Find the first three terms in the expansion of:
\((4a - 2b)^9\)
\(=262144a^9 - 1179648a^8b \\+2359296a^7b^2 ...\)
If £160 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 6 years. £215.58
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,3),(7,7),(0,6)\)
(3,10)
\( X \sim N(50, 5^2)\)
Find
\( P(40\lt X \lt60) \)
\(0.955\)
Factorise:
\(x^2-x-12\)
\((x+3)(x-4)\)
Factorise:
\(2x^2-3x-9\)
\((2x+3)(x-3)\)
Draw a rough sketch of the graph of:
\(y=2x\)
Gradient 2
y intercept 0
What is the value of:
\(2^{0}\)
\(= 1\)
Find angle ABC if AC = 4.7m and BC = 6.1m. 50.4o
Find BC if angle BCA = 60o and AB = 6m. 6.93m
Describe the red region.
\(y = 2x^3 - 6x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 12x + 2\)
\(y = \dfrac{3}{x^{5}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{15}{x^{6}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=e^{6x+7}\)
Find \( \dfrac{dy}{dx}\)
\(6e^{6x+7}\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =9x^2 - 18x + 7\)
Find \( \int y \quad dx\)
\(3x^3 - 9x^2 + 7x+c\)
A game is played 19 times and the probability of winning is 0.7. Calculate the probability of winning exactly 9 times. 0.0220
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:
\(u_{6} = 0\)
\(u_{18} = -24\)
Find the sum of the first 32 terms.-672
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
BC = 9.4cm.
CA = 13.5cm.
BĈA = 28.5°
Find AB to 1 dp.
6.9cm
Evaluate:
$$\sum_{n=2}^{7} 90 - n^2$$
401
\(f(x)=6x^2+5x-4\)
What is the value of the discriminant and what does it indicate?
121, Two distinct roots
\(f(x)=x^2-3x-3\)
By completing the square find the coordinates of the vertex.
(1.5, -5.25)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int 3xe^{x^2} \;dx\)
\(\frac{3}{2}e^{x^2}+c\)
Find the equation of the straight line that passes through:
(-3, -4) and (1, 4)
\(y=2x+2\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-2}\)
\(x²+2\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
Draw a rough sketch of
\(y=x(5-x)\)
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
$$\tan{5\pi}$$\(0\)
Solve:
\(2x+y-3z= 1 \\ 3x+y+z= 41 \\ x-y+2z = 15\)
x = 8, y = 9, z = 8
Find the area of a sector with radius 3.9cm and angle \( \frac{5\pi}{6}\)
🍕
19.9cm2
How many ways can thirteen children sit in a row without the youngest being in the middle?
5748019200
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The 4th term of a geometric sequence is 250 and the sum of the first 4 terms is 312. Find the first term.
2
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{3}_{0} e^x dx\)
\(e^{3}- 1 \approx 19.1\)
Tin A contains 6 red balls and 7 green balls. Tin B contains 10 red balls and 12 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.
\(\frac{65}{98}\)
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
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
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
What is the difference between a rational and an irrational number?
Rational can be expressed as a fraction with integer numerator and denominator
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 \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
Of the 22 people on boat, 3 are professional singers. If 4 people get sea sick, determine the chance that all three singers do not.
204/385 or 53.0%
Prove by mathematical induction that \( 11^n - 6 \) is divisible by 5 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{12}$$
\(2\sqrt{3}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\((3 + \sqrt{5})(3 - \sqrt{5})\)
\(4\)
Simplify:
$$\dfrac{8}{3 + \sqrt{6}}$$\(\frac{24 - 8\sqrt{6}}{3}\)
Calculate the standard deviation of the following numbers:
21, 21, 21, 29, 29, 29
4
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