Find the first three terms in the expansion of:

\((2a - 3b)^8\)

\(=256a^8 - 3072a^7b \\+16128a^6b^2 ...\)

If £140 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 5 years. £179.67

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

\((1,2),(5,7),(-4,6)\)

(0,11)

\( X \sim N(300, 10^2)\)

Find

\( P(270\lt X \lt330) \)

\(0.997\)

Factorise:

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

\((x+4)(x-1)\)

Factorise:

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

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

Draw a rough sketch of the graph of:

\(y=x-1\)

Gradient 1

y intercept -1

What is the value of:

\(5^{-3}\)

\(= \frac{1}{125}\)

Find angle ABC if AC = 4.7m and BC = 6.6m. 45.4^{o}

Find AC if angle ABC = 22^{o} and BC = 5.2m. 1.95m

Describe the red region.

\(y = 4x^3 - 5x^2 + 9x\)

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

\(12x^2 - 10x + 9\)

\(y = \dfrac{9}{x^6} - 3\sqrt[4]{x}\)

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

\(-\frac{54}{x^7} - \frac{3}{4}x^{-\frac{3}{4}}\)

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

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

\(108x(9x^2-3)^5\)

\(y=\sin x \cos x\)

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

\(cos^2x-sin^2x\)

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

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:

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

where \(x = 2\)

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

\(y =27x^2 - 14x + 8\)

Find \( \int y \quad dx\)

\(9x^3 - 7x^2 + 8x+c\)

A game is played 17 times and the probability of winning is 0.2. Calculate the probability of winning exactly 6 times. 0.0680

What's this?

\( \int \dfrac{1}{x} = \ln |x| + c\)

Reciprocal Integral formula

What letter is this?

Two terms of an arithmetic sequence:

\(u_{10} = -82\)

\(u_{13} = -106\)

Find the sum of the first 23 terms.-2254

Find the equations of the asymptotes of:

\(y=\dfrac{4-7x}{3-14x}\)

\(x=\frac{3}{14},y=\frac{1}{2}\)

In the triangle ABC,

AB = 5.3cm.

BC = 7.9cm.

CÂB = 95.2°.

Find angle BĈA.

41.9°

Evaluate:

$$\sum_{n=0}^{8} 116 - n^2$$

840

\(f(x)=6x^2-5x-9\)

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

241, Two distinct roots

\(f(x)=x^2+8x-7\)

By completing the square find the coordinates of the vertex.

(-4, -23)

Solve for x:

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

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

Find the integral:

\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)

\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)

Find the equation of the straight line that passes through:

(-7, 5) and (4, -17)

\(y=-2x-9\)

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

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

\((x+7)²\)

\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)

\(225x^2+30x+1\)

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

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

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

Without a calculator find the exact value of

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

Without a calculator find the exact value of

$$\sin{5\pi}$$\(0\)

Solve:

\(2d+3e-4f = 23 \\ d-e-f= -3\\ 9d+2e-2f=71\)

d = 7, e = 7, f = 3

Find the perimeter of a sector with radius 3.2cm and angle \( \frac{\pi}{3}\)

🍕

9.75cm

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

96

Find the equations of the asymptotes of:

$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1

The 6^{th} term of a geometric sequence is 160 and the sum of the first 6 terms is 315. Find the first term.

5

Find the first 4 terms in the expansion of:

\(\dfrac{1}{(1+3x)^3}\)

\(1-9x+54x^2-270x^3\)

Evaluate:

\(\int^{5}_{2} x^2-2x+7 \; dx\)

\(6\)

27 Scouts went hiking. 16 got lost, 15 got blisters, and 9 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.

\(\dfrac{6}{11}\)

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

$$ \sqrt{5-12i} $$

\(3-2i \; \text{ or } -3+2i\)

Evaluate:

\(\int x\cos{x}\; dx\)

\(xsinx+cosx+c\)

Simplify:

$$\cosec{x}\tan{x}$$\(\sec{x}\)

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

How do you solve a quadratic inequality?

Factorise the quadratic, then analyze the sign of each factor over its domain.

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

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

\(x^3 \text{ only 1 term}\)

Expand and simplify:

$$ (\sqrt{3}+i)^8 $$

\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)

A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.

55/153 or 35.9%

Prove by mathematical induction that the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)

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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