Given either (a) ax+bx+cy+dy, or (b) ax^2+bx+c, (c) ax^2+bx^2+cx^2, where a,b,c,d are randomised constants, and x and y are randomised letters, simplify by collecting like terms (if possible).

Part of HELM Book 1.3

Given an expression in one or two variables, with two or three terms, collect like terms, if possible. Part of HELM Book 1.3

Compare ax-bx, and ax(bx) and simplify, where a and b are +ve or -ve integers, and x is a randomised variable. Part of HELM Book 1.3

State if a function is increasing at given points or on given intervals

Derivatives from first principles, quadratic

Rewrite the expression $\frac{cx+d}{kx^2+mx+n}$ as partial fractions in the form $\frac{A}{kx+a}+\frac{B}{x+b}$, where the quadratic $kx^2+mx+n=(kx+a)(x+b)$.

Rewrite the expression $\frac{cx+d}{x^2+mx+n}$ as partial fractions in the form $\frac{A}{x+a}+\frac{B}{x+b}$, where the quadratic $x^2+mx+n=(x+a)(x+b)$.

HELM Book 1.2.6 exercises

Write a large number and a small number in scientific notation. (Numbers contain 5 digits). Indices range from -7 to +7, excluding 0 and 1

Part of HELM Book 1.2

HELM Book 1.2.5 exercises

HELM Book 1.2.2 exercises

Part of HELM Book 1.2

HELM Book 1.2.4 exercises

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 positive 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

Identify whether or not an expression is a polynomial. Part of HELM Book 1.2

Identify whether or not an expression is a polynomial. Part of HELM Book 1.2

HELM Book 1.2.3 exercises

Subtract indices. Part of HELM Book 1.2

Multiply indices. Part of HELM Book 1.2

Add indices. Part of HELM Book 1.2

Use a calculator to compute (base)^index. Part of HELM Book 1.2

HELM Book 1.2.1 exercises

Evaluate a decimal: either 0.1,0.2,0.3,0.4,0.01,0.02,0.03,0.04 squared or cubed. 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.

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers

Identify the truth value of an inequality (T/F) between two numbers