Practice using the log rules to add and subtract logarithms

The student is shown a circuit diagram with three logic gates. It's always in the form (a OP b) OP (b OP c).

They have to fill in a truth table for the circuit. There is a step which expands the truth table, adding a column for each of the first two gates.

Dealing with adding, subtracting, multiplying, dividing, and taking powers of negative numbers.

Face, Place and actual value, adding, subtracting, multiplying, dividing and rounding decimals.

Adding, subtracting and multiplying two and three digit numbers. Now with worked solutions.

AMRC Skills Audit - covering the following programmes:

Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.

This question uses a Geogebra applet to solve a linear program with two variables using the graphical method. It contains three steps:

1. Construct the feasible area (polygon) by adding the constraints one by one. The students can see what happens when the constraints are added.
2. Add the objective function, and the level set of the objective value is shown, as well as its (normalised) gradient.
3. Compute the optimal solution by moving the level set of the objective around.

No description given

Generates two sets of matrices that can be added and asks the student to add them. Will ensure that the dimensions in part a) are different to the dimensions in part b) to offer some variety.

Add (a/b).x +/- (c/d) where a,b,c,d are randomised positive integers, and x is a randomised letter.

Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

Fractions already have a common denominator. Addition and subtraction 50:50 split. Students shouldn't have to worry about reducing fractions by design.

No description given

No description given

Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

Practice with adding, subtracting and dividing basic algebraic fractions

Fractions already have a common denominator. Addition and subtraction 50:50 split, when subtracting, the answer is negative half the time. Students shouldn't have to worry about reducing fractions by design.

Fractions don't have a common denominator. Need to find one. Addition and subtraction 50:50 split.

The student is asked to give the roots of a quadratic equation. They should be able to enter the numbers in any order, and each correct number should earn a mark.

When there's only one root, the student can only fill in one of the answer fields.

This is implemented with a gap-fill with two number entry gaps. The gaps have a custom marking algorithm to allow an empty answer. The gap-fill considers the student's two answers as a set, and compares with the set of correct answers.

The marking corresponds to this table:

A custom marking algorithm picks out the names of the constants of integration that the student has used in their answer, and tries mapping them to every permutation of the constants used in the expected answer. The version that agrees the most with the expected answer is used for testing equivalence.

If the student uses fewer constants of integration, it still works (but they must be wrong), and if they use too many, it's still marked correct if the other variables have no impact on the result. For example, adding $+0t$ to an expression which otherwise doesn't use $t$ would have no impact.

There are two parts: 

(3x)/4-x/5+x/3 and (3x/4)-(x/5+x/3).

The numbers are randomised to small, coprime, positive integers.

This is a fixed, unmarked, question:

Show that (x1)/((1/x3)-(1/x2))) = (x1x2x3)/(x2-x3)

Simplify (qx+a)/(rx+b) +/- (sx+c)/(rx+b)^2

x is a randomised variable. a,b,c,d,q,r are randomised integers.

Simplify (qx+a)/(rx+b) +/- (sx+c)/(tx+d)

x is a randomised variable. a,b,c,d,q,r,s,t are randomised integers. a,b,c,d run from -5 to 5, including 0. q,r,s,t run from -3 to 3, and can be 0 if the constant term is nonzero, but are mostly 1.

Adding and subtracting two 3x3 matrices.

No description given

Add indices. Part of HELM Book 1.2

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.

This is a set of questions designed to help you practice adding, subtracting, multiplying and dividing fractions.

All of these can be done without a calculator.