Find the first three terms in the expansion of:
\((3a - 4b)^8\)
\(=6561a^8 - 69984a^7b \\+326592a^6b^2 ...\)
If £120 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 7 years. £148.00
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,1),(6,5),(-2,5)\)
(2,9)
\( X \sim N(100, 7^2)\)
Find
\( P(93\lt X \lt107) \)
\(0.683\)
Factorise:
\(x^2+x-12\)
\((x+4)(x-3)\)
Factorise:
\(3x^2-4x-4\)
\((3x+2)(x-2)\)
Draw a rough sketch of the graph of:
\(y=-2x-1\)
Gradient -2
y intercept -1
What is the value of:
\(27^{\frac{1}{3}}\)
\(= 3\)
Find angle ABC if AB = 5.2m and BC = 6.6m. 38.0o
Find BC if angle BCA = 66o and AB = 5.7m. 6.24m
Describe the red region.
\(y = 5x^3 - 3x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 6x + 6\)
\(y = \dfrac{4}{x^{7}} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{28}{x^{8}} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=\frac{1}{(4x+5)^6}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{24}{(4x+5)^7}\)
\(y=\sin x \sqrt{ x^2 + 4}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+4}+\frac{xsinx}{\sqrt{x^2+4}}\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =18x^2 - 18x + 2\)
Find \( \int y \quad dx\)
\(6x^3 - 9x^2 + 2x+c\)
A game is played 18 times and the probability of winning is 0.8. Calculate the probability of winning exactly 2 times. 0.000000000642
Make up a maths question using this:
\(z=\dfrac{x-\mu}{\sigma}\)
Standardised Normal Variable
What letter is this?
Two terms of an arithmetic sequence:
\(u_{6} = -26\)
\(u_{14} = -82\)
Find the sum of the first 38 terms.-4579
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
AB = 7.5cm.
BC = 8.3cm.
CA = 11.7cm.
Find angle CÂB.
44.9°
Evaluate:
$$\sum_{n=2}^{8} n^2 - 8n$$
-77
\(f(x)=-9x^2+9x+4\)
What is the value of the discriminant and what does it indicate?
225, Two distinct roots
\(f(x)=x^2+8x-2\)
By completing the square find the coordinates of the vertex.
(-4, -18)
What is the value of \(\ln{e^3}\) ?
3
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:
(-6, -13) and (1, 1)
\(y=2x-1\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-2}{2}}\)
\(2x²+2\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
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
\(y=x^2-8\)
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
$$\tan{\dfrac{19\pi}{6}}$$\(\dfrac{1}{\sqrt{3}}\)
Solve:
\( 5a+2b+c=36 \\ 3a+4b+2c= 37 \\ a+5b+c=28\)
a = 5, b = 4, c = 3
Find the area of a sector with radius 6.8cm and angle \( \frac{\pi}{4}\)
🍕
18.2cm2
Ansh is with five people in a queue. How many ways can they line up without Ansh being at the back?
600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The 5th term of a geometric sequence is 64 and the sum of the first 5 terms is 124. Find the first term.
4
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:
\(\int^{160}_{80} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.12. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.532\)
Find the vector product:
\( \begin{pmatrix} 9 \\ 5 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 9 \\ -3 \\ 4 \end{pmatrix} \)
\( \begin{pmatrix} 20 \\ -36 \\ -72 \end{pmatrix} \)
Simplify
$$ \dfrac{i(2-i)}{3-2i}$$
\(-\frac{1}{13}+\frac{8}{13}i\)
Evaluate:
\(\int x\tan^{-1}x\; dx\)
\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt{x}\) is rotated about the y-axis for \(1 \le y \le 4\)
\(\frac{1023\pi}{5}\) cubic units
How do you determine if a geometric series converges?
Clue: common ratio test
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
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
Simplify:
$$\sqrt{50}$$
\(5\sqrt{2}\)
Simplify:
$$\dfrac{6}{\sqrt{11}}$$\(\frac{6\sqrt{11}}{11}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
Calculate the standard deviation of the following numbers:
4, 2, 5, 8, 6
2
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