Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

9 questions: Expanding out expressions such  $(ax+b)(cx+d)$ etc.

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).

9 questions: Expanding out expressions such  $(ax+b)(cx+d)$ etc.

9 questions: Expanding out expressions such  $(ax+b)(cx+d)$ etc.

Use the rule $\log_a(n^b) = b\log_a(n)$ to rearrange some expressions.

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

A method of randomly choosing variable names - use the expression() JME function to create a variable name from a randomly chosen string.

(This question also uses a custom marking script to check that the student has simplified the expression)

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 $b^{\log_b(x)}$.

Multiplication and addition of complex numbers. Four parts.

Multiplication and addition of complex numbers. Four parts.

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 $b^{\log_b(x)}$.

Instructions on inputting ratios of algebraic expressions.

rebelmaths

The expression $p\Rightarrow q\Rightarrow r$ is ambiguous.

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

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

Create a truth table for a logical expression of the form $((a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d))\operatorname{op4}e $ where each of $a, \;b,\;c,\;d,\;e$ can be one the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3},\;\operatorname{op4}$ one of $\lor,\;\land,\;\to$.

For example: $((q \lor \neg p) \to (p \land \neg q)) \lor \neg q$

Create a truth table for a logical expression of the form $(a \operatorname{op1} b) \operatorname{op2}(c \operatorname{op3} d)$ where $a, \;b,\;c,\;d$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and each of $\operatorname{op1},\;\operatorname{op2},\;\operatorname{op3}$ one of $\lor,\;\land,\;\to$.

For example: $(p \lor \neg q) \land(q \to \neg p)$.

Create a truth table for a logical expression of the form $a \operatorname{op} b$ where $a, \;b$ can be the Boolean variables $p,\;q,\;\neg p,\;\neg q$ and $\operatorname{op}$ one of $\lor,\;\land,\;\to$.

For example $\neg q \to \neg p$.

Simplifying algebraic expressions

Simplifying algebraic expressions

A basic introduction to differentiation

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