Find the first three terms in the expansion of:
\((3a - 2b)^8\)
\(=6561a^8 - 34992a^7b \\+81648a^6b^2 ...\)
If £200 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 7 years. £246.67
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,1),(10,4),(2,6)\)
(7,9)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2-2x-8\)
\((x+2)(x-4)\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Draw a rough sketch of the graph of:
\(y=2x\)
Gradient 2
y intercept 0
What is the value of:
\(5^{-3}\)
\(= \frac{1}{125}\)
Find angle BCA if AC = 4.1m and BC = 5.4m. 40.6o
Find AB if angle ABC = 39o and BC = 3.6m. 2.80m
Describe the red region.
\(y = 9x^3 - 7x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 14x + 9\)
\(y = \dfrac{5}{x^{5}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{25}{x^{6}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=6\ln (3x^2+4)\)
Find \( \dfrac{dy}{dx}\)
\(36x(3x^2+4)^{-1}\)
\(y=\sin x \sqrt{ x^2 + 3}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+3}+\frac{xsinx}{\sqrt{x^2+3}}\)
\(y=\frac{x+2}{x-2}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{4}{(x-2)^2}\)
Find the equation of the tangent to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 17x - 2\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =12x^2 - 18x + 3\)
Find \( \int y \quad dx\)
\(4x^3 - 9x^2 + 3x+c\)
A game is played 12 times and the probability of winning is 0.3. Calculate the probability of winning exactly 11 times. 0.0000149
Make up a maths question using this:
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -10\)
\(u_{19} = -32\)
Find the sum of the first 44 terms.-1716
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BĈA = 44.6°.
BC = 9.3cm.
AB̂C = 81.55°.
Find CA to 1 dp.
11.4cm
Evaluate:
$$\sum_{n=1}^{4} 2^n$$
30
\(f(x)=-2x^2-7x+8\)
What is the value of the discriminant and what does it indicate?
113, Two distinct roots
\(f(x)=x^2-5x-3\)
By completing the square find the coordinates of the vertex.
(2.5, -9.25)
Solve for x:
\(\log_3x = 2\)
9
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-6, 12) and (3, -6)
\(y=-2x+0\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+8}{2}\)
\(2x-8\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
Draw a rough sketch of
\(y=x^2+7x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$\(0\)
Without a calculator find the exact value of
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\( j+k+l= 20 \\ 2j-3k+9l= 49\\ -j+k-3l=-18\)
j = 5, k = 8, l = 7
Find the area of a sector with radius 3.2cm and angle \( \frac{5\pi}{6}\)
🍕
13.4cm2
In how many ways can 11 different books be arranged on a shelf if 4 of them must be together?
967680
Find the equations of the asymptotes of:
$$y=\dfrac{8x^2-19x-15}{1-2x}$$x=1/2,y=15/2-4x
The first term of a geometric sequence is 30 and the fourth term is twice this value. What is the common ratio?
\( \sqrt[3]{2} \)
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{6}_{0} x^2-2x+7 \; dx\)
\(78.0\)
Given equal populations of Type X and Type Y bacteria, with mutation rates of 40% and 60% respectively, if a mutated bacterium is found, what's the probability it's Type Y?
\(0.600\)
Find the vector equation of the line:
\( \dfrac{x-6}{7} = \dfrac{4-y}{9} = \dfrac{z}{3} \)
\( \mathbf{r} = \begin{pmatrix} 6 \\ 4 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 7 \\ -9 \\ 3 \end{pmatrix} \)
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int \ln{x}\; dx\)
\(x\ln|x|-x+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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 use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
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 \( 5^n - 1 \) is divisible by 4 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{48}$$
\(4\sqrt{3}\)
Simplify:
$$\dfrac{8}{3\sqrt{7}}$$\(\frac{8\sqrt{7}}{21}\)
Simplify
\((9 + 2\sqrt{2})(9 - 2\sqrt{2})\)
\(73\)
Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)
Calculate the standard deviation of the following numbers:
4, 2, 5, 8, 6
2
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