Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

An order of operation question using +,-,* with signed integers, with up to 4 variables.

The questions are the exercises from Q3 of HELM Book 1.1.5

The student is shown a GeoGebra worksheet containing a single point at the origin. They must move the point to the required coordinates.

The part is marked as correct if the point is in the right position.

Factorise a quadratic. Part of HELM Book 1.3

Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Given an expression 10^-k, rewrite it as a fraction with no index. k is a random positive integer from 1 to 6.

Part of HELM Book 1.2

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised and can be positive or negative numbers.

Part of HELM Book 1.2

Given an expression (either a^-k or 1/a^-k) with a negative index, rewrite it with a positive index.

The variable a and the index k are randomised.

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2

Students are given three expanded products and asked to write them in index notation. Part of HELM Book 1.2

Part of HELM Book 1.1

Part of HELM Book 1.1

Expand (x+a)(x+b)(x+c), where x is a randomised variable, and a,b,c are randomised integers.

Note that the pattern restriction in the marking checks that there are no brackets and that the expression is simplified to at most a single x^3, x^2, x and constant term; but it will let you get away with an additional -x^2 and/or -x term. (e.g., you could write 3x as 4x -x and the marking would accept this. This was to stop the pattern matching getting too complicated.

Part of HELM Book 1.3

Divisor is single digit. There is a remainder which we express as a decimal by continuing the long division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Eight expressions, of increasing complexity. The student must simplify them by expanding brackets and collecting like terms.

Use the BODMAS rule to determine the order in which to evaluate some arithmetic expressions. 

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Recovering original function given some information such as derivative and value at some point.

Find $\displaystyle \int ae ^ {bx}+ c\sin(dx) + px ^ {q} + k/x \;dx$.

Introduction to using the product rule

$x$ is given and (sin(x),cos(x)) is plotted on a unit circle.  Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

A quadratic equation (equivalent to $(x+a)^2-b$) is given and sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Finding X-Y intercepts for quadratic and cubic equations.

No description given

Factorise three quadratic equations of the form $x^2+bx+c$.

The first has two negative roots, the second has one negative and one positive, and the third is the difference of two squares.

Using indices rules to rewrite an expression from $\left(\frac{a^n}{b^n}\right)^{-1/n}$ to $\frac{b}{a}$.