Find the first three terms in the expansion of:
\((4a - 2b)^6\)
\(=4096a^6 - 12288a^5b \\+15360a^4b^2 ...\)
If £220 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 6 years. £296.78
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,3),(7,8),(-2,7)\)
(2,12)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2-4\)
\((x+2)(x-2)\)
Factorise:
\(20x^2+7x-6\)
\((4x+3)(5x-2)\)
Draw a rough sketch of the graph of:
\(y=x+2\)
Gradient 1
y intercept 2
What is the value of:
\(5^{1}\)
\(= 5\)
Find angle ABC if AC = 5.7m and AB = 7.3m. 38.0o
Find AC if angle BCA = 55o and AB = 3.7m. 2.59m
Describe the red region.
\(y = 2x^3 - 3x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 6x + 3\)
\(y = \dfrac{3}{x^{6}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{18}{x^{7}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=\sqrt{4x^2-2x}\)
Find \( \dfrac{dy}{dx}\)
\((4x^1-1)(4x^2-2x)^{-\frac{1}{2}}\)
\(y=x(2x^2+3)^5\)
Find \( \dfrac{dy}{dx}\)
\((2x^2+3)^5+20x^2(2x^2+3)^4\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
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:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =9x^2 - 12x + 3\)
Find \( \int y \quad dx\)
\(3x^3 - 6x^2 + 3x+c\)
A game is played 14 times and the probability of winning is 0.1. Calculate the probability of winning exactly 4 times. 0.0349
Make up a maths question using 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:
\(u_{8} = -71\)
\(u_{11} = -101\)
Find the sum of the first 24 terms.-2784
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
AB = 6.1cm.
BC = 7.5cm.
CÂB = 51.4°.
Find angle BĈA.
39.4°
Evaluate:
$$\sum_{n=1}^{8} n^2 - 9n$$
-120
\(f(x)=2x^2+4x+4\)
What is the value of the discriminant and what does it indicate?
-16, No real roots
\(f(x)=x^2+6x-1\)
By completing the square find the coordinates of the vertex.
(-3, -10)
Evaluate \(\log_5(625) \)
4
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-8, -20) and (4, 16)
\(y=3x+4\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-9}{3}}\)
\(3x²+9\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
Write in standard form:
\((a \times 10^2) \div (b\times 10^4)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{-2}\)
Draw a rough sketch of
\(y=\dfrac{5}{x}\)
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
$$\sin{5\pi}$$\(0\)
Solve:
\( 5a+2b+c=41 \\ 3a+4b+2c= 47 \\ a+5b+c=36\)
a = 5, b = 5, c = 6
Find the area of a sector with radius 3.7cm and angle \( \frac{\pi}{4}\)
🍕
5.38cm2
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 7th term of a geometric sequence is 8192 and the sum of the first 7 terms is 10922. Find the first term.
2
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:
\(\int^{6}_{0} x^2-2x+7 \; dx\)
\(78.0\)
Given equal populations of Type X and Type Y bacteria, with mutation rates of 20% and 80% respectively, if a mutated bacterium is found, what's the probability it's Type Y?
\(0.800\)
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:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the x-axis for \(-2 \le x \le 2\)
\(\frac{64\pi}{5}\) cubic units
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
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 \( 2^n > n^2 \) for all integers \( n \) greater
than four
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{20}$$
\(2\sqrt{5}\)
Simplify:
$$\dfrac{5}{\sqrt{8}}$$\(\frac{5\sqrt{8}}{8} = \frac{5\sqrt{2}}{4}\)
Simplify
\((2 - 2\sqrt{2})^2\)
\(12 - 8\sqrt{2}\)
Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$\(\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}\)
Calculate the standard deviation of the following numbers:
7, 9, 10, 11, 13
2
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