A Level Mathematics Syllabus Statement

Syllabus Content

Differentiate xⁿ, for rational values of n, and related constant multiples, sums and differences. Differentiate e^kx and a^kx, sin kx, cos kx, tan kx and related sums, differences and constant multiples. Understand and use the derivative of ln x

Here are some exam-style questions on this statement:

"Find the value of \( a \) and the value of \( b \) if:" ... more

"A function is given as \(f(x)=3x^2-6x+4+\frac3x,-2\le x \le 4, x\ne 0\)." ... more

"Consider the graph of the function \(f(x)=7-3x^2-x^3\)" ... more

"A package is in the shape of a cuboid and has a length \(l\) cm, width \(w\) cm and height of 12 cm." ... more

"Let \(f(x)=\frac{2x}{x^2+3}\)" ... more

"Consider the function \(f(x)=6 - ax+\frac 3{x^2},x\neq 0\)" ... more

"Consider the function \(f\) defined by \(f(x)= \ln{(x^2 - 9)}\) for \(x > 3\)." ... more

"If \(f(x)=x\sin{x}\), for \(-3\le x\le3\)" ... more

"Consider the cubic function \(f(x)=\frac{1}{6}x^3-2x^2+6x-2\)" ... more

"Consider the function \(f(x)=x^3-9x+2\)." ... more

"The displacement, in millimetres, of a particle from an origin, O, at time t seconds, is given by \(s(t) = t^3 cos t + 5t sin t\) where \( 0 \le t \le 5 \) ." ... more

"The function \(f\) is defined as follows:" ... more

"Consider the functions" ... more

"Let \(f(x)=jx^3+jx^2+kx+m\) where \(j, k\) and \(m\) are constants." ... more

"Make a sketch of a graph showing the velocity (in \(ms^{-1}\)) against time of a particle travelling for six seconds according to the equation:" ... more

"The function \(f\) is such that \(f(x) = \frac{\ln2x}{x^3} \) where \(x \gt 0\)." ... more

"Consider the function \(f\) defined by \(f(x) = 25e^{x-5}\) for \(x \in \mathbb{R}^+\)." ... more

"Let \(f(x) = \frac{ln3x}{kx} \) where \( x \gt 0\) and \( k \in \mathbf Q^+ \)." ... more

"Consider the function \(f(x)=\frac{20}{x^2}+kx\) where \(k\) is a constant and \(x\neq0\)." ... more

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Calculus It is said that the word calculus comes from the Latin word for the small pebble used for counting and calculations. The two major branches, differentiation and integration, are studied by pupils only towards the end of their school days but does then form a major part of their studies. A course in calculus is a prerequisite for other, more advanced courses in mathematical analysis. Isaac Newton is best known for developing calculus. He was born in England in 1642 and is considered one of the most influential scientists and mathematicians in history.

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A Level Mathematics Syllabus Statement

Differentiation

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