Find the first three terms in the expansion of:
\((2a - 3b)^5\)
\(=32a^5 - 240a^4b \\+720a^3b^2 ...\)
If £240 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 5 years. £278.79
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,1),(7,6),(-2,5)\)
(2,10)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(3x^2-11x-4\)
\((3x+1)(x-4)\)
Draw a rough sketch of the graph of:
\(y=2x+2\)
Gradient 2
y intercept 2
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle ABC if AC = 5.2m and AB = 7.2m. 35.8o
Find BC if angle BCA = 36o and AC = 4.7m. 5.81m
Describe the red region.
\(y = 6x^3 - 2x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 4x + 9\)
\(y = \dfrac{9}{x^{9}} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{81}{x^{10}} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=x^4 \ln x\)
Find \( \dfrac{dy}{dx}\)
\(4x^3lnx+x^3\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
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:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =27x^2 - 18x + 9\)
Find \( \int y \quad dx\)
\(9x^3 - 9x^2 + 9x+c\)
A game is played 17 times and the probability of winning is 0.2. Calculate the probability of winning exactly 12 times. 0.00000831
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:
\(u_{9} = 28\)
\(u_{17} = 60\)
Find the sum of the first 35 terms.2240
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 5.2cm.
BC = 6.4cm.
CÂB = 66.0°.
Find angle BĈA.
47.9°
Evaluate:
$$\sum_{n=1}^{7} n^2 - 7n$$
-56
\(f(x)=2x^2+5x-6\)
What is the value of the discriminant and what does it indicate?
73, Two distinct roots
\(f(x)=x^2+6x-2\)
By completing the square find the coordinates of the vertex.
(-3, -11)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
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:
(-1, -1) and (4, 14)
\(y=3x+2\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-3}}{3}\)
\(9x²+3\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(y+x=2\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{30°} \times \tan{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{6}}$$\(\dfrac{1}{\sqrt{3}}\)
Solve:
\(2x+y-3z= 10 \\ 3x+y+z= 25 \\ x-y+2z = 9\)
x = 7, y = 2, z = 2
Find the perimeter of a sector with radius 9.6cm and angle \( \frac{2\pi}{3}\)
🍕
39.3cm
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:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The sum of the first 6 terms of a geometric sequence is 11718 and the sum of the first 7 terms is 58593. 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:
\(\int^{40}_{20} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.1. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.526\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 2 \\ 9 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 8 \\ -7 \\ 7 \end{pmatrix} \; \text{and} \; \begin{pmatrix} 6 \\ -16 \\ 7 \end{pmatrix} \)
53.8 square units
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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 solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
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 the sum of the first \( n \) natural numbers is \( \frac{n(n + 1)}{2} \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{20}$$
\(2\sqrt{5}\)
Simplify:
$$\dfrac{2}{\sqrt{10}}$$\(\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}\)
Simplify
\((3 + \sqrt{5})(3 - \sqrt{5})\)
\(4\)
Simplify:
$$\dfrac{3}{4 + \sqrt{2}}$$\(\frac{12 - 3\sqrt{2}}{14} = \frac{6 - \sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
43, 45, 49, 51, 55, 57
5
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