Find the first three terms in the expansion of:
\((3a - 2b)^5\)
\(=243a^5 - 810a^4b \\+1080a^3b^2 ...\)
If £140 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 6 years. £188.86
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,5),(9,9),(1,9)\)
(5,13)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-1\)
\((x+1)(x-1)\)
Factorise:
\(3x^2-4x-4\)
\((3x+2)(x-2)\)
Draw a rough sketch of the graph of:
\(y=x+2\)
Gradient 1
y intercept 2
What is the value of:
\(2^{-1}\)
\(= \frac{1}{2}\)
Find angle BCA if AC = 5.2m and BC = 6.6m. 38.0o
Find AC if angle ABC = 41o and AB = 4.5m. 3.91m
Describe the red region.
\(y = 9x^3 - 8x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 16x + 4\)
\(y = \dfrac{4}{x^{8}} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{32}{x^{9}} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=(5x+9)^3\)
Find \( \dfrac{dy}{dx}\)
\(15(5x+9)^2\)
\(y=\sin x \sqrt{ x^2 + 3}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+3}+\frac{xsinx}{\sqrt{x^2+3}}\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =12x^2 - 4x + 9\)
Find \( \int y \quad dx\)
\(4x^3 - 2x^2 + 9x+c\)
A game is played 20 times and the probability of winning is 0.8. Calculate the probability of winning exactly 11 times. 0.00739
Make up a maths question using this:
\(\log_ax=\dfrac{\log_bx}{\log_ba}\)
Logarithm changing base formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{7} = 41\)
\(u_{15} = 105\)
Find the sum of the first 37 terms.5069
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
AB = 6.5cm.
BC = 8.3cm.
CÂB = 80.8°.
Find angle BĈA.
50.6°
Evaluate:
$$\sum_{n=3}^{9} 2n+4$$
112
\(f(x)=2x^2-3x-4\)
What is the value of the discriminant and what does it indicate?
41, Two distinct roots
\(f(x)=x^2+2x-7\)
By completing the square find the coordinates of the vertex.
(-1, -8)
Simplify \(\log_{10}10^5\)
5
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:
(-9, 24) and (2, 2)
\(y=-2x+6\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+2}{9}\)
\(9x-2\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
Draw a rough sketch of
\(y=2^x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{30°} \div \sin{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( g-7h-7i=-82 \\ 2g-2h+i= -8\\ 5g+3h+i = 38\)
g = 2, h = 8, i = 4
Find the perimeter of a sector with radius 3.3cm and angle \( \frac{\pi}{3}\)
🍕
10.1cm
Ansh is with seven people in a queue. How many ways can they line up without Ansh being at the back?
35280
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\((1+x)^{-8}\)
\(1-8x-36x^2-120x^3\)
Evaluate:
\(\int^{3}_{0} (x-8)^2 \; dx\)
\(129\)
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 7% chance of breaking down on any given day?
\(0.601\)
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:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) 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
\(f(x) = \ln(1 + x)\)
\(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}\)
Solve for \(z\)
$$ z^4 = - 16 $$
\(\sqrt{2}+i\sqrt{2},-\sqrt{2}+i\sqrt{2} \\ \sqrt{2}-i\sqrt{2},-\sqrt{2}-i\sqrt{2}\)
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:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{6}{\sqrt{11}}$$\(\frac{6\sqrt{11}}{11}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$\(\frac{10 + 2\sqrt{7}}{18}\)
Calculate the standard deviation of the following numbers:
9, 13, 15, 17, 21
4
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