Find the first three terms in the expansion of:
\((2a - 4b)^7\)
\(=128a^7 - 1792a^6b \\+10752a^5b^2 ...\)
If £100 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 9 years. £170.91
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,5),(5,9),(-2,8)\)
(1,12)
\( X \sim N(43, 7^2)\)
Find
\( P(32\lt X \lt45) \)
\(0.554\)
Factorise:
\(x^2-4\)
\((x+2)(x-2)\)
Factorise:
\(8x^2+10x-3\)
\((2x+3)(4x-1)\)
Draw a rough sketch of the graph of:
\(y=-2x-2\)
Gradient -2
y intercept -2
What is the value of:
\(3^{0}\)
\(= 1\)
Find angle ABC if AC = 5.7m and BC = 7.4m. 50.4o
Find AB if angle ABC = 30o and BC = 5.2m. 4.50m
Describe the red region.
\(y = 6x^3 - 6x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 12x + 4\)
\(y = \dfrac{6}{x^{5}} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{30}{x^{6}} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=\frac{1}{(7x+8)^6}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{42}{(7x+8)^7}\)
\(y=e^{7x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(7e^{7x}cosx-e^{7x}sinx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(x = -3\)
\(y =15x^2 - 18x + 6\)
Find \( \int y \quad dx\)
\(5x^3 - 9x^2 + 6x+c\)
A game is played 14 times and the probability of winning is 0.7. Calculate the probability of winning exactly 11 times. 0.194
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:
\(u_{9} = 107\)
\(u_{12} = 146\)
Find the sum of the first 22 terms.3069
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 7.5cm.
BC = 6.7cm.
CÂB = 42.6°.
Find angle BĈA.
49.2° or 130.8°
Evaluate:
$$\sum_{n=2}^{7} n^2 - 5n$$
4
\(f(x)=5x^2+8x+4\)
What is the value of the discriminant and what does it indicate?
-16, No real roots
\(f(x)=x^2+2x+5\)
By completing the square find the coordinates of the vertex.
(-1, 4)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-3, -9) and (0, -3)
\(y=2x-3\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-9}{9}}\)
\(9x²+9\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
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
\(y+x=2\)
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
$$\tan{4\pi}$$\(0\)
Solve:
\( j+k+l= 10 \\ 2j-3k+9l= 64\\ -j+k-3l=-22\)
j = 2, k = 1, l = 7
Find the area of a sector with radius 6.2cm and angle \( \frac{\pi}{6}\)
🍕
10.1cm2
How many ways can twenty four people be divided into two equal groups?
1352078
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The sum of the first 6 terms of a geometric sequence is 5460 and the sum of the first 7 terms is 21844. What is the first term?
4
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
Every family in Happyland has either has a car or a motor scooter or both. 72% of the families have a car. 84% 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.
\(\dfrac{7}{9}\)
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
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
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 use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
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 \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
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 \( 11^n - 6 \) is divisible by 5 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{20}$$
\(2\sqrt{5}\)
Simplify:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$\(\frac{10 + 2\sqrt{7}}{18}\)
Calculate the standard deviation of the following numbers:
21, 21, 21, 29, 29, 29
4
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