Find the first three terms in the expansion of:
\((3a - 4b)^6\)
\(=729a^6 - 5832a^5b \\+19440a^4b^2 ...\)
If £120 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 6 years. £161.68
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,1),(10,4),(1,7)\)
(7,10)
\( X \sim N(100, 7^2)\)
Find
\( P(93\lt X \lt107) \)
\(0.683\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Factorise:
\(5x^2+14x-3\)
\((x+3)(5x-1)\)
Draw a rough sketch of the graph of:
\(y=-2x-1\)
Gradient -2
y intercept -1
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle BCA if AB = 4m and BC = 5.5m. 46.7o
Find BC if angle BCA = 58o and AC = 4.1m. 7.74m
Describe the red region.
\(y = 8x^3 - 8x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(24x^2 - 16x + 4\)
\(y = \dfrac{6}{x^5} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{30}{x^6} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=9\ln (3x^2+4)\)
Find \( \dfrac{dy}{dx}\)
\(54x(3x^2+4)^{-1}\)
\(y=x \tan x\)
Find \( \dfrac{dy}{dx}\)
\(tanx+\frac{x}{cos^2x}\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
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:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =15x^2 - 10x + 7\)
Find \( \int y \quad dx\)
\(5x^3 - 5x^2 + 7x+c\)
A game is played 12 times and the probability of winning is 0.9. Calculate the probability of winning exactly 9 times. 0.0852
Make up a maths question using this:
\( P(A|B) = \dfrac{P(A \cap B)}{P(B)} \)
Conditional probability formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = 40\)
\(u_{15} = 110\)
Find the sum of the first 23 terms.2047
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
AB = 8.1cm.
BC = 6.8cm.
CA = 5.5cm.
Find angle CÂB.
56.2°
Evaluate:
$$\sum_{n=1}^{5} 2^n$$
62
\(f(x)=6x^2-4x-8\)
What is the value of the discriminent and what does it indicate?
208, Two distinct roots
\(f(x)=x^2+8x+6\)
By completing the square find the coordinates of the vertex.
(-4, -10)
Evaluate \(\log_5(625) \)
4
Find the integral:
\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)
\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-5, 6) and (6, -27)
\(y=-3x-9\)
Find the inverse of the function \(f\):
\(f(x)=\frac{9+ x}{8}\)
\(8x-9\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
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
\(y=\dfrac{5}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\(2x+y-3z= 13 \\ 3x+y+z= 33 \\ x-y+2z = 8\)
x = 8, y = 6, z = 3
Find the area of a sector with radius 8.5cm and angle \( \frac{\pi}{3}\)
🍕
37.8cm2
How many ways can eighteen people be divided into two equal groups?
24310
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:
\(\dfrac{1}{\sqrt[3]{1+x}}\)
\(1 - \frac{x}{3} + \frac{2x^2}{9} - \frac{14x^3}{81}\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
31 Scouts went hiking. 13 got lost, 14 got blisters, and 6 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{4}{9}\)
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
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\cos^3{x}+\sin^2{x}\cos{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x(4-x)\) is rotated about the x-axis for \(0 \le x \le 4\)
\(\frac{512\pi}{15}\) cubic units
Describe the graph of an exponential function.
Clue: grow or decay rapidly, horizontal asymptote
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Given |z| = 8, find:
$$ |(3+4i)z| $$
\(40\)
A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.
55/153 or 35.9%
Prove by mathematical induction that \( 2^n > n^2 \) for all integers \( n \) greater
than four
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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