Refreshing Revision

Binomial Theorem (1)

Find the first three terms in the expansion of:

\((4a - 3b)^8\)

\(=65536a^8 - 393216a^7b \\+1032192a^6b^2 ...\)

Compound Interest

If £240 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 9 years. £343.38

Coordinates (Square)

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?



Normal Distribution

\( X \sim N(-25, 3^2)\)


\( P(-20\lt X \lt-10) \)


Factorise (Quadratic 1)




Factorise (Quadratic 2)




Graph (Linear)

Draw a rough sketch of the graph of:


Gradient 2
y intercept 2


What is the value of:


\(= 1\)

Trigonometry (Angle)

Find angle BCA if AC = 4.1m and BC = 5.5m. 41.8o

Trigonometry (Side)

Find AB if angle ABC = 50o and BC = 3m. 1.93m

Venn Diagrams

Describe the red region.

Circle part Circle part

Differentiation (1)

\(y = 7x^3 - 5x^2 + 9x\)

Find \( \dfrac{dy}{dx}\)

\(21x^2 - 10x + 9\)

Differentiation (2)

\(y = \dfrac{9}{x^5} - 4\sqrt[5]{x}\)

Find \( \frac{dy}{dx}\)

\(-\frac{45}{x^6} - \frac{4}{5}x^{-\frac{4}{5}}\)

Differentiation (3)

\(y=e^{\cos x}\)

Find \( \dfrac{dy}{dx}\)


Differentiation (4)

\(y=\sin x \sqrt{ x^2 + 5}\)

Find \( \dfrac{dy}{dx}\)

\(cosx \sqrt{x^2+5}+\frac{xsinx}{\sqrt{x^2+5}}\)

Differentiation (5)


Find \( \dfrac{dy}{dx}\)


Differentiation (6)

Find the equation of the tangent to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)

Differentiation (7)

Find the equation of the normal to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)

Integration (1)

\(y =21x^2 - 10x + 2\)

Find \( \int y \quad dx\)

\(7x^3 - 5x^2 + 2x+c\)

Binomial Distribution

A game is played 14 times and the probability of winning is 0.5. Calculate the probability of winning exactly 11 times.   0.0222


What's this?


Standardised Normal Variable

Greek Letters

What letter is this?

Greek Letter Greek Letter

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
\(u_{9} = -54\)
\(u_{15} = -102\)
Find the sum of the first 49 terms.-8918

Asymptotes (HV)

Find the equations of the asymptotes of:



Trig Advanced

In the triangle ABC,
AB = 9.3cm.
BC = 9.4cm.
CÂB = 67.1°.
Find angle BĈA.




$$\sum_{n=0}^{6} 101 - n^2$$




What is the value of the discriminent and what does it indicate?
45, Two distinct roots

Completing The Square


By completing the square find the coordinates of the vertex.
(-1.5, 5.75)


Simplify \(\log_{10}10^5\)


Integration (3)

Find the integral:

\(\int \cos(x)e^{\sin(x)} \;dx\)


Graph (2 points)

Find the equation of the straight line that passes through:

(-7, 3) and (2, -6)


Functions (Inverse)

Find the inverse of the function \(f\):



Functions (Composite)

\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)


Standard Form

Write in standard form:
\((a \times 10^3) \div (b\times 10^5)\)
where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)


Graph (Mixed)

Draw a rough sketch of



Graph (Fill)

Sketch a height-time graph as this jar is filled.

Jar Graph

Trig (Special Angles)

Without a calculator find the exact value of

$$\tan{30°} \times \tan{\frac{\pi}{3}}$$


Trig (Large Angles)

Without a calculator find the exact value of



Simultaneous Eqns (3)*


\(2d+3e-4f = -2 \\ d-e-f= -2\\ 9d+2e-2f=32\)

d = 4, e = 2, f = 4

Radian Measures

Find the area of a sector with radius 6.9cm and angle \( \frac{2\pi}{3}\)




In how many ways can 7 different books be arranged on a shelf if 4 of them must be together?


Asymptotes (Ob)*

Find the equations of the asymptotes of:



Sequences (Geometric)

$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$


Binomial Theorem (2)*

Find the first 4 terms in the expansion of:



Integration (2)


\(\int^{160}_{80} \dfrac{1}{x} dx\)

\(\ln{2} \approx 0.693\)

Probability (Conditional)

What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 5% chance and machine B has a 8% chance of breaking down on any given day?



Find the cartesian equation of this plane:

\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)


Graph (Advanced)*

Sketch the graph of:


Graph Plotter

Complex Numbers 1*

$$ (1+i)^{4} $$


Integration (4)


\(\int e^x\sin{x}\; dx\)


Trig (Identities)*




$$ \DeclareMathOperator{cosec}{cosec} $$

Integration (Volume)*

Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)

\(\frac{65\pi}{4}\) cubic units


What is the difference between a permutation and a combination?

Permutations consider order; combinations do not.

Maclaurin Series*

Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)

\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)

Complex Numbers 2*

Find the five 5th roots of 1

\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)

Probability (Counting)*

A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.

1/26 or 3.85%

Proof by Induction*

Prove by mathematical induction that \( 2^n > n^2 \) for all integers \( n \) greater
than four

Show true for n=1, assume true for n=k, prove for n=k+1

Last Lesson

Write down a summary of your last Maths lesson focussing on what you learnt.


An Advanced Mathematics Lesson Starter Of The Day


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