Currency Conversion

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Convert kilometers to miles

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Convert from one measurement scale to another

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Convert from one measurement scale to another

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Decimal Places and Significant Figures

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Decimal Places and Significant Figures

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Multiplying and dividing decimals

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Arithmetic

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Order of Operations

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Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

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Given vectors $\boldsymbol{a,\;b}$, find $\boldsymbol{a\times b}$

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Stem and leaf, summation notation, cumulative frequency, relative cumulative frequency.

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15 questions based on module so far. 

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Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

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Definite Intgerals

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Indefinite Integrals

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Antiderivatives

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Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ by differentiating an implicit equation.

A collection of true/false questions aiming to reveal misconceptions about concepts encountered in a first year pure maths course.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Given polynomial $f(X)$, $g(X)$ over $\mathbb{Q}$, find polynomials $q(X)$ and $r(X)$ over $\mathbb{Q}$ such that $f(X)=q(X)g(X)+r(X)$ and $\operatorname{deg}r(X) \lt \operatorname{deg}g(X)$.

Factorise 4 polynomials over $\mathbb{Z}_5$.

$f(X)$ and $g(X)$ are polynomials over $\mathbb{Z}_n$.

Find their greatest common divisor (GCD) and enter it as a monic polynomial.

Hence factorize $f(X)$ into irreducible factors.

Given two propositions in mathematics using quantifiers, choose the corresponding negation of the proposition. For example, the negation of: $\displaystyle \exists a \in \mathbb{R^+},\;\exists b \in \mathbb{N},\;\exists c \in \mathbb{N}\;\left[(c \lt b+1) \land \left(\frac{1}{2^n} \geq 3a\right)\right]$