Refreshing Revision

Binomial Theorem (1)

Find the first three terms in the expansion of:

$(2a - 3b)^6$

$=64a^6 - 576a^5b \\+2160a^4b^2 ...$

Compound Interest

If £180 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 7 years. £238.05

Coordinates (Square)

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

$(3,2),(8,6),(-1,7)$

(4,11)

Normal Distribution

$ X \sim N(43, 7^2)$

Find

$ P(32\lt X \lt45) $

$0.554$

Factorise (Quadratic 1)

Factorise:

$x^2+3x-4$

$(x+4)(x-1)$

Factorise (Quadratic 2)

Factorise:

$x^2-16$

$(x+4)(x-4)$

Graph (Linear)

Draw a rough sketch of the graph of:

$y=-2x+1$

Gradient -2
y intercept 1

Indices

What is the value of:

$9^{\frac{1}{2}}$

$= 3$

Trigonometry (Angle)

Find angle BCA if AB = 3.5m and AC = 4.8m. 36.1^o

Trigonometry (Side)

Find AC if angle ABC = 22^o and AB = 5.8m. 2.34m

Venn Diagrams

Describe the red region.

Differentiation (1)

$y = 7x^3 - 7x^2 + 9x$

Find $ \dfrac{dy}{dx}$

$21x^2 - 14x + 9$

Differentiation (2)

$y = \dfrac{4}{x^{3}} - 2\sqrt[3]{x}$

Find $ \frac{dy}{dx}$

$-\frac{12}{x^{4}} - \frac{2}{3}x^{-\frac{2}{3}}$

Differentiation (3)

$y=e^{3x+4}$

Find $ \dfrac{dy}{dx}$

$3e^{3x+4}$

Differentiation (4)

$y=(2x+8)(7x-4)$

Find $ \dfrac{dy}{dx}$

$28x+48$

Differentiation (5)

$y=\frac{x}{\sin x}$

Find $ \dfrac{dy}{dx}$

$\frac{(sinx-xcosx)}{sin^2x}$

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:
$y = 5x^2 + 7x + 3$
where $x = 1$
$y = 15\frac{1}{17} - \frac{x}{17}$

Integration (1)

$y =27x^2 - 10x + 7$

Find $ \int y \quad dx$

$9x^3 - 5x^2 + 7x+c$

Binomial Distribution

A game is played 17 times and the probability of winning is 0.2. Calculate the probability of winning exactly 16 times. 0.0000000000891

Formulas

Make up a maths question using this:

$ A = 4\pi r^2 $

Surface area of a sphere

Greek Letters

What letter is this?

Sequences (Arithmetic)

Two terms of an arithmetic sequence:
$u_{8} = -24$
$u_{14} = -54$
Find the sum of the first 47 terms.-4888

Asymptotes (HV)

Find the equations of the asymptotes of:

$y=12-\dfrac{4x+3}{7-2x}$

$x=\frac{7}{2},y=14$

Trig Advanced

In the triangle ABC,
BC = 5.8cm.
CA = 8.5cm.
BĈA = 37.9°
Find AB to 1 dp.

5.3cm

Sigma

Evaluate:

$$\sum_{n=0}^{5} 114 - n^2$$

629

Discriminant

$f(x)=5x^2-9x+1$

What is the value of the discriminant and what does it indicate?
61, Two distinct roots

Completing The Square

$f(x)=x^2-9x-4$

By completing the square find the coordinates of the vertex.
(4.5, -24.25)

Logarithms

Write the following in terms of logs to base 10:
$\log_a(z)$

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

Integration (3)

Find the integral:

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

$\frac{1}{3}(x^2+3)^{\frac32}+c$

Graph (2 points)

Find the equation of the straight line that passes through:

(-7, 10) and (9, -6)

$y=-x+3$

Functions (Inverse)

Find the inverse of the function $f$:

$f(x)=\frac{\sqrt{x-4}}{5}$

$25x²+4$

Functions (Composite)

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

$16x^2+48x+39$

Standard Form

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

$\frac{ab}{10}\times10^{p+q+1}$

Graph (Mixed)

Draw a rough sketch of

$y=x(5-x)$

Graph (Fill)

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

Trig (Special Angles)

Without a calculator find the exact value of

$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$

$0$

Trig (Large Angles)

Without a calculator find the exact value of

$$\cos{\dfrac{16\pi}{3}}$$

$-\dfrac{1}{2}$

Simultaneous Eqns (3)*

Solve:

$ g-7h-7i=-50 \\ 2g-2h+i= 11\\ 5g+3h+i = 44$

g = 6, h = 3, i = 5

Radian Measures

Find the perimeter of a sector with radius 7.6cm and angle $ \frac{2\pi}{3}$

🍕

31.1cm

Combinatorics*

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

352716

Asymptotes (Ob)*

Find the equations of the asymptotes of:

$$y=\dfrac{-6x^2-4x-1}{3x+2}$$

x=-2/3, y=-2x

Sequences (Geometric)

Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$

-109230

Binomial Theorem (2)*

Find the first 4 terms in the expansion of:

$\dfrac{1}{2-x}$

$\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{16}$

Integration (2)

Evaluate:

$\int^{6}_{1} x^2-2x+7 \; dx$

$71.7$

Probability (Conditional)

The probability that I drop and brake my phone when I visit a coffee shop is 0.09. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?

