Refreshing Revision

Binomial Theorem (1)

Find the first three terms in the expansion of:

\((5a - 3b)^7\)

\(=78125a^7 - 328125a^6b \\+590625a^5b^2 ...\)

Compound Interest

If £120 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 4 years. £135.28

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:


\(= 3\)

Trigonometry (Angle)

Find angle ABC if AC = 4.4m and BC = 6.3m. 44.3o

Trigonometry (Side)

Find BC if angle BCA = 56o and AB = 4.7m. 5.67m

Venn Diagrams

Describe the red region.

Circle part Circle part

Differentiation (1)

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

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

\(6x^2 - 18x + 2\)

Differentiation (2)

\(y = \dfrac{5}{x^9} - 3\sqrt[4]{x}\)

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

\(-\frac{45}{x^10} - \frac{3}{4}x^{-\frac{3}{4}}\)

Differentiation (3)


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


Differentiation (4)


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


Differentiation (5)

\(y=\frac{e^{3x}}{ \cos 4x}\)

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


Differentiation (6)

Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)

Differentiation (7)

Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)

Integration (1)

\(y =24x^2 - 14x + 4\)

Find \( \int y \quad dx\)

\(8x^3 - 7x^2 + 4x+c\)

Binomial Distribution

A game is played 17 times and the probability of winning is 0.1. Calculate the probability of winning exactly 10 times.   0.000000930


What's this?

\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)

Trigonometric identity

Greek Letters

What letter is this?

Greek Letter Greek Letter

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
\(u_{9} = 59\)
\(u_{19} = 129\)
Find the sum of the first 23 terms.1840

Asymptotes (HV)

Find the equations of the asymptotes of:



Trig Advanced

In the triangle ABC,
BC = 9.3cm.
CA = 12.9cm.
BĈA = 26.6°
Find AB to 1 dp.




$$\sum_{n=1}^{8} 2n+6$$




What is the value of the discriminent and what does it indicate?
-87, No real roots

Completing The Square


By completing the square find the coordinates of the vertex.
(-4.5, -21.25)


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, -12) and (0, 2)


Functions (Inverse)

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

\(f(x)= \sqrt{x+13}\)


Functions (Composite)

\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)


Standard Form

Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)


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

$$\cos{\frac{\pi}{6}} \times \cos{60°}$$


Trig (Large Angles)

Without a calculator find the exact value of



Simultaneous Eqns (3)


\( 5a+2b+c=25 \\ 3a+4b+2c= 29 \\ a+5b+c=19\)

x=3, y=2, z=6

Radian Measures

Find the perimeter of a sector with radius 4.6cm and angle \( \frac{\pi}{6}\)




How many ways can eleven children sit in a row without the youngest being in the middle?


Asymptotes (Ob)

Find the equations of the asymptotes of:



Sequences (Geometric)

The sum of the first 7 terms of a geometric sequence is 58593 and the sum of the first 8 terms is 292968. What is the first term?


Binomial Theorem (2)

Find the first 4 terms in the expansion of:



Integration (2)


\(\int^{4}_{0} e^x dx\)

\(e^{4}- 1 \approx 53.6\)

Probability (Conditional)

What is the probability that it was machine B that broke down if at least one of the machines broke down today, given machine A has a 8% chance and machine B has a 13% chance of breaking down on any given day?


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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Random Recap


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