Find the first three terms in the expansion of:
\((3a - 2b)^7\)
\(=2187a^7 - 10206a^6b \\+20412a^5b^2 ...\)
If £160 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 8 years. £219.99
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,5),(6,8),(0,8)\)
(3,11)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2-4\)
\((x+2)(x-2)\)
Factorise:
\(3x^2+2x-8\)
\((x+2)(3x-4)\)
Draw a rough sketch of the graph of:
\(2y=x-2\)
Gradient 0.5
y intercept -1
What is the value of:
\(27^{\frac{1}{3}}\)
\(= 3\)
Find angle BCA if AB = 5.9m and BC = 7.3m. 53.9o
Find BC if angle BCA = 59o and AC = 5.6m. 10.9m
Describe the red region.
\(y = 6x^3 - 4x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 8x + 9\)
\(y = \dfrac{9}{x^5} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{45}{x^6} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=(6x+8)^4\)
Find \( \dfrac{dy}{dx}\)
\(24(6x+8)^3\)
\(y=e^{9x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(9e^{9x}cosx-e^{9x}sinx\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = 17 - 13x\)
Find the equation of the normal to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =24x^2 - 6x + 9\)
Find \( \int y \quad dx\)
\(8x^3 - 3x^2 + 9x+c\)
A game is played 10 times and the probability of winning is 0.2. Calculate the probability of winning exactly 3 times. 0.201
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:
\(u_{9} = -72\)
\(u_{15} = -126\)
Find the sum of the first 41 terms.-7380
Find the equations of the asymptotes of:
\(y=3\left(\dfrac{2x+3}{7-x}\right)\)
\(x=7,y=-6\)
In the triangle ABC,
AB = 5.7cm.
BC = 8.8cm.
CA = 12.2cm.
Find angle CÂB.
41.7°
Evaluate:
$$\sum_{n=2}^{5} 3n+5$$
62
\(f(x)=-5x^2+3x+8\)
What is the value of the discriminent and what does it indicate?
169, Two distinct roots
\(f(x)=x^2-4x-2\)
By completing the square find the coordinates of the vertex.
(2, -6)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-4, 14) and (3, 0)
\(y=-2x+6\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-3}\)
\(x²+3\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
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
\(y=\dfrac{5}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{2}} \div \cos{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\cos{720°}$$\(1\)
Solve:
\( g-7h-7i=-71 \\ 2g-2h+i= -1\\ 5g+3h+i = 57\)
g = 6, h = 8, i = 3
Find the perimeter of a sector with radius 9.7cm and angle \( \frac{\pi}{6}\)
🍕
24.5cm
How many ways can sixteen people be divided into two equal groups?
6435
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\((1+x)^{-8}\)
\(1-8x-36x^2-120x^3\)
Evaluate:
\(\int^{3}_{0} x^2-2x+7 \; dx\)
\(6\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.05. 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?
\(0.513\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 3 \\ 2 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 4 \\ -5 \\ 3 \end{pmatrix} \; \text{and} \; \begin{pmatrix} 1 \\ -7 \\ 3 \end{pmatrix} \)
12.7 square units
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\ln{x}\) is rotated about the y-axis for \(0 \le y \le 1\)
\(\approx 10.0\) cubic units
What is the inverse of a function?
Clue: swaps the roles of x and y
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sec(x)\)
\(1 + \frac{x^2}{2} + \frac{5x^4}{24} + \frac{61x^6}{720}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
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 squares of the first \( n \) natural numbers is \( \frac{n(n + 1)(2n + 1)}{6} \)
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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