4 questions on integrating by parts.

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!

Questions about percentage and ratio, applied to finance.

Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.

10 questions on the product rule in differentiation.

Diagnostic testing on differentiation.

8 questions on the quotient rule in differentiation.

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

3 questions. One question on limits of standard sequences. Other two on finding least $N$ such that $|a_n-L |\lt 10^{-r},\;\;n \geq N$ where $L$ is limit of $(a_n)$.

3 questions. Finding the stationary points of functions of 2 variables.

Partial differentiation.

8 questions using logarithms. 7 questions use logarithms to solve equations.

5 questions on finding local and global maxima and minima on compact intervals and on the real line for differentiable functions.

4 questions. Qualitative, quantitative random variables, types of sampling, frequencies, stem and leaf plot, descriptive statistics.

7 questions on numeric fractions.

2 questions. First question divides a cubic by a linear polynomial. The second divides a degree 4 polynomial by a degree 2 polynomial.

6 questions on standard statistical distributions.

Binomial, Poisson, Normal, Uniform, Exponential.

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

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.

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

3 questions on factorising quadratics. The second question also asks for the roots of the quadratic. The third question involves factorising quartic polynomials but which are quadratics in $x^2$.

4 questions involving hyperbolic functions.

5 questions on using substitution to find indefinite integrals.

4 questions on integrating by parts.

4 questions on using partial fractions to solve indefinite integrals.

Statistics and probability. 2 questions. Both simple regression. First with 8 data points, second with 10. Find $a$ and $b$ such that $Y=a+bX$. Then find the residual value for one of the data points.

11 Questions on the chain rule.

13 questions on combining algebraic fractions. An area in which students often need practice. 

Two questions on completing the square. The first asks you to express $x^2+ax+b$ in the form $(x+c)^2+d$ for suitable numbers $c$ and $d$. The second asks you to complete the square on the quadratic of the form $ax^2+bx+c$ and then find its roots.

Statistics and probability. Practice on correlation questions.

Various questions on predicates and sets.

Split $\displaystyle \frac{ax+b}{(cx + d)(px+q)}$ into partial fractions.