Refreshing Revision

Binomial Theorem (1)

Find the first three terms in the expansion of:

\((2a - 3b)^8\)

\(=256a^8 - 3072a^7b \\+16128a^6b^2 ...\)

Compound Interest

If £140 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 5 years. £179.67

Coordinates (Square)

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



Normal Distribution

\( X \sim N(300, 10^2)\)


\( P(270\lt X \lt330) \)


Factorise (Quadratic 1)




Factorise (Quadratic 2)




Graph (Linear)

Draw a rough sketch of the graph of:


Gradient 1
y intercept -1


What is the value of:


\(= \frac{1}{125}\)

Trigonometry (Angle)

Find angle ABC if AC = 4.7m and BC = 6.6m. 45.4o

Trigonometry (Side)

Find AC if angle ABC = 22o and BC = 5.2m. 1.95m

Venn Diagrams

Describe the red region.

Circle part Circle part

Differentiation (1)

\(y = 4x^3 - 5x^2 + 9x\)

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

\(12x^2 - 10x + 9\)

Differentiation (2)

\(y = \dfrac{9}{x^6} - 3\sqrt[4]{x}\)

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

\(-\frac{54}{x^7} - \frac{3}{4}x^{-\frac{3}{4}}\)

Differentiation (3)


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


Differentiation (4)

\(y=\sin x \cos x\)

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:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)

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)

\(y =27x^2 - 14x + 8\)

Find \( \int y \quad dx\)

\(9x^3 - 7x^2 + 8x+c\)

Binomial Distribution

A game is played 17 times and the probability of winning is 0.2. Calculate the probability of winning exactly 6 times.   0.0680


What's this?

\( \int \dfrac{1}{x} = \ln |x| + c\)

Reciprocal Integral formula

Greek Letters

What letter is this?

Greek Letter Greek Letter

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
\(u_{10} = -82\)
\(u_{13} = -106\)
Find the sum of the first 23 terms.-2254

Asymptotes (HV)

Find the equations of the asymptotes of:



Trig Advanced

In the triangle ABC,
AB = 5.3cm.
BC = 7.9cm.
CÂB = 95.2°.
Find angle BĈA.




$$\sum_{n=0}^{8} 116 - n^2$$




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

Completing The Square


By completing the square find the coordinates of the vertex.
(-4, -23)


Solve for x:

\( \log(x) + \log(29-x) = 2\)

\(x = 4 \text{ or } x = 25 \)

Integration (3)

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:

(-7, 5) and (4, -17)


Functions (Inverse)

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

\(f(x)= \sqrt{x}-7\)


Functions (Composite)

\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)


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

\(x=\pm \sqrt{y}\)


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

$$\sin{\frac{\pi}{2}} \div \cos{45°}$$


Trig (Large Angles)

Without a calculator find the exact value of



Simultaneous Eqns (3)*


\(2d+3e-4f = 23 \\ d-e-f= -3\\ 9d+2e-2f=71\)

d = 7, e = 7, f = 3

Radian Measures

Find the perimeter of a sector with radius 3.2cm and angle \( \frac{\pi}{3}\)




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


Asymptotes (Ob)*

Find the equations of the asymptotes of:



Sequences (Geometric)

The 6th term of a geometric sequence is 160 and the sum of the first 6 terms is 315. Find the first term.


Binomial Theorem (2)*

Find the first 4 terms in the expansion of:



Integration (2)


\(\int^{5}_{2} x^2-2x+7 \; dx\)


Probability (Conditional)

27 Scouts went hiking. 16 got lost, 15 got blisters, and 9 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.



There are eight different ways that three planes can relate in three dimensions. One is where they all intersect at a point. How many of the other seven ways can you sketch or describe?


Graph (Advanced)*

Sketch the graph of:


Graph Plotter

Complex Numbers 1*

$$ \sqrt{5-12i} $$

\(3-2i \; \text{ or } -3+2i\)

Integration (4)


\(\int x\cos{x}\; dx\)


Trig (Identities)*




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

Integration (Volume)*

Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)

\(\approx 4.10\) cubic units


How do you solve a quadratic inequality?

Factorise the quadratic, then analyze the sign of each factor over its domain.

Maclaurin Series*

Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)

\(x^3 \text{ only 1 term}\)

Complex Numbers 2*

Expand and simplify:
$$ (\sqrt{3}+i)^8 $$

\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)

Probability (Counting)*

A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.

55/153 or 35.9%

Proof by Induction*

Prove by mathematical induction that the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)

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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