Find the first three terms in the expansion of:
\((3a - 2b)^7\)
\(=2187a^7 - 10206a^6b \\+20412a^5b^2 ...\)
If £240 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 4 years. £293.01
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,2),(6,5),(-1,6)\)
(3,9)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2-2x-8\)
\((x+2)(x-4)\)
Factorise:
\(8x^2-10x-3\)
\((4x+1)(2x-3)\)
Draw a rough sketch of the graph of:
\(y=x+1\)
Gradient 1
y intercept 1
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle ABC if AC = 4.5m and BC = 6m. 48.6o
Find BC if angle BCA = 20o and AB = 4.8m. 14.0m
Describe the red region.
\(y = 6x^3 - 5x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 10x + 8\)
\(y = \dfrac{5}{x^{2}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{10}{x^{3}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=e^{7x+8}\)
Find \( \dfrac{dy}{dx}\)
\(7e^{7x+8}\)
\(y=\sin x \sqrt{ x^2 + 7}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+7}+\frac{xsinx}{\sqrt{x^2+7}}\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =24x^2 - 6x + 6\)
Find \( \int y \quad dx\)
\(8x^3 - 3x^2 + 6x+c\)
A game is played 16 times and the probability of winning is 0.7. Calculate the probability of winning exactly 14 times. 0.0732
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:
\(u_{5} = 28\)
\(u_{13} = 92\)
Find the sum of the first 37 terms.5180
Find the equations of the asymptotes of:
\(y=\dfrac{4-7x}{3-14x}\)
\(x=\frac{3}{14},y=\frac{1}{2}\)
In the triangle ABC,
BĈA = 64.4°.
BC = 8.5cm.
AB̂C = 53.92°.
Find CA to 1 dp.
7.8cm
Evaluate:
$$\sum_{n=0}^{5} 2^n$$
63
\(f(x)=-7x^2-9x+5\)
What is the value of the discriminant and what does it indicate?
221, Two distinct roots
\(f(x)=x^2+8x+1\)
By completing the square find the coordinates of the vertex.
(-4, -15)
What is the value of \(\ln{e^3}\) ?
3
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:
(-2, -7) and (2, -11)
\(y=-x-9\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-4}\)
\(x²+4\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
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
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\cos{7\pi}$$\(-1\)
Solve:
\( g-7h-7i=-89 \\ 2g-2h+i= -1\\ 5g+3h+i = 35\)
g = 2, h = 6, i = 7
Find the perimeter of a sector with radius 8.3cm and angle \( \frac{\pi}{6}\)
🍕
20.9cm
How many ways can sixteen people be divided into two equal groups?
6435
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The sum of the first 4 terms of a geometric sequence is 75 and the sum of the first 5 terms is 155. What is the first term?
5
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
Box A contains 6 red and 7 blue cubes, and box B contains 10 red and 13 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?
\(\dfrac{65}{134}\)
Find the vector product:
\( \begin{pmatrix} 8 \\ 3 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 4 \\ -5 \\ 6 \end{pmatrix} \)
\( \begin{pmatrix} 18 \\ -48 \\ -52 \end{pmatrix} \)
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
How do you determine the domain of a function?
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \frac{1}{1-x}\)
\(1 + x + x^2 + x^3\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
Of the 22 people on boat, 3 are professional singers. If 4 people get sea sick, determine the chance that all three singers do not.
204/385 or 53.0%
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:
$$\dfrac{5}{\sqrt{8}}$$\(\frac{5\sqrt{8}}{8} = \frac{5\sqrt{2}}{4}\)
Simplify
\(7\sqrt{13} - 9\sqrt{13}\)
\(-2\sqrt{13}\)
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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