Find the first three terms in the expansion of:
\((4a - 3b)^8\)
\(=65536a^8 - 393216a^7b \\+1032192a^6b^2 ...\)
If £240 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 9 years. £343.38
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,2),(9,5),(0,8)\)
(6,11)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Factorise:
\(5x^2+18x-8\)
\((x+4)(5x-2)\)
Draw a rough sketch of the graph of:
\(y=2x+2\)
Gradient 2
y intercept 2
What is the value of:
\(1^{-2}\)
\(= 1\)
Find angle BCA if AC = 4.1m and BC = 5.5m. 41.8o
Find AB if angle ABC = 50o and BC = 3m. 1.93m
Describe the red region.
\(y = 7x^3 - 5x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 10x + 9\)
\(y = \dfrac{9}{x^5} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{45}{x^6} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=\sin x \sqrt{ x^2 + 5}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+5}+\frac{xsinx}{\sqrt{x^2+5}}\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)
Find the equation of the normal to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =21x^2 - 10x + 2\)
Find \( \int y \quad dx\)
\(7x^3 - 5x^2 + 2x+c\)
A game is played 14 times and the probability of winning is 0.5. Calculate the probability of winning exactly 11 times. 0.0222
What's this?
\(z=\dfrac{x-\mu}{\sigma}\)
Standardised Normal Variable
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = -54\)
\(u_{15} = -102\)
Find the sum of the first 49 terms.-8918
Find the equations of the asymptotes of:
\(y=10+\dfrac{9x}{5-3x}\)
\(x=\frac{5}{3},y=7\)
In the triangle ABC,
AB = 9.3cm.
BC = 9.4cm.
CÂB = 67.1°.
Find angle BĈA.
65.7°
Evaluate:
$$\sum_{n=0}^{6} 101 - n^2$$
616
\(f(x)=3x^2-3x-3\)
What is the value of the discriminent and what does it indicate?
45, Two distinct roots
\(f(x)=x^2+3x+8\)
By completing the square find the coordinates of the vertex.
(-1.5, 5.75)
Simplify \(\log_{10}10^5\)
5
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-7, 3) and (2, -6)
\(y=-x-4\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-6}{4}}\)
\(4x²+6\)
\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)
\(f(x)=x+2\)
Write in standard form:
\((a \times 10^3) \div (b\times 10^5)\)
where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)
\(\frac{a}{10b}\times10^{-1}\)
Draw a rough sketch of
\(y=3-\dfrac{10}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{30°} \times \tan{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\(2d+3e-4f = -2 \\ d-e-f= -2\\ 9d+2e-2f=32\)
d = 4, e = 2, f = 4
Find the area of a sector with radius 6.9cm and angle \( \frac{2\pi}{3}\)
🍕
49.9cm2
In how many ways can 7 different books be arranged on a shelf if 4 of them must be together?
576
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\((1+2x)^{\frac12}\)
\(1+x-\frac{x^2}{2}+\frac{x^3}{2}\)
Evaluate:
\(\int^{160}_{80} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 5% chance and machine B has a 8% chance of breaking down on any given day?
\(0.635\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ (1+i)^{4} $$
\(-4\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)
\(\frac{65\pi}{4}\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
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 \( 2^n > n^2 \) for all integers \( n \) greater
than four
Show true for n=1, assume true for n=k, prove for n=k+1
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