Find the first three terms in the expansion of:
\((2a - 3b)^6\)
\(=64a^6 - 576a^5b \\+2160a^4b^2 ...\)
If £160 is invested with an interest rate of 2% compounded monthly, find the value of the investment after 5 years. £176.81
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,1),(9,6),(-2,7)\)
(4,12)
\( X \sim N(100, 7^2)\)
Find
\( P(93\lt X \lt107) \)
\(0.683\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(4x^2+13x-12\)
\((x+4)(4x-3)\)
Draw a rough sketch of the graph of:
\(y=-2x-1\)
Gradient -2
y intercept -1
What is the value of:
\(5^{0}\)
\(= 1\)
Find angle ABC if AB = 4.2m and BC = 5.8m. 43.6o
Find AB if angle ABC = 53o and BC = 5.5m. 3.31m
Describe the red region.
\(y = 5x^3 - 3x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 6x + 4\)
\(y = \dfrac{8}{x^4} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{32}{x^5} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=\sqrt{2x^6+3}\)
Find \( \dfrac{dy}{dx}\)
\(6x^5(2x^6+3)^{-\frac{1}{2}}\)
\(y=x \tan x\)
Find \( \dfrac{dy}{dx}\)
\(tanx+\frac{x}{cos^2x}\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
Find the equation of the tangent to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =6x^2 - 14x + 2\)
Find \( \int y \quad dx\)
\(2x^3 - 7x^2 + 2x+c\)
A game is played 14 times and the probability of winning is 0.8. Calculate the probability of winning exactly 6 times. 0.00202
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:
\(u_{6} = -32\)
\(u_{13} = -81\)
Find the sum of the first 20 terms.-1270
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
AB = 9.8cm.
BC = 5.5cm.
CÂB = 33.5°.
Find angle BĈA.
100° or 80°
Evaluate:
$$\sum_{n=2}^{6} 2^n$$
124
\(f(x)=6x^2+8x+7\)
What is the value of the discriminent and what does it indicate?
-104, No real roots
\(f(x)=x^2-6x+1\)
By completing the square find the coordinates of the vertex.
(3, -8)
Solve for x:
\(\log_3x = 2\)
9
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:
(-4, -13) and (9, 13)
\(y=2x-5\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-9}{9}}\)
\(9x²+9\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
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
\(y=x^3-4x\)
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
$$\tan{4\pi}$$\(0\)
Solve:
\(2x+y-3z= 5 \\ 3x+y+z= 16 \\ x-y+2z = 2\)
x = 3, y = 5, z = 2
Find the area of a sector with radius 2.9cm and angle \( \frac{\pi}{6}\)
🍕
2.20cm2
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:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{40}_{20} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.08. 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?
\(0.521\)
Find the vector product:
\( \begin{pmatrix} 9 \\ 8 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 6 \\ -6 \\ 8 \end{pmatrix} \)
\( \begin{pmatrix} 64 \\ -72 \\ -102 \end{pmatrix} \)
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=e^x\) is rotated about the x-axis for \(0 \le x \le 3\)
\(\frac{\pi}{2}(e^6-1)\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Expand and simplify:
$$ (i-\sqrt{3})^5 $$
\(16\sqrt{3} + 16i \\ \text{or } 16(\sqrt{3} + i)\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
Prove by mathematical induction that \( n! > 2^n \) for all integers \( n \) greater than 4
Show true for n=1, assume true for n=k, prove for n=k+1
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