Find the first three terms in the expansion of:
\((2a - 3b)^4\)
\(=16a^4 - 96a^3b \\+216a^2b^2 ...\)
If £100 is invested with an interest rate of 6% compounded monthly, find the value of the investment after 8 years. £161.41
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,3),(5,6),(-1,6)\)
(2,9)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2-2x-3\)
\((x+1)(x-3)\)
Factorise:
\(8x^2-2x-1\)
\((4x+1)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=-x+1\)
Gradient -1
y intercept 1
What is the value of:
\(1^{\frac{1}{2}}\)
\(= 1\)
Find angle BCA if AB = 3m and AC = 4.2m. 35.5o
Find BC if angle BCA = 22o and AB = 5.3m. 14.1m
Describe the red region.
\(y = 3x^3 - 6x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 12x + 3\)
\(y = \dfrac{3}{x^7} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{21}{x^8} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=4\ln (4x^2+5)\)
Find \( \dfrac{dy}{dx}\)
\(32x(4x^2+5)^{-1}\)
\(y=x(3x+5)^3\)
Find \( \dfrac{dy}{dx}\)
\((3x+5)^3+9x(3x+5)^2\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =12x^2 - 14x + 6\)
Find \( \int y \quad dx\)
\(4x^3 - 7x^2 + 6x+c\)
A game is played 11 times and the probability of winning is 0.7. Calculate the probability of winning exactly 5 times. 0.0566
Make up a maths question using this:
\(u_n=u_1+(n-1)d\)
The nth term of an arithmetic sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = 12\)
\(u_{20} = 24\)
Find the sum of the first 21 terms.315
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
AB = 8.8cm.
BC = 8.2cm.
CA = 14.2cm.
Find angle CÂB.
32.0°
Evaluate:
$$\sum_{n=0}^{6} 2^n$$
127
\(f(x)=2x^2+4x-5\)
What is the value of the discriminent and what does it indicate?
56, Two distinct roots
\(f(x)=x^2+2x+2\)
By completing the square find the coordinates of the vertex.
(-1, 1)
Solve for x:
\(\log_2(x) = 4\)
16
Find the integral:
\(\int \dfrac{x^2}{x^3-1} \;dx\)
\(\frac{1}{3} \ln(x^3-1)+c\)
Find the equation of the straight line that passes through:
(-6, 15) and (5, 4)
\(y=-x+9\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-7}\)
\(x²+7\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
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
\(y=2^x\)
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
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( g-7h-7i=-55 \\ 2g-2h+i= 19\\ 5g+3h+i = 53\)
g = 8, h = 2, i = 7
Find the area of a sector with radius 3.1cm and angle \( \frac{\pi}{4}\)
🍕
3.77cm2
How many ways can eleven children sit in a row without the youngest being in the middle?
36288000
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
Given equal populations of Type X and Type Y bacteria, with mutation rates of 80% and 20% respectively, if a mutated bacterium is found, what's the probability it's Type Y?
\(0.200\)
Find the angle between the plane and the line:
\(\Pi: \quad 4x+4y-2z=7\)
\(L: \quad x+1= \dfrac{4-y}{2} = 3-z \)
\( \approx 7.82^o \)
Simplify
$$ (6+4i)(2+4i) $$
\(-4+32i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x\) is rotated about the x-axis for \(0 \le x \le 1\)
\(\frac{\pi}{3}\) 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
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
A committee of 5 is chosen from 15 people by random selection. Two Londoners were amongst the group from which the selection was made. Find the probability that both Londoners are chosen for the committee.
2/21 or 9.52%
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
Write down a summary of your last Maths lesson focussing on what you learnt.
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