A two part question. Students are first given the formula for the time for a ball to come to rest after being dropped on a block. Part a) asks the students to rearrange the formula to make e, the coefficient of restitution, the subject of the formula. Part b) gives students realistic values for variables in the formula and asks them to calculate the coefficient of restitution using the formula derived in part a). 

The relationship between the frequency of an allele A, $x$, at a genetic locus in a diploid population and the fitness of a population with this frequency of allele A, $w$, is described by the function $w=ax^2+x(b-x)+c(b-x)^2$ . The aims are (a) ti simplify the algebraic expression, (b) calculate the fitness of a population with a given allele A frequency, and (c) calculate the allele A frequency when the fitness of the population is given.

The proportion of the sodium carbonate, $p$, which has dissolved by time $t$ seconds is given by the formula $ p=\frac{bt-at^2}{c}$. The aim is to calculate the proportion of sodium carbonate in a solution at a given time and vice versa.

The dimensions of a rectangle are given in m and cm. Compute the area or perimeter.

The student is given a quadratic formula and asked to fill in a table of values of $f(x)$ for a given range of $x$.

There is also a plot of the points, which updates when the table is filled in, or the student can move the points to fill in the table.

The table uses the spreadsheet and JSXgraph extensions.

HELM Book 1.5 Formulae and substitution exercises.

A difficult question that involves rearranging a complicated formula, then applying unit conversions to variable values, then evaluating the formula for the selected value. The variable values are randomised.

Rearrange a linear formula au + bv + cw = d to make one of u,v,w the subject.

Choice of 2 formulae. The first is a fraction of the form y=(r+x)(1-rx). The second is of the form y=sqrt[(1-x)/(1+x) ]. Rearrange to make x the subject.

Rearrange a formula with a square root to make a variable under the root the subject.

Rearrange a complex formula involving squares, square roots, fractions and additions. This is a fixed question with no randomisation.

Rearrange a linear function in x and y to make y the subject. Line variables are randomised.

Transpose PV=RT to make a random variable the subject.

Given the formula for a cone or a cylinder, and values for r and h, find the volume.

evaluate a function (4a)/(pi*b^2cd) given random values for a,b,c,d.

Evaluate pi / (2r+s) given values for r and s (r>0, s positive or negative)

evaluate sqrt(x/z) where x and z are random positive decimals.

Compute P = 3/(QR) given values for Q and R.

HELM Book 1.5.1: using formulae and substitution: task 1

Given the original formula the student enters the transformed formula

Working 26_10_16

Given the original formula the student enters the transformed formula

Factorising a quadratic expression of the form $a^2x^2-b^2$ to $(ax+b)(ax-b)$, using the difference of two squares formula.

A quick practice set of problems for education students to take in preparation for their numeracy test.

LP: Formulating dual problems

Formulating duality problems

Formulating duality problems

Formulating duality problems

Formulating duality problems

Formulating duality problems

Formulating duality problems