Find the first three terms in the expansion of:
\((2a - 4b)^7\)
\(=128a^7 - 1792a^6b \\+10752a^5b^2 ...\)
If £160 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 6 years. £215.58
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,4),(6,10),(-3,7)\)
(0,13)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(4x^2-4x-3\)
\((2x+1)(2x-3)\)
Draw a rough sketch of the graph of:
\(2y=x+2\)
Gradient 0.5
y intercept 1
What is the value of:
\(4^{0}\)
\(= 1\)
Find angle ABC if AC = 5.9m and AB = 7.8m. 37.1o
Find AC if angle BCA = 25o and AB = 5m. 10.7m
Describe the red region.
\(y = 3x^3 - 5x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 10x + 6\)
\(y = \dfrac{2}{x^{7}} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{14}{x^{8}} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=5\ln (6x^2+7)\)
Find \( \dfrac{dy}{dx}\)
\(60x(6x^2+7)^{-1}\)
\(y=x(4x^2+5)^6\)
Find \( \dfrac{dy}{dx}\)
\((4x^2+5)^6+48x^2(4x^2+5)^5\)
\(y=\frac{x+4}{x-2}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{6}{(x-2)^2}\)
Find the equation of the tangent to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 17x - 2\)
Find the equation of the normal to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = \frac{x}{2} + 1\)
\(y =21x^2 - 16x + 2\)
Find \( \int y \quad dx\)
\(7x^3 - 8x^2 + 2x+c\)
A game is played 20 times and the probability of winning is 0.6. Calculate the probability of winning exactly 19 times. 0.000487
Make up a maths question using this:
\( \int \dfrac{1}{x} = \ln |x| + c\)
Reciprocal Integral formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 78\)
\(u_{18} = 177\)
Find the sum of the first 20 terms.1890
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 7.9cm.
BC = 8.1cm.
CA = 10.3cm.
Find angle CÂB.
50.8°
Evaluate:
$$\sum_{n=4}^{9} 78 - n^2$$
197
\(f(x)=9x^2+3x+2\)
What is the value of the discriminant and what does it indicate?
-63, No real roots
\(f(x)=x^2+6x-7\)
By completing the square find the coordinates of the vertex.
(-3, -16)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
Find the integral:
\(\int 3xe^{x^2} \;dx\)
\(\frac{3}{2}e^{x^2}+c\)
Find the equation of the straight line that passes through:
(-2, -6) and (2, 2)
\(y=2x-2\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+7}{4}\)
\(4x-7\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
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
$$\cos{\frac{\pi}{4}} + \sin{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( 5a+2b+c=30 \\ 3a+4b+2c= 32 \\ a+5b+c=23\)
a = 4, b = 3, c = 4
Find the perimeter of a sector with radius 5.2cm and angle \( \frac{2\pi}{3}\)
🍕
21.3cm
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
201600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The sum of the first 3 terms of a geometric sequence is 28 and the sum of the first 4 terms is 60. What is the first term?
4
Find the first 4 terms in the expansion of:
\(\dfrac{1}{2-x}\)
\(\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{16}\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
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 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:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=e^x\) is rotated about the x-axis for \(0 \le x \le 3\)
\(\frac{\pi}{2}(e^6-1)\) cubic units
What is the difference between a rational and an irrational number?
Rational can be expressed as a fraction with integer numerator and denominator
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
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 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:
$$\sqrt{18}$$
\(3\sqrt{2}\)
Simplify:
$$\dfrac{4}{5\sqrt{3}}$$\(\frac{4\sqrt{3}}{15}\)
Simplify
\((3 + \sqrt{5})(3 - \sqrt{5})\)
\(4\)
Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$\(\frac{10 + 2\sqrt{7}}{18}\)
Calculate the standard deviation of the following numbers:
6, 10, 12, 14, 18
4
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