$0.524$

Vectors*

Find the point of intersection of $L_1$ and $L_2$ if:

$L_1: \quad \dfrac{x+4}{3} = y-2 = \dfrac{z+1}{2} $

$L_2: \quad x = \dfrac{y-5}{2} = \dfrac{-z-1}{2} $

$ (-1,3,1) $

Graph (Advanced)*

Sketch the graph of:

$$y=\sin{|x|} + 1$$

Graph Plotter

Complex Numbers 1*

Simplify
$$ (2-i)^{-2} $$

$\frac{3}{25}+\frac{4}{25}i$

Integration (4)*

Evaluate:

$\int e^x\sin{x}\; dx$

$\frac{e^x}{2}(sinx-cosx)+c$

Trig (Identities)*

Simplify:

$$\cosec{x}\tan{x}$$

$\sec{x}$

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

Integration (Volume)*

Find the volume of revolution when $y=\frac{1}{x}$ is rotated about the x-axis for $1 \le x \le 2$

$\frac{\pi}{2}$ cubic units

Miscellaneous

Describe the behavior of a function at its inflection point.

The concavity of the function changes

Maclaurin Series*

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

$1 + \frac{x^2}{2} + \frac{5x^4}{24} + \frac{61x^6}{720}$

Complex Numbers 2*

Solve for $z$
$$ z^4 = - 16 $$

$\sqrt{2}+i\sqrt{2},-\sqrt{2}+i\sqrt{2} \\ \sqrt{2}-i\sqrt{2},-\sqrt{2}-i\sqrt{2}$

Probability (Counting)*

A committee of 5 is chosen from 15 people by random selection. Two Londoners were amongst the group from which the selection was made. Find the probability that both Londoners are chosen for the committee.

2/21 or 9.52%

Proof by Induction*

Prove by mathematical induction that the sum of the first $ n $ even numbers is $ n(n + 1) $

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

Surds (1)

Simplify:
$$\sqrt{12}$$
$2\sqrt{3}$

Surds (2)

Simplify:
$$\dfrac{4}{5\sqrt{3}}$$$\frac{4\sqrt{3}}{15}$

Surds (3)

Simplify

$4\sqrt{7} - \sqrt{63}$

$\sqrt{7}$

Surds (4)

Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$$\frac{24 + 4\sqrt{5}}{31}$

Standard Deviation

Calculate the standard deviation of the following numbers:

21, 21, 21, 29, 29, 29

4

Last Lesson

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

?

ADVANCED

Binomial Theorem (1)

Compound Interest

Coordinates (Square)

Normal Distribution

Factorise (Quadratic 1)

Factorise (Quadratic 2)

Graph (Linear)

Indices

Trigonometry (Angle)

Trigonometry (Side)

Venn Diagrams

Differentiation (1)

Differentiation (2)

Differentiation (3)

Differentiation (4)

Differentiation (5)

Differentiation (6)

Differentiation (7)

Integration (1)

Binomial Distribution

Formulas

Greek Letters

Sequences (Arithmetic)

Asymptotes (HV)

Trig Advanced

Sigma

Discriminant

Completing The Square

Logarithms

Integration (3)

Graph (2 points)

Functions (Inverse)

Functions (Composite)

Standard Form

Graph (Mixed)

Graph (Fill)

Trig (Special Angles)

Trig (Large Angles)

Simultaneous Eqns (3)*

Radian Measures

Combinatorics*

Asymptotes (Ob)*

Sequences (Geometric)

Binomial Theorem (2)*

Integration (2)

Probability (Conditional)

Vectors*

Graph (Advanced)*

Complex Numbers 1*

Integration (4)*

Trig (Identities)*

Integration (Volume)*

Miscellaneous

Maclaurin Series*

Complex Numbers 2*

Probability (Counting)*

Proof by Induction*

Surds (1)

Surds (2)

Surds (3)

Surds (4)

Standard Deviation

Last Lesson

An Advanced Mathematics Lesson Starter Of The Day

Concept Selection

Answers