Find the first three terms in the expansion of:
\((4a - 2b)^5\)
\(=1024a^5 - 2560a^4b \\+2560a^3b^2 ...\)
If £160 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 9 years. £209.52
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,3),(10,6),(2,8)\)
(7,11)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2-2x-3\)
\((x+1)(x-3)\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Draw a rough sketch of the graph of:
\(y=x\)
Gradient 1
y intercept 0
What is the value of:
\(4^{0}\)
\(= 1\)
Find angle ABC if AC = 5.8m and BC = 7.1m. 54.8o
Find AC if angle BCA = 35o and AB = 4.8m. 6.86m
Describe the red region.
\(y = 9x^3 - 9x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 18x + 6\)
\(y = \dfrac{8}{x^{7}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{56}{x^{8}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=(7x^7+2)^9\)
Find \( \dfrac{dy}{dx}\)
\(441x^6(7x^7+2)^8\)
\(y=x(3x+5)^3\)
Find \( \dfrac{dy}{dx}\)
\((3x+5)^3+9x(3x+5)^2\)
\(y=\frac{x+5}{x-2}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{7}{(x-2)^2}\)
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:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =18x^2 - 14x + 9\)
Find \( \int y \quad dx\)
\(6x^3 - 7x^2 + 9x+c\)
A game is played 17 times and the probability of winning is 0.1. Calculate the probability of winning exactly 4 times. 0.0605
Make up a maths question using this:
\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)
The sum of a geometric sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 8\)
\(u_{15} = 20\)
Find the sum of the first 37 terms.1036
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
BC = 5.2cm.
CA = 8.6cm.
BĈA = 37.7°
Find AB to 1 dp.
5.5cm
Evaluate:
$$\sum_{n=4}^{6} 5n+4$$
87
\(f(x)=4x^2-8x+3\)
What is the value of the discriminant and what does it indicate?
16, Two distinct roots
\(f(x)=x^2-6x+4\)
By completing the square find the coordinates of the vertex.
(3, -5)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
Find the integral:
\(\int \dfrac{\ln(x)}{x} \;dx\)
\(\dfrac{\ln(x)^2}{2}+c\)
Find the equation of the straight line that passes through:
(-9, -19) and (0, -1)
\(y=2x-1\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x+17}\)
\(x²-17\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\((a \times 10^4) \div (b\times 10^{-2})\)
where \(a \div b \) is a decimal number \((0.1 \le \frac{a}{b} \lt 1)\)
\(\frac{10a}{b}\times10^5\)
Draw a rough sketch of
\(y=x(5-x)\)
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
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\( 5a+2b+c=22 \\ 3a+4b+2c= 30 \\ a+5b+c=29\)
a = 2, b = 5, c = 2
Find the perimeter of a sector with radius 7.9cm and angle \( \frac{\pi}{6}\)
🍕
19.9cm
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
201600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The sum of the first 3 terms of a geometric sequence is 93 and the sum of the first 4 terms is 468. What is the first term?
3
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
The probability that it is cloudy on a particular day is 0.5. The probability that it is cloudy with a high level of pollution on a particular day is 0.2. Find the probability that there will be a high level of pollution on a day when it is cloudy.
\(0.400\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
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
\(f(x) = \frac{1}{x^2 + 1}\)
\(1 - x^2 + x^4 - x^6\)
Given |z| = 8, find:
$$ |(3+4i)z| $$
\(40\)
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 first \( n \) odd numbers is \( n^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{75}$$
\(5\sqrt{3}\)
Simplify:
$$\dfrac{5}{\sqrt{8}}$$\(\frac{5\sqrt{8}}{8} = \frac{5\sqrt{2}}{4}\)
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:
30, 38, 38, 42, 42, 50
6
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