Find the first three terms in the expansion of:
\((2a - 3b)^6\)
\(=64a^6 - 576a^5b \\+2160a^4b^2 ...\)
If £120 is invested with an interest rate of 6% compounded monthly, find the value of the investment after 8 years. £193.70
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,4),(9,7),(0,10)\)
(6,13)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2-x-12\)
\((x+3)(x-4)\)
Factorise:
\(9x^2-6x-8\)
\((3x+2)(3x-4)\)
Draw a rough sketch of the graph of:
\(y=2x+2\)
Gradient 2
y intercept 2
What is the value of:
\(2^{-3}\)
\(= \frac{1}{8}\)
Find angle ABC if AC = 4.1m and BC = 5.3m. 50.7o
Find AC if angle ABC = 27o and AB = 5.4m. 2.75m
Describe the red region.
\(y = 3x^3 - 3x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 6x + 3\)
\(y = \dfrac{7}{x^{4}} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{28}{x^{5}} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=(8x^3+3)^7\)
Find \( \dfrac{dy}{dx}\)
\(168x^2(8x^3+3)^6\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{x+2}{x-5}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{7}{(x-5)^2}\)
Find the equation of the tangent to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(y = 0\)
Find the equation of the normal to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = \frac{x}{2} + 1\)
\(y =6x^2 - 14x + 9\)
Find \( \int y \quad dx\)
\(2x^3 - 7x^2 + 9x+c\)
A game is played 11 times and the probability of winning is 0.5. Calculate the probability of winning exactly 7 times. 0.161
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:
\(u_{7} = -16\)
\(u_{11} = -32\)
Find the sum of the first 47 terms.-3948
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BĈA = 45.0°.
BC = 7.7cm.
AB̂C = 75.06°.
Find CA to 1 dp.
8.6cm
Evaluate:
$$\sum_{n=1}^{5} 2^n$$
62
\(f(x)=-7x^2+2x+4\)
What is the value of the discriminant and what does it indicate?
116, Two distinct roots
\(f(x)=x^2-2x+7\)
By completing the square find the coordinates of the vertex.
(1, 6)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-7, -14) and (3, 16)
\(y=3x+7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{3+ x}{2}\)
\(2x-3\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=\sin(x)\)
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
$$\tan{5\pi}$$\(0\)
Solve:
\( 5a+2b+c=37 \\ 3a+4b+2c= 39 \\ a+5b+c=29\)
a = 5, b = 4, c = 4
Find the area of a sector with radius 7.8cm and angle \( \frac{\pi}{6}\)
🍕
15.9cm2
Ansh is with nine people in a queue. How many ways can they line up without Ansh being at the back?
3265920
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The first term of a geometric sequence is 41 and the fourth term is twice this value. What is the common ratio?
\( \sqrt[3]{2} \)
Find the first 4 terms in the expansion of:
\((1-\dfrac{x}{2})^{\frac13}\)
\(1-\frac{x}{6}-\frac{x^2}{36}-\frac{5x^3}{648}\)
Evaluate:
\(\int^{2}_{0} e^x dx\)
\(e^{2}- 1 \approx 6.39\)
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 9% chance and machine B has a 13% chance of breaking down on any given day?
\(0.624\)
There are eight different ways that three planes can relate in three dimensions. One is where they all intersect at a point. How many of the other seven ways can you sketch or describe?
Simplify
$$ \dfrac{1-4i}{1+5i}$$
\(-\frac{19}{26}-\frac{9}{26}i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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 inverse of a function?
Clue: swaps the roles of x and y
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Expand and simplify:
$$ (i-\sqrt{3})^5 $$
\(16\sqrt{3} + 16i \\ \text{or } 16(\sqrt{3} + i)\)
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 \( 2^n > n^2 \) for all integers \( n \) greater
than four
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{45}$$
\(3\sqrt{5}\)
Simplify:
$$\dfrac{9}{\sqrt{6}}$$\(\frac{9\sqrt{6}}{6} = \frac{3\sqrt{6}}{2}\)
Simplify
\(7\sqrt{13} - 9\sqrt{13}\)
\(-2\sqrt{13}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
Calculate the standard deviation of the following numbers:
21, 21, 21, 29, 29, 29
4
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