Find the first three terms in the expansion of:

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

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

If £120 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 7 years. £169.92

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

\((4,4),(9,9),(-1,9)\)

(4,14)

\( X \sim N(9.03, 0.89^2)\)

Find

\( P(7.15\lt X \lt9.01) \)

\(0.474\)

Factorise:

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

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

Factorise:

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

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

Draw a rough sketch of the graph of:

\(y=2x+2\)

Gradient 2

y intercept 2

What is the value of:

\(2^{0}\)

\(= 1\)

Find angle ABC if AB = 5.7m and BC = 7.6m. 41.4^{o}

Find BC if angle BCA = 57^{o} and AB = 3.9m. 4.65m

Describe the red region.

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

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

\(27x^2 - 18x + 3\)

\(y = \dfrac{2}{x^9} - 7\sqrt[8]{x}\)

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

\(-\frac{18}{x^10} - \frac{7}{8}x^{-\frac{7}{8}}\)

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

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

\(-sinxe^{cosx}\)

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

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

\((5x+7)^3+15x(5x+7)^2\)

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

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:

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

where \(x = 1\)

\(y = 5\frac{1}{2} - \frac{x}{2}\)

\(y =24x^2 - 16x + 2\)

Find \( \int y \quad dx\)

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

A game is played 12 times and the probability of winning is 0.5. Calculate the probability of winning exactly 9 times. 0.0537

Make up a maths question using 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:

\(u_{9} = -37\)

\(u_{11} = -47\)

Find the sum of the first 27 terms.-1674

Find the equations of the asymptotes of:

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

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

In the triangle ABC,

BC = 9.6cm.

CA = 7.8cm.

BĈA = 34.2°

Find AB to 1 dp.

5.4cm

Evaluate:

$$\sum_{n=1}^{4} 2^n$$

30

\(f(x)=-6x^2-3x-4\)

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

-87, No real roots

\(f(x)=x^2+6x-1\)

By completing the square find the coordinates of the vertex.

(-3, -10)

Evaluate \(\log_5(625) \)

4

Find the integral:

\(\int \sin(x)\cos^2(x) \;dx\)

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

Find the equation of the straight line that passes through:

(-4, 19) and (2, 1)

\(y=-3x+7\)

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

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

\(x²+2\)

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

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

Write in standard form:

\((a \times 10^4) \div (b\times 10^{-2})\)

where \(a \div b \) is a decimal number \((0.1 \le \frac{a}{b} \lt 1)\)

\(\frac{10a}{b}\times10^5\)

Draw a rough sketch of

\(y=x(5-x)\)

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

Without a calculator find the exact value of

$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)

Without a calculator find the exact value of

$$\cos{720°}$$\(1\)

Solve:

\(2d+3e-4f = -6 \\ d-e-f= -4\\ 9d+2e-2f=14\)

d = 2, e = 2, f = 4

Find the area of a sector with radius 5.3cm and angle \( \frac{\pi}{4}\)

🍕

11.0cm^{2}

In how many ways can 9 different books be arranged on a shelf if 4 of them must be together?

17280

Find the equations of the asymptotes of:

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

Evaluate:

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

7.97

Find the first 4 terms in the expansion of:

\(\dfrac{1}{(3+x)^2}\)

\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)

Evaluate:

\(\int^{6}_{2} (x-8)^2 \; dx\)

\(69.3333333333333\)

Tin A contains 6 red balls and 8 green balls. Tin B contains 10 red balls and 13 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.

\(\frac{140}{209}\)

Find the area of the triangle with sides:

\( \begin{pmatrix} 9 \\ 8 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 8 \\ -3 \\ 7 \end{pmatrix} \; \text{and} \; \begin{pmatrix} -1 \\ -11 \\ 7 \end{pmatrix} \)

62.0 square units

Simplify

$$ \dfrac{1-4i}{1+5i}$$

\(-\frac{19}{26}-\frac{9}{26}i\)

Evaluate:

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

\(x\ln|x|-x+c\)

Simplify:

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

$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the y-axis for \(0 \le y \le 4\)

\(8\pi\) cubic units

Describe the behavior of a function at its asymptote.

Clue: approaches but never reaches

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

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

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

Expand and simplify:

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

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

A committee of 4 is randomly selected from 8 men and 11 women. Determine the likelihood that it consists of all men.

35/1938 or 1.81%

Prove by mathematical induction that the sum of the first \( n \) even numbers is \( n(n + 1) \)

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

Simplify

\((3 + 2\sqrt{5})(6 - 3\sqrt{5})\)

\(3\sqrt{5}-12\)

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