Xiaodan Leng

Three graphs are given with areas underneath them shaded. The student is asked to calculate their areas, using integration.  Q1 has a polynomial. Q2 has exponentials and fractional functions. Q3 requires solving a trig equation and integration by parts.

Three graphs are given with areas underneath them shaded. Student is asked to determine the minimum and maximum $x$-values of the regions. This will involve solving a linear equation and two trigonmetric equations.

Graphs are given and students are required to match them with their equation.

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

rebelmaths

Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

rebelmaths

Elementary Exercises in multiplying matrices. 

Find the determinant of a $3 \times 3$ matrix.

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

Cofactors Determinant and inverse of a 3x3 matrix.

Introduces students to the floor and ceiling functions

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

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Slope of a curve at a point

Evaluate $\int_0^{\,m}e^{ax}\;dx$, $\int_0^{p}\frac{1}{bx+d}\;dx,\;\int_0^{\pi/2} \sin(qx) \;dx$. 

No solutions given in Advice to parts a and c.

Tolerance of 0.001 in answers to parts a and b. Perhaps should indicate to the student that a tolerance is set. The feedback on submitting an incorrect answer within the tolerance says that the answer is correct - perhaps there should be a different feedback in this case if possible for all such questions with tolerances.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Given vectors $\boldsymbol{A,\;B}$, find $\boldsymbol{A\times B}$

Dividing a cubic polynomial by a linear polynomial. Find quotient and remainder.

Find roots and the area under a parabola

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.

Given vectors  $\boldsymbol{v,\;w}$, find the angle between them.

Given vectors $\boldsymbol{v}$ and $\boldsymbol{w}$, find their inner product.

Find the nth term of an Arithmetic progression

Display a fraction, given as a numerator and a denominator, as a mixed fraction when appropriate.

Entering numbers and algebraic symbols  in Numbas.

Details on inputting numbers into Numbas.