Refreshing Revision

Binomial Theorem

Find the first three terms in the expansion of:

\((5a - 2b)^6\)

\(=15625a^6 - 37500a^5b \\+37500a^4b^2 ...\)

Compound Interest

If £180 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 5 years. £219.78

Coordinates (Square)

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



Normal Distribution

\( X \sim N(9.03, 0.89^2)\)


\( P(7.15\lt X \lt9.01) \)


Factorise (Quadratic 1)




Factorise (Quadratic 2)




Graph (Linear)

Draw a rough sketch of the graph of:


Gradient 1
y intercept 2


What is the value of:


\(= 5\)

Trigonometry (Angle)

Find angle ABC if AB = 5.5m and BC = 6.5m. 32.2o

Trigonometry (Side)

Find AC if angle ABC = 53o and BC = 3.7m. 2.95m

Venn Diagrams

Describe the red region.

Circle part Circle part

Differentiation (1)

\(y = 4x^3 - 5x^2 + 3x\)

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

\(12x^2 - 10x + 3\)

Differentiation (2)

\(y = \dfrac{8}{x^7} - 4\sqrt[5]{x}\)

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

\(-\frac{56}{x^8} - \frac{4}{5}x^{-\frac{4}{5}}\)

Differentiation (3)


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


Differentiation (4)


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


Differentiation (5)

\(y=\frac{ \ln x}{x^2}\)

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


Differentiation (6)

Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)

Differentiation (7)

Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)

Integration (1)

\(y =15x^2 - 14x + 6\)

Find \( \int y \quad dx\)

\(5x^3 - 7x^2 + 6x+c\)

Binomial Distribution

A game is played 13 times and the probability of winning is 0.4. Calculate the probability of winning exactly 4 times.   0.184


What's this?


(from n choose r)

Greek Letters

What letter is this?

Greek Letter Greek Letter

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
\(u_{7} = 40\)
\(u_{20} = 131\)
Find the sum of the first 32 terms.3408

Asymptotes (HV)

Find the equations of the asymptotes of:



Trig Advanced

In the triangle ABC,
BC = 8.7cm.
CA = 11.5cm.
BĈA = 44.7°
Find AB to 1 dp.




$$\sum_{n=0}^{5} 2^n$$




What is the value of the discriminent and what does it indicate?
-68, No real roots

Completing The Square


By completing the square find the coordinates of the vertex.
(4, -12)


Write the following in terms of logs to base 10:

\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)

Integration (2)

Find the integral:

\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)


Graph (2 points)

Find the equation of the straight line that passes through:

(-9, -11) and (8, 23)


Functions (Inverse)

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



Functions (Composite)

\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)


Standard Form

Write in standard form:
\(a \times 10^2 \times b\times 10^3\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)


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

$$\cos{\frac{\pi}{6}} \times \sin{45°}$$


Trig (Large Angles)

Without a calculator find the exact value of



Simultaneous Eqns (3)


\( 5a+2b+c=19 \\ 3a+4b+2c= 24 \\ a+5b+c=20\)

x=2, y=3, z=3

Radian Measures

Find the perimeter of a sector with radius 9.4cm and angle \( \frac{2\pi}{3}\)




How many ways can fourteen people be divided into two equal groups?


Asymptotes (Ob)

Find the equations of the asymptotes of:



Sequences (Geometric)

$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$


Last Lesson

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


An Advanced Mathematics Lesson Starter Of The Day


Concept Selection

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Random Recap


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