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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

Differentiation of  polynomials, cos, sin, exp, log functions. Product, quotient and chain rules.

rebelmaths

Implicit differentiation.

Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.

Differentiate $f(x) = x^m(a x+b)^n$.

Introduction to using the product rule

Differentiating exponentials and Logs

More work on differentiation with trigonometric functions

Differentiate the function $f(x)=(a + b x)^m  e ^ {n x}$ using the product rule. Find $g(x)$ such that $f^{\prime}(x)= (a + b x)^{m-1}  e ^ {n x}g(x)$.

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Fairly simple questions using differentiation "power rule" and "sum or difference rules" to differentiate single term functions and polynomials.

Some co-efficients and indices can be negative and/or fractional.

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Find the derivative of a function of the form $y=ax^b$ using a table of derivatives.

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Recoginising different forms of calculus notation.

Using geogebra to draw lines tangent to a curve and calculate their gradient.

A function $f(x) = cln(ax^2+bx) -x$ is sketched and tangent is also drawn. The equation of the tangent line is asked for and $x$-coordinate for horizontal tangent is asked for. Calculator.

Q1 is true/false question covering some core facts, notation and basic examples.  Q2 has two functions for which second derivative needs to be determined.

Calculating the derivative of a function of the form $\sin(ax^m+bx^n)$ using the chain rule.

A graph is drawn. A student is to identify the derivative of this graph from four other graphs. There are four such questions.

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