Find the first three terms in the expansion of:
\((4a - 5b)^5\)
\(=1024a^5 - 6400a^4b \\+16000a^3b^2 ...\)
If £200 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 7 years. £283.61
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,1),(9,6),(0,5)\)
(4,10)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+x-2\)
\((x+2)(x-1)\)
Factorise:
\(4x^2+5x-6\)
\((x+2)(4x-3)\)
Draw a rough sketch of the graph of:
\(y=-x\)
Gradient -1
y intercept 0
What is the value of:
\(4^{1}\)
\(= 4\)
Find angle ABC if AC = 5.1m and AB = 6.2m. 39.4o
Find AB if angle ABC = 34o and BC = 3.5m. 2.90m
Describe the red region.
\(y = 6x^3 - 6x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 12x + 9\)
\(y = \dfrac{2}{x^9} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{18}{x^10} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=(8x^2-3)^6\)
Find \( \dfrac{dy}{dx}\)
\(96x(8x^2-3)^5\)
\(y=9x^2e^x\)
Find \( \dfrac{dy}{dx}\)
\(18xe^x+9x^2e^x\)
\(y=\frac{ \ln x}{x^2}\)
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:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =24x^2 - 14x + 2\)
Find \( \int y \quad dx\)
\(8x^3 - 7x^2 + 2x+c\)
A game is played 17 times and the probability of winning is 0.3. Calculate the probability of winning exactly 9 times. 0.0276
Make up a maths question using this:
\( \triangle = b^2-4ac\)
Quadratic equation discriminant
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -30\)
\(u_{15} = -110\)
Find the sum of the first 46 terms.-8188
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
AB = 9.7cm.
BC = 7.1cm.
CA = 12.8cm.
Find angle CÂB.
33.3°
Evaluate:
$$\sum_{n=2}^{5} 111 - n^2$$
390
\(f(x)=7x^2+6x-5\)
What is the value of the discriminent and what does it indicate?
176, Two distinct roots
\(f(x)=x^2-2x+4\)
By completing the square find the coordinates of the vertex.
(1, 3)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-8, 15) and (0, -1)
\(y=-2x-1\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-7}\)
\(x²+7\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=\sin(x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{\frac{\pi}{6}} \times \cos{45°}$$\(\dfrac{1}{\sqrt{6}}\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\( j+k+l= 9 \\ 2j-3k+9l= 17\\ -j+k-3l=-7\)
j = 4, k = 3, l = 2
Find the area of a sector with radius 8.9cm and angle \( \frac{5\pi}{6}\)
🍕
104cm2
A safe has a six-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
75600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\(\dfrac{1}{2-x}\)
\(\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{16}\)
Evaluate:
\(\int^{60}_{30} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (70% of fiction, 20% of non-fiction are hardcovers), what's the probability it's non-fiction?
\(0.222\)
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
$$ \dfrac{1-4i}{1+5i}$$
\(\frac{21}{26}-\frac{9}{26}i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt{x}\) is rotated about the y-axis for \(1 \le y \le 4\)
\(\frac{1023\pi}{5}\) cubic units
How do you solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sin(x)\)
\(x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040}\)
Solve for \(z\)
$$ z^4 = - 16 $$
\(\sqrt{2}+i\sqrt{2},-\sqrt{2}+i\sqrt{2} \\ \sqrt{2}-i\sqrt{2},-\sqrt{2}-i\sqrt{2}\)
5 alphabet blocks A, E, P, R and S are placed at random in a row. What is the likelihood that they spell out either SPEAR or PARSE?
1/60 or 1.67%
Prove by mathematical induction that the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
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