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This page explains vector representation and addition in mathematics, showing how vectors can be equal and combined.
Vocabulary: Vectors are quantities that have both magnitude and direction.
Highlight: Vector addition is demonstrated through the relationship a + b = c, where vectors can be combined to form new vectors.
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The page demonstrates solving simultaneous equations using substitution and elimination methods.
Example: Two sets of equations are solved:
Highlight: Solutions show step-by-step working to find values for x and y.
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This section explains the concept of inverse proportion and its mathematical representation.
Definition: When two quantities are inversely proportional, as one increases, the other decreases in proportion so their product remains constant.
Formula: A = k/B, where k is the constant of proportionality.
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The page covers direct proportion relationships between variables.
Definition: Two quantities are directly proportional when they increase or decrease in the same ratio.
Example: Using y = kx, when y = 20 and x = 5, finding k = 4 to solve for other values.
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This section focuses on expanding algebraic expressions with single and squared terms.
Highlight: Special attention is given to squared terms, noting that they must be multiplied by themselves.
Example: 2x+1$$3x+3 is expanded to 6x² + 13x + 3
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Continues with more complex bracket expansion examples.
Example: Multiple expansions including:
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Explains how to calculate compound interest using a calculator.
Formula: Initial × Multiplier^Time
Example: £8000 invested at 3% for 4 years, calculating to £9004.07
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Shows manual calculation method for compound interest.
Example: £3000 invested at 10% for 2 years, with step-by-step calculations.
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Provides formulas for calculating areas of different shapes and introduces 3D shape terminology.
Vocabulary:
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Explains how to calculate percentages of amounts.
Method: Two-step process:
