Find the first three terms in the expansion of:

\((4a - 2b)^6\)

\(=4096a^6 - 12288a^5b \\+15360a^4b^2 ...\)

If £180 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 4 years. £194.95

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

\((5,2),(11,5),(2,8)\)

(8,11)

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

Find

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

\(0.0288\)

Factorise:

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

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

Factorise:

\(4x^2+3x-1\)

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

Draw a rough sketch of the graph of:

\(2y=x-4\)

Gradient 0.5

y intercept -2

What is the value of:

\(1^{0}\)

\(= 1\)

Find angle BCA if AB = 5.2m and BC = 6.4m. 54.3^{o}

Find AB if angle ABC = 22^{o} and BC = 5.3m. 4.91m

Describe the red region.

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

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

\(21x^2 - 6x + 9\)

\(y = \dfrac{9}{x^8} - 6\sqrt[7]{x}\)

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

\(-\frac{72}{x^9} - \frac{6}{7}x^{-\frac{6}{7}}\)

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

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

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

\(y=(3x+7)(7x-5)\)

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

\(42x+34\)

\(y=\frac{x^2+5}{3x-7}\)

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

\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)

Find the equation of the tangent to the curve:

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

where \(x = -2\)

\(y = -14x - 17\)

Find the equation of the normal to the curve:

\(y = -2x^2 - 4x + 6\)

where \(x = 3\)

\(y = \frac{x}{16} - \frac{387}{16}\)

\(y =12x^2 - 12x + 3\)

Find \( \int y \quad dx\)

\(4x^3 - 6x^2 + 3x+c\)

A game is played 15 times and the probability of winning is 0.5. Calculate the probability of winning exactly 12 times. 0.0139

What's this?

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

Reciprocal Integral formula

What letter is this?

Two terms of an arithmetic sequence:

\(u_{9} = 28\)

\(u_{15} = 46\)

Find the sum of the first 28 terms.1246

Find the equations of the asymptotes of:

\(y=\dfrac{10-2x}{10x}\)

\(x=0,y=-{1}{5}\)

In the triangle ABC,

AB = 9.3cm.

BC = 5.5cm.

CÂB = 23.9°.

Find angle BĈA.

43.3° or 136.7°

Evaluate:

$$\sum_{n=1}^{5} 2^n$$

62

\(f(x)=-5x^2+4x+6\)

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

136, Two distinct roots

\(f(x)=x^2+5x+5\)

By completing the square find the coordinates of the vertex.

(-2.5, -1.25)

Evaluate \(\log_2(32) \)

5

Find the integral:

\(\int \dfrac{\ln(x)}{x} \;dx\)

\(\dfrac{\ln(x)^2}{2}+c\)

Find the equation of the straight line that passes through:

(-9, -8) and (7, 8)

\(y=x+1\)

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

\(f(x)=\frac{\sqrt{x}-14}{14}\)

\((14x+14)²\)

\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)

\(-5-4\sqrt{m}\)

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

\(y=\dfrac{5}{x}\)

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

Without a calculator find the exact value of

$$\tan{\frac{\pi}{6}} \times \cos{45°}$$\(\dfrac{1}{\sqrt{6}}\)

Without a calculator find the exact value of

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

Solve:

\( j+k+l= 11 \\ 2j-3k+9l= 31\\ -j+k-3l=-13\)

x=8, y=1, z=2

Find the perimeter of a sector with radius 4.3cm and angle \( \frac{5\pi}{6}\)

🍕

19.9cm

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:

$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2

Evaluate:

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

7.97

Find the first 4 terms in the expansion of:

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

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

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