Find $\displaystyle\int \frac{ax+b}{(x+c)(x+d)}\;dx,\;a\neq 0,\;c \neq d $.

Three questions on parametric hypothesis testing and confidence intervals, aimed at psychology students.

Mini-test on concentration of solutions.

Mini-test on diluting solutions.

Testing your ability to manipulate SI units.

Given two numbers, find the gcd, then use Bézout's algorithm to find $s$ and $t$ such that $as+bt=\operatorname{gcd}(a,b)$.

Finally, find all solutions of an equation $\mod b$.

Three questions on using the Student $t$ distribution to perform hypothesis tests.

Following part 2, "Questions on Data Tables", from the Maths Aid workbook "Numerical reasoning tests".

Only doing the first 4 questions because the others involve trends that need lots more thinking about how to randomise.

Not finished!

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Diagnostic testing on differentiation.

4 questions testing the precedence of operations applied to integers. In other words testing BIDMAS: Brackets, Indices, Division/Multiplication and Addition/Subtraction.

26 questions: Product Rule, Quotient Rule and Chain Rule. For those that want a thorough testing of their basic differentiation using the standard rules.

No description given

No description given

Find the determinant and inverse of three $2 \times 2$ invertible matrices.

Paired t-test to see if there is a difference between responses after treatment.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Testing an hypothesis about the mean of one group.

Testing an hypothesis about the mean of one group.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $0$ and $2 \pi$ and careful with quadrants!

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Paired t-test to see if there is a difference between responses after treatment.

Given the pdf  $f(x)=\frac{a-bx}{c},\;r \leq x \leq s,\;f(x)=0$ else, find $P(X \gt p)$, $P(X \gt q | X \gt t)$.

Template question. The student is asked to perform a two factor ANOVA to test the null hypotheses that the measurement does not depend on each of the factors, and that there is no interaction between the factors.

Given a probability mass function $P(X=i)$ with outcomes $i \in \{0,1,2,\ldots 8\}$, find the expectation $E$ and $P(X \gt E)$.

Determine if the following describes a probability mass function.

$P(X=x) = \frac{ax+b}{c},\;\;x \in S=\{n_1,\;n_2,\;n_3,\;n_4\}\subset \mathbb{R}$.

Two numbers from a set of $5$ numbers are chosen at random, without replacement. Find the distribution $X$ of their sum and $E[X]$.

The random variable $X$ has a PDF which involves a parameter $c$. Find the value of $c$. Find the distribution function $F_X(x)$ and $P(a \lt X \lt b)$.

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!