Two double integrals with numerical limits

Double integrals (2) with numerical limits

Two double integrals with numerical limits

Double integrals (2) with numerical limits

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

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Students are given six graphs, corresponding to curves $\gamma(t)$. They must match each with its signed curvature function, $\kappa(t)$.

The graphs are generated by calculating $\theta(t)=\int \kappa(t) \mathrm{d}t$ (by hand: these are given to the question as functions of a variable '#', in string form), and solving $x^{\prime}=\cos(\theta(t)-\theta(0))$ and $y^{\prime}(t)=\sin(\theta(t)-\theta(0))$ numerically (using the RKF method) with a JavaScript extension.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Add, subtract, multiply and divide numerical fractions.

Adapted from 'Algebraic fractions: operations involving algebraic fractions' by Ben Brawn.

Questions about percentage and ratio, applied to finance.

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

Arithmetic operations involving fractions; converting between decimals and fractions; deciding if fractions are equivalent.

Practice with fractions

Practice with fractions

No description given

A few simple functions are provided of the form ax, x+b and cx+d. Values of the functions, inverses and compositions are asked for. Most are numerical but the last few questions are algebraic.

Examples of the following custom part types: Yes/no, List of numbers, Give a numerical input for an expression, Number entry modulo.

Differentiate $f(x) = (a x + b)/ \sqrt{c x + d}$ and find $g(x)$ such that $ f^{\prime}(x) = g(x)/ (2(c x + d)^{3/2})$.

Add, subtract, multiply and divide numerical fractions.

No description given

Given ratio of ingredients in a preparation, and amounts of each ingredient, work out how much of the preparation you can make.

Based on question 5 from section 3 of the maths-aid workbook on numerical reasoning.

Add, subtract, multiply and divide numerical fractions.

Practice with fractions

Two double integrals with numerical limits

No description given

Write down the Newton-Raphson formula for finding a numerical solution to the equation $e^{mx}+bx-a=0$. If $x_0=1$ find $x_1$.

Included in the Advice of this question are:

6 iterations of the method.

Graph of the NR process using jsxgraph. Also user interaction allowing change of starting value and its effect on the process.

Newton-Raphson numerical method question to solve $g(x)=0$

Includes a graph of the function $g(x)$ in Advice using Jsxgraph.

Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.

(Added to calculator test.)

Given percentages of males and females working on a project, and the percentage of the total staff who are male (or female), find the percentage of all staff working on the project.

Based on question 3 from section 3 of the maths-aid workbook on numerical reasoning.

Added to calculator test.

Added advice on using decimals.

Scale a page to some percentage of its original size, then increase/decrease by another percentage. Find the size of the final copy as a percentage of the original.

Based on question 2 from section 3 of the Maths-Aid workbook on numerical reasoning.

(Added a decimal version to advice - and changed increased to enlarged)

Used in non-calculator quiz.

Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.

Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.

(Used in Non-Calculator test.)