Eight questions on finding least upper bounds and greatest lower bounds of various sets.

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

What is the value of the expression given a choice of n?

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Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

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

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

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

Questions involving various techniques for rearranging and solving quadratic expressions and equations

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

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

Rearrange expressions in the form $ax^2+bx+c$ to $a(x+b)^2+c$.

Apply the factor and remainder theorems to manipulate polynomial expressions

Questions on rearranging expressions, expanding brackets and collecting like terms.

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

Factorise polynomials by identifying common factors. The first expression has a constant common factor; the rest have common factors involving variables.

Translation to Dutch of 

"Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

The word problem is about the costs of sweets in a sweet shop."

Testing factorisation of quadratics.

Instructions on inputting ratios of algebraic expressions.

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

One question on determining whether statements are propositions.

Four questions about truth tables for various logical expressions.

A basic introduction to differentiation

A basic introduction to differentiation

Testing factorisation of quadratics.

Using $\cos^2\theta+\sin^2\theta=1$ to evaluate expressions.

Factorise a quadratic expression of the form $x^2+akx+bk^2$ for $x$, in terms of $k$. $a$ and $b$ are constants.

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.

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

Rearrange some expressions involving logarithms by applying the relation $\log_b(a) = c \iff a = b^c$.