The 3rd task in HELM book 1.4 section 1.

The 2nd task in HELM book 1.4 section 1.

The first task in HELM book 1.4 section 1.

HELM Book 1.3.1 exercises

Factorise a quadratic, x^2+bx+c. An exam can choose whether or not a=1. Part of HELM Book 1.3

Factorise a quadratic, ax^2+bx+c. An exam can choose whether or not a=1. Part of HELM Book 1.3

Factorise a quadratic. Part of HELM Book 1.3

Factorise a quadratic. Part of HELM Book 1.3

HELM Book 1.3.5 exercises

Factorise the difference of two squares, t^2-number^2. Number is a random perfect square, or 1 over a perfect square.

The purpose of this question is to ask the students to go through one Rijndael round from the AES algorithm.

This question runs the students through the Elliptic Curves version of Diffie Hellman.

In this question the students are given the public and private keys for El Gamal through Elliptic Curve and a message to decrypt. They have to decrypt the message.

HELM Book 1.3.4 exercises

Explain why one variable is a factor but the other is not. Factorise the expression, whose factor is alphanumeric. Part of HELM Book 1.3

Factorise a 2-term expression where the gcd can be alphanumeric. Part of HELM Book 1.3

Factorise an expression of 2 or 3 terms where the gcd is a letter times a number. Part of HELM Book 1.3.4

Expand (a+b)(c+d). a,b,c,d are random terms that can be +ve or -ve, and can consist of a number and/or a letter.

The answer must contain no brackets but will be accepted if it is not simplified from there.

Part of HELM Book 1.3

Solving $\cos(nx)=a$ for $x\in (0,\pi)$, where $n$ is an integer and $a\in(0,1)$.

Factorise two algebraic terms that have a numerical gcd > 1. Part of HELM book 1.3

Factorise a 2-term expression by pulling out a numeric gcd. Part of HELM Book 1.3

Factorise a+bk where a and b are non-coprime integers, and k is a letter. Part of HELM Book 1.3.4

Expand something like a(b+c) or (b+c)a or a(bc), where a, b and c can be +ve or -ve expressions. Part of HELM Book 1.3

Expand a binomial. Part of HELM Book 1.3

Solving a pair of simultaneous equations of the form $a_1x+b_1y=c_1$ and $a_2 x^2+b_2y^2=c_2$ by forming a quadratic equation.

Solving a pair of simultaneous equations of the form $a_1xy=c_1$ and $a_2x+b_2y=c_2$ by forming a quadratic equation.

This question asks students to solve a discrete logarithm problem with Pollard's rho algorithm as exposed in the book "introduction to cryptography with open source software" by McAndrew.

Use your calculator to calculate a factorial between 5 and 11

Calculating the area enclosed between a linear function and a quadratic function by integration. The limits (points of intersection) are given in the question.

Calculating the definite integral $\int_{n_1}^{n_2}ax^b dx$.