Shaheen Charlwood

Topics:
Algebra, Calculus, Trigonometeric Equations, Complex numbers & Partial Derivatives

Students must complete the exam within 120 mins (standard time).

Questions have variables to produce randomised questions.

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Find the stationary point $(p,q)$ of the function: $f(x,y)=ax^2+bxy+cy^2+dx+gy$. Calculate $f(p,q)$.

Given two complex numbers, find by inspection the one that is a root of a given quartic real polynomial and hence find the other roots. 

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

More difficult trigonometric equations with radians

Topics: Trigonometeric equations and complex numbers
Students must complete the exam within 90 mins (standard time).
Questions have variables to produce randomised questions.

No description given

Finding the modulus and argument (in radians) of four complex numbers; the arguments between $-\pi$ and $\pi$ and careful with quadrants!

Direct calculation of low positive and negative powers of complex numbers. Calculations involving a complex conjugate. Powers of $i$. Four parts.

Inverse and division of complex numbers.  Four parts.

Multiplication and addition of complex numbers. Four parts.

Elementary examples of multiplication and addition of complex numbers. Four parts.

Trigonometric equations with degrees

Simple trig equations with radians

Convert degrees to radians and radians to degrees.

Definite integation of basic functions.

Differentiate $\displaystyle (ax^m+b)^{n}$.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Some quadratics are to be solved by factorising

A quadratic and a graph of it is given. A tangent is also sketched. The equation of the tangent line is asked for.

No time limit - unlimited regeneration of questions allowed from these groups:

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

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Addition and subtraction of matrices; multiplication by scalar.

Simple trig equations with radians

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