HELM Book 1.4.3 Exercises: addition and subtraction of algebraic fractions

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)

Given 2 or 3 fractions such as A/(2x+5), add them.

There are 5 possible versions.

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.

Simplify ax/b +/- cx/d, where x is a randomised variable, and a,b,c,d are randomised integers.

Add two algebraic fractions. Part of HELM Book 1.4.3.

6 Exercises from HELM Book 1.4 Part 2: Multiplication and Division of Algebraic Fractions.

Part of HELM Book 1.4.2

The student is asked to calculate a division by the method of long division, which they should enter in a grid.

The process is simulated and the order in which cells are filled in is recorded, so the marking feedback tries to identify the first cell that the student got wrong, or should try to fill in next.

They're asked to give the quotient as a plain number in a second part, to check that they can interpret the finished grid properly.

Shows how to switch to the 3D graphics view of a geogebra applet using an extension function.

Should not be used: this relies on a custom JavaScript which is not guaranteed to continue working.

Wrap the student's answer in set() so it's marked as a set.

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Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Shows how the "give a number which satisfies an equation" part type can be used to makr the student's number correct if it satisfies an equation of the form $f(x) = 0$.

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

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This question shows a JSXGraph diagram above a mathematical expression input, containing a plot of the expression the student enters.

Directional derivative of a scalar field.

Given an equation with variable x in the power on two different bases, students must solve for x. Hints are included in the question to aid the student as needed.

Basic fraction arithmetic, giving answers in lowest form.

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

Given an equation where x is the base of a log term, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation involving x as a power on e, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Given an equation with log terms added together, the student must solve for x. Hints are included in the question to aid the student as needed.

Uke 7