Refreshing Revision

Binomial Theorem (1)

Find the first three terms in the expansion of:

\((3a - 2b)^4\)

\(=81a^4 - 216a^3b \\+216a^2b^2 ...\)

Compound Interest

If £120 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 5 years. £146.42

Coordinates (Square)

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



Normal Distribution

\( X \sim N(65, 9^2)\)


\( P(36\lt X \lt48) \)


Factorise (Quadratic 1)




Factorise (Quadratic 2)




Graph (Linear)

Draw a rough sketch of the graph of:


Gradient 1
y intercept 0


What is the value of:


\(= 1\)

Trigonometry (Angle)

Find angle BCA if AB = 4.8m and BC = 6.1m. 51.9o

Trigonometry (Side)

Find AB if angle ABC = 33o and BC = 4.2m. 3.52m

Venn Diagrams

Describe the red region.

Circle part Circle part

Differentiation (1)

\(y = 5x^3 - 6x^2 + 5x\)

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

\(15x^2 - 12x + 5\)

Differentiation (2)

\(y = \dfrac{5}{x^3} - 7\sqrt[8]{x}\)

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

\(-\frac{15}{x^4} - \frac{7}{8}x^{-\frac{7}{8}}\)

Differentiation (3)

\(y=5\ln (4x^2+5)\)

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


Differentiation (4)


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


Differentiation (5)


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


Differentiation (6)

Find the equation of the tangent to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = 17 - 13x\)

Differentiation (7)

Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)

Integration (1)

\(y =6x^2 - 4x + 2\)

Find \( \int y \quad dx\)

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

Binomial Distribution

A game is played 16 times and the probability of winning is 0.6. Calculate the probability of winning exactly 6 times.   0.0392


What's this?

\( P(A|B) = \dfrac{P(A \cap B)}{P(B)} \)

Conditional probability formula

Greek Letters

What letter is this?

Greek Letter Greek Letter

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
\(u_{8} = -31\)
\(u_{18} = -61\)
Find the sum of the first 47 terms.-3713

Asymptotes (HV)

Find the equations of the asymptotes of:



Trig Advanced

In the triangle ABC,
AB = 9.3cm.
BC = 8.4cm.
CA = 12.5cm.
Find angle CÂB.




$$\sum_{n=1}^{4} 2^n$$




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

Completing The Square


By completing the square find the coordinates of the vertex.
(1.5, -3.25)


What is the value of \(\ln{e^3}\) ?


Integration (3)

Find the integral:

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


Graph (2 points)

Find the equation of the straight line that passes through:

(-8, -18) and (2, 2)


Functions (Inverse)

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



Functions (Composite)

\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)


Standard Form

Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)


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

$$\cos{30°} \div \sin{\frac{\pi}{3}}$$


Trig (Large Angles)

Without a calculator find the exact value of



Simultaneous Eqns (3)*


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

x = 2, y = 2, z = 1

Radian Measures

Find the perimeter of a sector with radius 6.6cm and angle \( \frac{\pi}{4}\)




A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?


Asymptotes (Ob)*

Find the equations of the asymptotes of:


x=3, y=2x-2

Sequences (Geometric)

The sum of the first 7 terms of a geometric sequence is 39062 and the sum of the first 8 terms is 195312. What is the first term?


Binomial Theorem (2)*

Find the first 4 terms in the expansion of:



Integration (2)


\(\int^{80}_{40} \dfrac{1}{x} dx\)

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

Probability (Conditional)

In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (70% of fiction, 40% of non-fiction are hardcovers), what's the probability it's non-fiction?



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*

$$ \dfrac{1-4i}{1+5i}$$


Integration (4)


\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)


Trig (Identities)*




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

Integration (Volume)*

Find the volume of revolution when \(y=x\) is rotated about the x-axis for \(0 \le x \le 1\)

\(\frac{\pi}{3}\) cubic units


What is the binomial theorem?

Clue: Expand \( (a + b)^n \)

Maclaurin Series*

Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)

\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)

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 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 the sum of the first \( n \) odd numbers is \( n^2 \)

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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