Find the first three terms in the expansion of:
\((3a - 4b)^4\)
\(=81a^4 - 432a^3b \\+864a^2b^2 ...\)
If £200 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 9 years. £341.83
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,4),(5,10),(-4,7)\)
(-1,13)
\( X \sim N(50, 5^2)\)
Find
\( P(40\lt X \lt60) \)
\(0.955\)
Factorise:
\(x^2-2x-8\)
\((x+2)(x-4)\)
Factorise:
\(3x^2-10x-8\)
\((3x+2)(x-4)\)
Draw a rough sketch of the graph of:
\(y=x-1\)
Gradient 1
y intercept -1
What is the value of:
\(27^{\frac{1}{3}}\)
\(= 3\)
Find angle ABC if AC = 4.9m and AB = 6.5m. 37.0o
Find BC if angle BCA = 25o and AC = 5.5m. 6.07m
Describe the red region.
\(y = 2x^3 - 9x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 18x + 3\)
\(y = \dfrac{7}{x^8} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{56}{x^9} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=e^{2x+3}\)
Find \( \dfrac{dy}{dx}\)
\(2e^{2x+3}\)
\(y=x^2 \ln x\)
Find \( \dfrac{dy}{dx}\)
\(2x^1lnx+x^1\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
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:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =21x^2 - 8x + 8\)
Find \( \int y \quad dx\)
\(7x^3 - 4x^2 + 8x+c\)
A game is played 20 times and the probability of winning is 0.6. Calculate the probability of winning exactly 5 times. 0.00129
What's this?
\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)
The sum of a geometric sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = 40\)
\(u_{12} = 117\)
Find the sum of the first 29 terms.4350
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 5.4cm.
BC = 7.8cm.
CÂB = 89.3°.
Find angle BĈA.
43.8°
Evaluate:
$$\sum_{n=4}^{5} n^2 - 3n$$
14
\(f(x)=-4x^2+7x-5\)
What is the value of the discriminent and what does it indicate?
-31, No real roots
\(f(x)=x^2+7x+2\)
By completing the square find the coordinates of the vertex.
(-3.5, -10.25)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-1, -7) and (5, -19)
\(y=-2x-9\)
Find the inverse of the function \(f\):
\(f(x)=\frac{8+ x}{6}\)
\(6x-8\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
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
\(x=\pm \sqrt{y}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{30°} \div \sin{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\( 5a+2b+c=45 \\ 3a+4b+2c= 48 \\ a+5b+c=36\)
x=6, y=5, z=5
Find the perimeter of a sector with radius 4.8cm and angle \( \frac{\pi}{6}\)
🍕
12.1cm
A safe has a four-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
2520
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+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:
\(\int^{100}_{50} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
Box A contains 5 red and 7 blue cubes, and box B contains 9 red and 12 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B?
\(\dfrac{36}{71}\)
There are eight different ways that three planes can relate in three dimensions. One is where they all intersect at a point. How many of the other seven ways can you sketch or describe?
Simplify
$$ (2-i)^{-2} $$
\(\frac{3}{25}+\frac{4}{25}i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) 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
\(f(x) = \ln(1 + x)\)
\(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}\)
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