Questions on manipulating logarithms.

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

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Power rule

Equating coefficients of a polynomial. Basic ones that don't require simultaneous equations.

Slope of a curve at a point

Convert from degrees to radians

Questions on powers, the laws of indices, and exponential growth.

 Some questions on working with surds.

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product and chain rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$. Non-calculator. Advice is given.

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In parts (a) and (b) rearrange linear inequalities to make $x$ the subject.

In the parts (c) and (d) correctly give the direction of the inequality sign after rearranging an inequality.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

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.

Very good feedback and corresponds to instance of randomisation

A graph of a straight line $f$ is given. Questions include determining values of $f$, of $f$ inverse, and determining the equation of the line.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs.

Version I. Graph is quadratic

Version II. Graph is horizontal

Version III. Graph is cubic

Version IV. Graph is sinusoidal

Multiply two numbers in standard form, then divide two numbers in standard form.

Needs marking algorithm to allow equal values in standard form to gain equal marks

Solve a quadratic equation by completing the square. The roots are not pretty!

Words

Students are presented with two random integers to add together. They are ieach n the range -10 to 10.

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The student will be given 2 integers between -9 and +9 to add together.

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The thicknesses of two sedimentary layers are given. The student has to add the thicknesses and give the answer to 2 siginificant figures.

Questions on manipulating logarithms.

A collection of questions (frequently updated) to demonstrate the usage of the Logic extension.

Current questions:

• Make syllogisms (either valid, invalid or valid under an additional assumption);
• Write statements in Polish and reverse Polish notation, find the truth table, determine satisfiability;
• Test whether a collection of statements $\Gamma$ models a statement $\phi$;
• Write the Disjunctive and Conjunctive Normal Forms for a statement.

Needs the Logic Extension!

Addition Formulas in Trigonometry. Range of Sinusoidal functions. 

Integration techniques for monomials and simple polynomials.