Find the first three terms in the expansion of:
\((3a - 4b)^9\)
\(=19683a^9 - 236196a^8b \\+1259712a^7b^2 ...\)
If £100 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 9 years. £156.39
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,1),(9,6),(-2,7)\)
(4,12)
\( X \sim N(43, 7^2)\)
Find
\( P(32\lt X \lt45) \)
\(0.554\)
Factorise:
\(x^2-2x-3\)
\((x+1)(x-3)\)
Factorise:
\(3x^2+2x-1\)
\((x+1)(3x-1)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(2^{1}\)
\(= 2\)
Find angle ABC if AC = 4.8m and BC = 5.9m. 54.4o
Find AC if angle BCA = 26o and AB = 4.9m. 10.0m
Describe the red region.
\(y = 2x^3 - 2x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 4x + 3\)
\(y = \dfrac{3}{x^4} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{12}{x^5} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=(6x^2-4)^5\)
Find \( \dfrac{dy}{dx}\)
\(60x(6x^2-4)^4\)
\(y=e^{9x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(9e^{9x}cosx-e^{9x}sinx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = \frac{x}{2} + 1\)
\(y =15x^2 - 18x + 8\)
Find \( \int y \quad dx\)
\(5x^3 - 9x^2 + 8x+c\)
A game is played 20 times and the probability of winning is 0.6. Calculate the probability of winning exactly 12 times. 0.180
Make up a maths question using this:
\( A = 4\pi r^2 \)
Surface area of a sphere
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -52\)
\(u_{14} = -94\)
Find the sum of the first 21 terms.-1533
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
AB = 6.6cm.
BC = 7.4cm.
CA = 8.2cm.
Find angle CÂB.
58.8°
Evaluate:
$$\sum_{n=4}^{6} 3n+6$$
63
\(f(x)=8x^2-5x-6\)
What is the value of the discriminent and what does it indicate?
217, Two distinct roots
\(f(x)=x^2-9x-3\)
By completing the square find the coordinates of the vertex.
(4.5, -23.25)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int \dfrac{x^2}{x^3-1} \;dx\)
\(\frac{1}{3} \ln(x^3-1)+c\)
Find the equation of the straight line that passes through:
(-3, 0) and (2, 15)
\(y=3x+9\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-7}\)
\(x²+7\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^{p+q}\)
Draw a rough sketch of
\(y=x^3-4x\)
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
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\( g-7h-7i=-54 \\ 2g-2h+i= 3\\ 5g+3h+i = 24\)
g = 2, h = 3, i = 5
Find the perimeter of a sector with radius 6.7cm and angle \( \frac{5\pi}{6}\)
🍕
30.9cm
In how many ways can 10 different books be arranged on a shelf if 2 of them must be together?
725760
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
The first term of a geometric sequence is 39 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:
\((1+x)^{-8}\)
\(1-8x-36x^2-120x^3\)
Evaluate:
\(\int^{4}_{1} x^2-2x+7 \; dx\)
\(6\)
Box A contains 5 red and 7 blue cubes, and box B contains 8 red and 10 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?
\(\dfrac{16}{31}\)
Find the point of intersection of \(L_1\) and \(L_2\) if:
\(L_1: \quad \dfrac{x+4}{3} = y-2 = \dfrac{z+1}{2} \)
\(L_2: \quad x = \dfrac{y-5}{2} = \dfrac{-z-1}{2} \)
\( (-1,3,1) \)
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x(4-x)\) is rotated about the x-axis for \(0 \le x \le 4\)
\(\frac{512\pi}{15}\) 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
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
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 the sum of the first \( n \) odd numbers is \( n^2 \)
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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