A variety of trigonometric equations which can be solved using inverse operations.

Practice using the log rules to add and subtract logarithms

Algebra:  Quadratic Factorisation.

              Coefficient of squared term is 1.

Factorising polynomials using the highest common factor

No caculation 'concept test' on confidence intervals.  A single multiple choice question interpreting a CI.

Modulus and argument of a single complex number $z=z_1/z_2$, where $\mathrm{Re}(z_1)=\mathrm{Im}(z_1)$ and $\mathrm{Re}(z_2)=-\mathrm{Im}(z_2)$.

Calculating the derivative of a function of the form $ax^n \ln(bx)$ using the product rule.

Find the derivative of a function of the form $y=a \sin(bx+c)$ using a table of derivatives.

Recoginising different forms of calculus notation.

Practice using the log rules to add and subtract logarithms

Solve equations involving logs and exponential functions, by using inverse operations.

Rewriting expressions of the form $n\log(a)\pm m\log(b)$ as a single logarithm.

Homework set.  Find 2-D moments or balance moments using Verignon's theorem:  $ M = \pm F_x d_y \pm F_y d_x$

Calculating the derivative of a function of the form $(ax+b)^n$ using the chain rule.

Homework set.  Variations on problems involving single particle equilibrium.

Homework set.  Determine the moment of a force using the definition of the moment, $M = F d_\perp$.

Horizontal and vertical shifts and scales of a random cubic spline

Calculating the derivative a function of the form $ax^n \sin(bx)$ using the product rule.

Homework set.  Rigid body equilibrium solved using the three-force body principle.

Homework Set.  Three problems to brush up on trig skills.  Right triangles and sine and cosine law.

Use Matlab (or Python) to fit a cubic polynomial to data, and determine where the x-axis is crossed.

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

rebelmaths

Factorising polynomials using the highest common factor.

Adapted from 'Factorisation' by Steve Kilgallon.

Calculate the moment of a force about three points using Verignon' theorem.  All forces and points are in the same plane.

testing sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees but in radians

testing sin, cos, tan of angles that are negative or greater than 2pi radians that result in nice exact values. 

exact value of testing sin, cos, tan of angles that are negative or greater than 360 degrees that result in nice exact values. 

multiple choice testing sin, cos, tan of  random(pi/6, pi/4, pi/3) radians

exact value of sin, cos, tan of  random(0,90,120,135,150,180,210,225,240,270,300,315,330) degrees