Find the first three terms in the expansion of:

\((4a - 3b)^8\)

\(=65536a^8 - 393216a^7b \\+1032192a^6b^2 ...\)

If £240 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 9 years. £343.38

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

\((3,2),(9,5),(0,8)\)

(6,11)

\( X \sim N(-25, 3^2)\)

Find

\( P(-20\lt X \lt-10) \)

\(0.0478\)

Factorise:

\(x^2-x-6\)

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

Factorise:

\(5x^2+18x-8\)

\((x+4)(5x-2)\)

Draw a rough sketch of the graph of:

\(y=2x+2\)

Gradient 2

y intercept 2

What is the value of:

\(1^{-2}\)

\(= 1\)

Find angle BCA if AC = 4.1m and BC = 5.5m. 41.8^{o}

Find AB if angle ABC = 50^{o} and BC = 3m. 1.93m

Describe the red region.

\(y = 7x^3 - 5x^2 + 9x\)

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

\(21x^2 - 10x + 9\)

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

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

\(-\frac{45}{x^6} - \frac{4}{5}x^{-\frac{4}{5}}\)

\(y=e^{\cos x}\)

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

\(-sinxe^{cosx}\)

\(y=\sin x \sqrt{ x^2 + 5}\)

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

\(cosx \sqrt{x^2+5}+\frac{xsinx}{\sqrt{x^2+5}}\)

\(y=\frac{2x^2}{4x-1}\)

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

\(\frac{(8x^2-4x)}{(4x-1)^2}\)

Find the equation of the tangent to the curve:

\(y = x^2 - 2x + 1\)

where \(x = 0\)

\(y = 1 - 2x\)

Find the equation of the normal to the curve:

\(y = 3x^2 - 6x + 9\)

where \(x = 2\)

\(y = 9\frac{1}{3} - \frac{x}{6}\)

\(y =21x^2 - 10x + 2\)

Find \( \int y \quad dx\)

\(7x^3 - 5x^2 + 2x+c\)

A game is played 14 times and the probability of winning is 0.5. Calculate the probability of winning exactly 11 times. 0.0222

What's this?

\(z=\dfrac{x-\mu}{\sigma}\)

Standardised Normal Variable

What letter is this?

Two terms of an arithmetic sequence:

\(u_{9} = -54\)

\(u_{15} = -102\)

Find the sum of the first 49 terms.-8918

Find the equations of the asymptotes of:

\(y=10+\dfrac{9x}{5-3x}\)

\(x=\frac{5}{3},y=7\)

In the triangle ABC,

AB = 9.3cm.

BC = 9.4cm.

CÂB = 67.1°.

Find angle BĈA.

65.7°

Evaluate:

$$\sum_{n=0}^{6} 101 - n^2$$

616

\(f(x)=3x^2-3x-3\)

What is the value of the discriminent and what does it indicate?

45, Two distinct roots

\(f(x)=x^2+3x+8\)

By completing the square find the coordinates of the vertex.

(-1.5, 5.75)

Simplify \(\log_{10}10^5\)

5

Find the integral:

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

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

Find the equation of the straight line that passes through:

(-7, 3) and (2, -6)

\(y=-x-4\)

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

\(f(x)=\sqrt{\frac{x-6}{4}}\)

\(4x²+6\)

\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)

\(f(x)=x+2\)

Write in standard form:

\((a \times 10^3) \div (b\times 10^5)\)

where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)

\(\frac{a}{10b}\times10^{-1}\)

Draw a rough sketch of

\(y=3-\dfrac{10}{x}\)

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

Without a calculator find the exact value of

$$\tan{30°} \times \tan{\frac{\pi}{3}}$$\(1\)

Without a calculator find the exact value of

$$\tan{4\pi}$$\(0\)

Solve:

\(2d+3e-4f = -2 \\ d-e-f= -2\\ 9d+2e-2f=32\)

d = 4, e = 2, f = 4

Find the area of a sector with radius 6.9cm and angle \( \frac{2\pi}{3}\)

🍕

49.9cm^{2}

In how many ways can 7 different books be arranged on a shelf if 4 of them must be together?

576

Find the equations of the asymptotes of:

$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x

Evaluate:

$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$

3069

Find the first 4 terms in the expansion of:

\((1+2x)^{\frac12}\)

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

Evaluate:

\(\int^{160}_{80} \dfrac{1}{x} dx\)

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

What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 5% chance and machine B has a 8% chance of breaking down on any given day?

\(0.635\)

Find the cartesian equation of this plane:

\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)

2x-6y+5z=-1

Simplify

$$ (1+i)^{4} $$

\(-4\)

Evaluate:

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

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

Simplify:

$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)

$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)

\(\frac{65\pi}{4}\) cubic units

What is the difference between a permutation and a combination?

Permutations consider order; combinations do not.

Show how the first four terms of the Maclaurin series are obtained for

\(f(x) = \cos(x)\)

\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)

Find the five 5th roots of 1

\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)

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%

Prove by mathematical induction that \( 2^n > n^2 \) for all integers \( n \) greater

than four

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

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