Find the first three terms in the expansion of:

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

\(=81a^4 - 432a^3b \\+864a^2b^2 ...\)

If £200 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 9 years. £341.83

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

\((2,4),(5,10),(-4,7)\)

(-1,13)

\( X \sim N(50, 5^2)\)

Find

\( P(40\lt X \lt60) \)

\(0.955\)

Factorise:

\(x^2-2x-8\)

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

Factorise:

\(3x^2-10x-8\)

\((3x+2)(x-4)\)

Draw a rough sketch of the graph of:

\(y=x-1\)

Gradient 1

y intercept -1

What is the value of:

\(27^{\frac{1}{3}}\)

\(= 3\)

Find angle ABC if AC = 4.9m and AB = 6.5m. 37.0^{o}

Find BC if angle BCA = 25^{o} and AC = 5.5m. 6.07m

Describe the red region.

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

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

\(6x^2 - 18x + 3\)

\(y = \dfrac{7}{x^8} - 5\sqrt[6]{x}\)

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

\(-\frac{56}{x^9} - \frac{5}{6}x^{-\frac{5}{6}}\)

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

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

\(2e^{2x+3}\)

\(y=x^2 \ln x\)

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

\(2x^1lnx+x^1\)

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

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

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

Find the equation of the tangent to the curve:

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

where \(x = -1\)

\(y = 1 - 5x\)

Find the equation of the normal to the curve:

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

where \(x = -2\)

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

\(y =21x^2 - 8x + 8\)

Find \( \int y \quad dx\)

\(7x^3 - 4x^2 + 8x+c\)

A game is played 20 times and the probability of winning is 0.6. Calculate the probability of winning exactly 5 times. 0.00129

What's this?

\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)

The sum of a geometric sequence

What letter is this?

Two terms of an arithmetic sequence:

\(u_{5} = 40\)

\(u_{12} = 117\)

Find the sum of the first 29 terms.4350

Find the equations of the asymptotes of:

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

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

In the triangle ABC,

AB = 5.4cm.

BC = 7.8cm.

CÂB = 89.3°.

Find angle BĈA.

43.8°

Evaluate:

$$\sum_{n=4}^{5} n^2 - 3n$$

14

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

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

-31, No real roots

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

By completing the square find the coordinates of the vertex.

(-3.5, -10.25)

Solve for x:

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

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

Find the integral:

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

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

Find the equation of the straight line that passes through:

(-1, -7) and (5, -19)

\(y=-2x-9\)

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

\(f(x)=\frac{8+ x}{6}\)

\(6x-8\)

\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)

\(147x^2-126x+27\)

Write in standard form:

\((a \times 10^p) \div (b\times 10^q)\)

where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)

\(\frac{a}{b}\times10^{p-q}\)

Draw a rough sketch of

\(x=\pm \sqrt{y}\)

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

Without a calculator find the exact value of

$$\cos{30°} \div \sin{\frac{\pi}{3}}$$\(1\)

Without a calculator find the exact value of

$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)

Solve:

\( 5a+2b+c=45 \\ 3a+4b+2c= 48 \\ a+5b+c=36\)

x=6, y=5, z=5

Find the perimeter of a sector with radius 4.8cm and angle \( \frac{\pi}{6}\)

🍕

12.1cm

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

2520

Find the equations of the asymptotes of:

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

Evaluate:

$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$

7.97

Find the first 4 terms in the expansion of:

\((1+x)^{-8}\)

\(1-8x-36x^2-120x^3\)

Evaluate:

\(\int^{100}_{50} \dfrac{1}{x} dx\)

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

Box A contains 5 red and 7 blue cubes, and box B contains 9 red and 12 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B?

\(\dfrac{36}{71}\)

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?

Simplify

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

\(\frac{3}{25}+\frac{4}{25}i\)

Evaluate:

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

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

Simplify:

$$\tan{x}\cot{x}$$\(1\)

$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)

\(\approx 4.10\) 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

\(f(x) = \ln(1 + x)\)

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

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