Find the first three terms in the expansion of:
\((4a - 5b)^7\)
\(=16384a^7 - 143360a^6b \\+537600a^5b^2 ...\)
If £180 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 4 years. £219.76
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,4),(5,7),(-2,8)\)
(2,11)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(8x^2+2x-1\)
\((2x+1)(4x-1)\)
Draw a rough sketch of the graph of:
\(y=-2x-1\)
Gradient -2
y intercept -1
What is the value of:
\(1^{\frac{1}{3}}\)
\(= 1\)
Find angle BCA if AB = 3.5m and BC = 5m. 44.4o
Find AC if angle ABC = 41o and BC = 3.4m. 2.23m
Describe the red region.
\(y = 3x^3 - 4x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 8x + 3\)
\(y = \dfrac{4}{x^{5}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{20}{x^{6}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\frac{1}{(3x+4)^6}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{18}{(3x+4)^7}\)
\(y=e^{3x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(3e^{3x}cosx-e^{3x}sinx\)
\(y=\frac{x+2}{x-4}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{6}{(x-4)^2}\)
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:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =9x^2 - 4x + 3\)
Find \( \int y \quad dx\)
\(3x^3 - 2x^2 + 3x+c\)
A game is played 11 times and the probability of winning is 0.5. Calculate the probability of winning exactly 5 times. 0.226
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:
\(u_{5} = -29\)
\(u_{16} = -128\)
Find the sum of the first 48 terms.-9816
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
AB = 8.7cm.
BC = 6.5cm.
CA = 11.5cm.
Find angle CÂB.
34.1°
Evaluate:
$$\sum_{n=0}^{8} 108 - n^2$$
768
\(f(x)=8x^2+2x-7\)
What is the value of the discriminant and what does it indicate?
228, Two distinct roots
\(f(x)=x^2-8x+9\)
By completing the square find the coordinates of the vertex.
(4, -7)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int x\sqrt{x^2+3} \;dx\)
\(\frac{1}{3}(x^2+3)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-9, -15) and (0, -6)
\(y=x-6\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x+18}\)
\(x²-18\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
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
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\( g-7h-7i=-56 \\ 2g-2h+i= 8\\ 5g+3h+i = 54\)
g = 7, h = 5, i = 4
Find the perimeter of a sector with radius 9.7cm and angle \( \frac{\pi}{3}\)
🍕
29.6cm
Ansh is with six people in a queue. How many ways can they line up without Ansh being at the back?
4320
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\((1-4x)^{-3}\)
\(1+12x+96x^2+640x^3\)
Evaluate:
\(\int^{4}_{0} e^x dx\)
\(e^{4}- 1 \approx 53.6\)
Every family in Happyland has either has a car or a motor scooter or both. 73% of the families have a car. 92% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.
\(\dfrac{65}{73}\)
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
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int \ln{x}\; dx\)
\(x\ln|x|-x+c\)
Simplify:
$$\cos^3{x}+\sin^2{x}\cos{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the y-axis for \(0 \le y \le 4\)
\(8\pi\) 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
\(f(x) = \ln(1 + x)\)
\(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
5 alphabet blocks A, E, P, R and S are placed at random in a row. What is the likelihood that they spell out either SPEAR or PARSE?
1/60 or 1.67%
Prove by mathematical induction that \( n! > 2^n \) for all integers \( n \) greater than 4
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{48}$$
\(4\sqrt{3}\)
Simplify:
$$\dfrac{8}{3\sqrt{7}}$$\(\frac{8\sqrt{7}}{21}\)
Simplify
\(8\sqrt{3}(1 - \sqrt{3})\)
\(8\sqrt{3} - 24\)
Simplify:
$$\dfrac{8}{3 + \sqrt{6}}$$\(\frac{24 - 8\sqrt{6}}{3}\)
Calculate the standard deviation of the following numbers:
43, 45, 49, 51, 55, 57
5
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