The 5th task in HELM book 1.4 section 1.

The 4th task in HELM book 1.4 section 1.

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.

DCS 2023 Maths Entrance Test to be used September 2023

1.5 hours with 3 randomised questions from each of these groups:

• Notation and Algebra
• Calculus - Differentiation
• Calculus - Integration
• Trigonometry

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

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More difficult trigonometric equations with radians

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