Video lecture (English) of C01 Algebraic Manipulations
C01 Algebraic Manipulations
What’s on the Specification
| M4.1 | Understand, use and interpret algebraic notation; for instance: $ab$ in place of $a \times b$; $3y$ in place of $y + y + y$ and $3 \times y$; $a^2$ in place of $a \times a$; $a³$ in place of $a \times a \times a$; $a²b$ in place of $a \times a \times b$; $\frac{a}{b}$ in place of $a\div b$. |
| M4.2 | Use index laws in algebra for multiplication and division of integer, fractional, and negative powers. |
| M4.3 | Substitute numerical values into formulae and expressions, including scientific formulae.
Understand and use the concepts and vocabulary: expressions, equations, formulae, identities, inequalities, terms and factors. |
| M4.4 | Collect like terms, multiply a single term over a bracket, take out common factors, and expand products of two or more binomials. |
| M4.5 | Factorise quadratic expressions of the form $x^2 + bx + c$, including the difference of two squares.
Factorise quadratic expressions of the form $ax^2 + bx + c$, including the difference of two squares. |
| M4.6 | Simplify expressions involving sums, products and powers, including the laws of indices.
Simplify rational expressions by cancelling, or factorising and cancelling. Use the four rules on algebraic rational expressions. |
| M4.7 | Rearrange formulae to change the subject. |
| M4.8 | Understand the difference between an equation and an identity.
Argue mathematically to show that algebraic expressions are equivalent. |
| MM1.1 | Laws of indices for all rational exponents. |
| MM1.2 | Use and manipulation of surds.
Simplifying expressions that contain surds, including rationalising the denominator. For example: simplifying $\frac{\sqrt{5}}{3+2\sqrt{5}}$ and $\frac{3}{\sqrt{7}-2\sqrt{3}}$ |
Learning Objectives
- Master the laws of indices to manipulate and simplify expressions involving integer, fractional, and negative exponents.
- Work fluently with advanced surds, including simplifying terms, rationalising complex denominators, and expertly applying methods (like completing the square) to denest nested surds.
- Distinguish logically between equations, identities, and formulae, and argue mathematically to prove algebraic equivalence.
- Expand and factorise complex expressions using high-level pattern recognition, including cross-multiplication for quadratics, the difference of two squares, perfect square trinomials, and the sum/difference of cubes.
- Manipulate and simplify algebraic fractions (rational expressions) by thoroughly factorising numerators and denominators before applying the four arithmetic rules.
- Rearrange complex formulae efficiently to change the subject, applying inverse operations in the strict algebraic order.
Suggested Time
| Task | No. of Questions | Suggested Time |
|---|---|---|
| Examples | 13 | 120 min min |
| Quiz | 8 | 15 min min |
| Practice A | 30 | 75 min min |
| Practice B | 20 | 75 min min |
| Total | 71 | approx. 4-5 hrs |
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