Find the first three terms in the expansion of:
\((4a - 2b)^5\)
\(=1024a^5 - 2560a^4b \\+2560a^3b^2 ...\)
If £220 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 4 years. £248.01
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,5),(8,11),(-4,11)\)
(2,17)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Factorise:
\(8x^2-2x-1\)
\((4x+1)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=x+1\)
Gradient 1
y intercept 1
What is the value of:
\(5^{-2}\)
\(= \frac{1}{25}\)
Find angle BCA if AC = 5m and BC = 6.2m. 36.2o
Find AC if angle ABC = 52o and BC = 3.7m. 2.92m
Describe the red region.
\(y = 5x^3 - 8x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 16x + 4\)
\(y = \dfrac{8}{x^9} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{72}{x^10} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=\frac{1}{(3x+4)^7}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{21}{(3x+4)^8}\)
\(y=(4x+9)(9x-5)\)
Find \( \dfrac{dy}{dx}\)
\(72x+61\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = 17 - 13x\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =9x^2 - 12x + 6\)
Find \( \int y \quad dx\)
\(3x^3 - 6x^2 + 6x+c\)
A game is played 20 times and the probability of winning is 0.4. Calculate the probability of winning exactly 11 times. 0.0710
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:
\(u_{7} = 11\)
\(u_{17} = 21\)
Find the sum of the first 40 terms.980
Find the equations of the asymptotes of:
\(y=3\left(\dfrac{2x+3}{7-x}\right)\)
\(x=7,y=-6\)
In the triangle ABC,
AB = 6.9cm.
BC = 8.8cm.
CÂB = 90.5°.
Find angle BĈA.
51.6°
Evaluate:
$$\sum_{n=1}^{6} 2^n$$
126
\(f(x)=4x^2+2x+9\)
What is the value of the discriminent and what does it indicate?
-140, No real roots
\(f(x)=x^2+2x+9\)
By completing the square find the coordinates of the vertex.
(-1, 8)
Solve for x:
\(\log_2(x) = 4\)
16
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-6, -1) and (4, 9)
\(y=x+5\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-6}}{9}\)
\(81x²+6\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
Draw a rough sketch of
\(y=x^2+7x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( g-7h-7i=-86 \\ 2g-2h+i= -1\\ 5g+3h+i = 54\)
g = 5, h = 8, i = 5
Find the perimeter of a sector with radius 2.3cm and angle \( \frac{5\pi}{6}\)
🍕
10.6cm
In how many ways can 10 different books be arranged on a shelf if 4 of them must be together?
120960
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:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{5}_{2} (x-8)^2 \; dx\)
\(63\)
Box A contains 3 red and 5 blue cubes, and box B contains 6 red and 8 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B?
\(\dfrac{8}{15}\)
Find the angle between two unit vectors \(u\) and \(v\) such that the vectors \(2u-3v\) and \(5u+2v\) are perpendicular. Give you answer correct to the nearest degree.
\( 69^o \)
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
Describe the behavior of a function at its inflection point.
The concavity of the function changes
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \ln(1 + x)\)
\(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}\)
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 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 product of \( n \) consecutive integers is divisible by \( n! \) (n factorial)
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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