Find the first three terms in the expansion of:

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

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

If £200 is invested with an interest rate of 3% compounded quarterly, find the value of the investment after 8 years. £254.02

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

\((5,1),(9,4),(2,5)\)

(6,8)

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

Find

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

\(0.0288\)

Factorise:

\(x^2-9\)

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

Factorise:

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

\((x+1)(2x-3)\)

Draw a rough sketch of the graph of:

\(y=-x-2\)

Gradient -1

y intercept -2

What is the value of:

\(125^{\frac{1}{3}}\)

\(= 5\)

Find angle ABC if AC = 3.8m and BC = 5.3m. 45.8^{o}

Find AC if angle ABC = 61^{o} and AB = 3.4m. 6.13m

Describe the red region.

\(y = 6x^3 - 3x^2 + 7x\)

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

\(18x^2 - 6x + 7\)

\(y = \dfrac{9}{x^3} - 8\sqrt[9]{x}\)

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

\(-\frac{27}{x^4} - \frac{8}{9}x^{-\frac{8}{9}}\)

\(y=(9x^7+8)^7\)

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

\(441x^6(9x^7+8)^6\)

\(y=\sin x \sqrt{ x^2 + 3}\)

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

\(cosx \sqrt{x^2+3}+\frac{xsinx}{\sqrt{x^2+3}}\)

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

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:

\(y = 4x^2 + 2x - 1\)

where \(x = -2\)

\(y = \frac{x}{14} + 11\frac{1}{7}\)

\(y =9x^2 - 16x + 2\)

Find \( \int y \quad dx\)

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

A game is played 14 times and the probability of winning is 0.8. Calculate the probability of winning exactly 3 times. 0.00000382

Make up a maths question using this:

\( A = 4\pi r^2 \)

Surface area of a sphere

What letter is this?

Two terms of an arithmetic sequence:

\(u_{10} = 90\)

\(u_{19} = 180\)

Find the sum of the first 32 terms.4960

Find the equations of the asymptotes of:

\(y=\dfrac{5x}{2-x}+3\)

\(x=2,y=-2\)

In the triangle ABC,

BC = 7.7cm.

CA = 9.2cm.

BĈA = 53.3°

Find AB to 1 dp.

7.7cm

Evaluate:

$$\sum_{n=2}^{6} n^2 - 8n$$

-70

\(f(x)=2x^2-4x+3\)

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

-8, No real roots

\(f(x)=x^2+7x-7\)

By completing the square find the coordinates of the vertex.

(-3.5, -19.25)

Solve for x:

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

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

Find the integral:

\(\int \dfrac{5x}{x^2-3} \;dx\)

\(\frac{5}{2} \ln(x^2-3)+c\)

Find the equation of the straight line that passes through:

(-9, -12) and (6, 3)

\(y=x-3\)

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

\(f(x)=\sqrt{\frac{x-2}{7}}\)

\(7x²+2\)

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

\(16x^2+48x+39\)

Write in standard form:

\(a \times 10^2 \times b\times 10^3\)

where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)

\(\frac{ab}{10}\times10^6\)

Draw a rough sketch of

\(y=x^3-4x\)

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

Without a calculator find the exact value of

$$\cos{\frac{\pi}{4}} + \sin{45°}$$\(\sqrt{2}\)

Without a calculator find the exact value of

$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)

Solve:

\( 5a+2b+c=33 \\ 3a+4b+2c= 45 \\ a+5b+c=39\)

a = 3, b = 6, c = 6

Find the perimeter of a sector with radius 4.3cm and angle \( \frac{\pi}{6}\)

🍕

10.9cm

Ansh is with six people in a queue. How many ways can they line up without Ansh being at the back?

4320

Find the equations of the asymptotes of:

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

The first term of a geometric sequence is 48 and the fourth term is twice this value. What is the common ratio?

\( \sqrt[3]{2} \)

Find the first 4 terms in the expansion of:

\((1-\dfrac{x}{2})^{\frac13}\)

\(1-\frac{x}{6}-\frac{x^2}{36}-\frac{5x^3}{648}\)

Evaluate:

\(\int^{8}_{1} x^2-2x+7 \; dx\)

\(14\)

28 Scouts went hiking. 11 got lost, 14 got blisters, and 5 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.

\(\dfrac{9}{17}\)

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

$$ \dfrac{3+2i}{4-i}$$

\(\frac{10}{17}+\frac{11}{17}i\)

Evaluate:

\(\int xe^x\; dx\)

\(xe^x-e^x+c\)

Simplify:

$$\sin{x}\cot{x}$$\(\cos{x}\)

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

What is the inverse of a function?

Clue: swaps the roles of x and y

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

\(f(x) = e^x\)

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

Given |z| = 8, find:

$$ |(3+4i)z| $$

\(40\)

6 girls sit at random on 6 seats in a row. Determine the probability that the two friends Karen and Julie sit at the ends of the row.

1/15 or 6.67%

Prove by mathematical induction that the product of \( n \) consecutive integers is divisible by \( n! \) (n factorial)

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

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

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