### 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?

$$(1,1),(4,4),(-2,4)$$

(1,7)

### Normal Distribution

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

Find

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

$$0.474$$

Factorise:

$$x^2-16$$

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

Factorise:

$$12x^2-5x-3$$

$$(3x+1)(4x-3)$$

### Graph (Linear)

Draw a rough sketch of the graph of:

$$y=-x+2$$

y intercept 2

### Indices

What is the value of:

$$3^{1}$$

$$= 3$$

### 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.

### 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)

$$y=(2x^6+4)^8$$

Find $$\dfrac{dy}{dx}$$

$$96x^5(2x^6+4)^7$$

### Differentiation (4)

$$y=x(3x+5)^3$$

Find $$\dfrac{dy}{dx}$$

$$(3x+5)^3+9x(3x+5)^2$$

### Differentiation (5)

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

Find $$\dfrac{dy}{dx}$$

$$\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}$$

### 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

### Formulas

What's this?

$$\tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}$$

Trigonometric identity

### Greek Letters

What letter is this?

### 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:

$$y=\dfrac{2x-7}{6-2x}-5$$

$$x=3,y=-6$$

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

6.2cm

### Sigma

Evaluate:

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

120

### Discriminant

$$f(x)=7x^2-5x+4$$

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

### Completing The Square

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

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

### Logarithms

Simplify $$\log_{10}10^5$$

5

### Integration (3)

Find the integral:

$$\int \cos(x)e^{\sin(x)} \;dx$$

$$e^{\sin(x)}+c$$

### Graph (2 points)

Find the equation of the straight line that passes through:

(-7, -12) and (0, 2)

$$y=2x+2$$

### Functions (Inverse)

Find the inverse of the function $$f$$:

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

$$x²-13$$

### 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:
$$a \times 10^{-1} \times b\times 10^{-1}$$
where $$a \times b$$ is a three digit number $$(100 \le ab \lt 1000)$$

$$\frac{ab}{100}\times10^0$$

### Graph (Mixed)

Draw a rough sketch of

$$y=x^2-8$$

### Graph (Fill)

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

### Trig (Special Angles)

Without a calculator find the exact value of

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

$$\dfrac{\sqrt{3}}{4}$$

### Trig (Large Angles)

Without a calculator find the exact value of

$$\tan{\dfrac{19\pi}{3}}$$

$$\sqrt{3}$$

### Simultaneous Eqns (3)

Solve:

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

x=3, y=2, z=6

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

🍕

11.6cm

### Combinatronics

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

36288000

### Asymptotes (Ob)

Find the equations of the asymptotes of:

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

x=1,y=x+2

### 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?

3

### Binomial Theorem (2)

Find the first 4 terms in the expansion of:

$$(1+4x)^{\frac{3}{2}}$$

$$1+6x+6x^2-4x^3$$

### Integration (2)

Evaluate:

$$\int^{4}_{0} e^x dx$$

$$e^{4}- 1 \approx 53.6$$

### 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?

$$0.651$$

### Last Lesson

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

?

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