Simplifying indices.

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Express $\log_a(x^{c}y^{d})$ in terms of $\log_a(x)$ and $\log_a(y)$. Find $q(x)$ such that $\frac{f}{g}\log_a(x)+\log_a(rx+s)-\log_a(x^{1/t})=\log_a(q(x))$

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

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Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Simplify fractions involving the products of factorials.

Cancelling to reduce a fraction to its lowest terms.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

A question to practice simplifying fractions with the use of factorisation (for binomial and quadratic expressions).

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Simplifying algebraic expressions

Simplifying algebraic expressions

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Use laws for addition and subtraction of logarithms to simplify a given logarithmic expression to an arbitrary base.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Cancelling to reduce a fraction to its lowest terms.

Simplifying expressions such as $b^{\log_b(x)}$ and $b^{\log_b(x)}$.

Simplifying algebraic expressions

Practice with fractions

Simplifying algebraic expressions

This exam covers 

• laws of indices
• using surds and rationalising the denominator
• expanding brackets
• simplifying expressions
• solving linear inequalities
• finding common factors
• dividing a polynomial with remainders, using algebraic division
• factor theorem
• remainder theorem
• inverse and composite functions

Cancelling to reduce a fraction to its lowest terms.

Simplify algebra expressions