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Welcome to GCSE Edexcel Maths revision.

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Topic M 7: Expressions and substitution.

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This video covers Foundation and Higher tiers.

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A variable represents a number that may be unknown or change.

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In 5 x plus 3, 5 is the coefficient of x, 3 is a constant, and 5 x and 3 are terms.

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An expression has no equality sign;

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an equation states two expressions are equal;

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a formula relates quantities;

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an inequality compares values;

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an identity is true for all allowed variable values.

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Write a multiplied by b as a b, y plus y plus y as 3 y, and a multiplied by a as a squared . 2 x means 2 multiplied by x, not a two-digit number.

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Like terms have the same variable part and powers: 4 x plus 3 x minus 2 equals 7 x minus 2.

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Terms such as x and x squared are not like terms.

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Worked example: 3 a plus 4 b minus a plus 2 b equals 2 a plus 6 b.

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Keep the sign with each term when collecting.

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Multiplication uses coefficient and index rules: 3 x multiplied by 4 x squared equals 12 x cubed .

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Addition is different: 3 x plus 4 x squared cannot be simplified to 7 x cubed .

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Substitution replaces each variable with its given value.

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Put negative values in brackets before powers or multiplication.

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Worked example: If x equals minus 2 and y equals 3,

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then 2 x squared minus 3 y equals 2 multiplied by open bracket minus 2 close bracket squared minus 3 multiplied by open bracket 3 close bracket equals 8 minus 9 equals minus 1.

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Worked example: For v equals u plus at,

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with u equals 5 metres per second,

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a equals 2 metres per second squared and t equals 4 seconds,

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v equals 5 plus 2 multiplied by 4 equals 13 metres per second.

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Include units and follow the order of operations.

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In a function machine, an input undergoes a fixed sequence of operations.

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Input x, multiply by 3 then add 2 gives output 3 x plus 2.

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A two-step function machine

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To recover the input, undo the operations in reverse order: output 17 gives open bracket 17 minus 2 close bracket divided by 3 equals 5.

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Subtracting after division would undo the wrong sequence.

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Five less than twice a number is 2 x minus 5.

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Five minus twice a number is 5 minus 2 x.

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Read the wording carefully before writing symbols.

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If one ticket costs p pounds, four tickets cost 4 p pounds.

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If a total charge includes a fixed 3 pounds fee, the formula is C equals 4 p plus 3, not 4 multiplied by open bracket p plus 3 close bracket .

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Evaluate and simplify are different instructions.

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Simplify keeps variables; evaluate finds a numerical value after substitution.

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Check a simplification by testing a sensible value, although one matching value alone is not a proof.

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That completes Expressions and substitution.

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Revisit the notes and test yourself on the revision website.