page 4: Number Representation

This page focuses on writing numbers in figures and words and understanding place value.

Example:

• "Five hundred and seven" written in figures: 507
• "Forty thousand" written in figures: 40,000
• The value of 7 in 476 is 70

Highlight: When rounding numbers to the nearest hundred, look at the tens digit to determine whether to round up or down.

Page 5: Solving Equations

This page covers solving various types of linear and algebraic equations.

Example: Solutions demonstrated:

• 2x-14 = 3x = 12
• 4x+4 = x-5
• 3$x-5$ = 15

Highlight: When solving equations, perform the same operation on both sides to maintain equality.

Page 6: Algebraic Expressions

This page demonstrates how to expand and simplify algebraic expressions through various operations.

Example:

• Simplifying: 7y + 4x - 6 + 3x + 7
• Factorising: 3x²-5x
• Expanding: 5-2$x+2$
• Expanding: x-6$$2x-4

Highlight: When expanding brackets, multiply each term inside by each term outside and combine like terms.

Page 1: Right-Angled Triangle Problems

This page introduces the application of Pythagoras' theorem in solving right-angled triangle problems. The problem demonstrates calculating the hypotenuse of a triangle with sides 16km and 7km.

Definition: Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides $a²+b²=c²$.

Example: For a triangle with sides 16km and 7km, the calculation is: x² = 16² + 7² x² = 256 + 49 x² = 305 x = √305 = 17.464

Highlight: When solving these problems, always remember to give answers to the specified number of significant figures.