Find the first three terms in the expansion of:
\((3a - 4b)^9\)
\(=19683a^9 - 236196a^8b \\+1259712a^7b^2 ...\)
If £200 is invested with an interest rate of 1% compounded quarterly, find the value of the investment after 8 years. £216.64
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,2),(10,7),(0,7)\)
(5,12)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(2x^2-5x-12\)
\((2x+3)(x-4)\)
Draw a rough sketch of the graph of:
\(y=2x+1\)
Gradient 2
y intercept 1
What is the value of:
\(4^{\frac{1}{2}}\)
\(= 2\)
Find angle BCA if AC = 3.3m and BC = 4.7m. 45.4o
Find AB if angle ABC = 65o and BC = 3.9m. 1.65m
Describe the red region.
\(y = 5x^3 - 8x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 16x + 9\)
\(y = \dfrac{6}{x^{8}} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{48}{x^{9}} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=e^{6x+7}\)
Find \( \dfrac{dy}{dx}\)
\(6e^{6x+7}\)
\(y=x^4 \ln x\)
Find \( \dfrac{dy}{dx}\)
\(4x^3lnx+x^3\)
\(y=\frac{x+4}{x-3}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{7}{(x-3)^2}\)
Find the equation of the tangent to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 17x - 2\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =6x^2 - 14x + 8\)
Find \( \int y \quad dx\)
\(2x^3 - 7x^2 + 8x+c\)
A game is played 19 times and the probability of winning is 0.4. Calculate the probability of winning exactly 7 times. 0.180
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:
\(u_{9} = 58\)
\(u_{19} = 138\)
Find the sum of the first 21 terms.1554
Find the equations of the asymptotes of:
\(y=3\left(\dfrac{2x+3}{7-x}\right)\)
\(x=7,y=-6\)
In the triangle ABC,
BĈA = 59.0°.
BC = 7.6cm.
AB̂C = 44.69°.
Find CA to 1 dp.
5.5cm
Evaluate:
$$\sum_{n=1}^{5} n^2 - 9n$$
-80
\(f(x)=-5x^2-6x+8\)
What is the value of the discriminant and what does it indicate?
196, Two distinct roots
\(f(x)=x^2-8x-6\)
By completing the square find the coordinates of the vertex.
(4, -22)
Solve for x:
\(\log_2(x) = 4\)
16
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-4, 15) and (2, -3)
\(y=-3x+3\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-5}{6}}\)
\(6x²+5\)
\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)
\(16x^2+48x+39\)
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
\(y=x(5-x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\cos{720°}$$\(1\)
Solve:
\( 5a+2b+c=18 \\ 3a+4b+2c= 22 \\ a+5b+c=16\)
a = 2, b = 2, c = 4
Find the area of a sector with radius 3.9cm and angle \( \frac{\pi}{4}\)
🍕
5.97cm2
How many ways can eleven children sit in a row without the youngest being in the middle?
36288000
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
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:
\(\int^{4}_{0} (x-8)^2 \; dx\)
\(149.333333333333\)
Box A contains 3 red and 6 blue cubes, and box B contains 9 red and 11 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?
\(\dfrac{27}{47}\)
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
$$ (1+i)^{4} $$
\(-4\)
Evaluate:
\(\int x\tan^{-1}x\; dx\)
\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the y-axis for \(0 \le y \le 4\)
\(8\pi\) cubic units
What is the formula for compound interest?
\( FV = PV(1 + \frac{r}{100k})^{kn} \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sec(x)\)
\(1 + \frac{x^2}{2} + \frac{5x^4}{24} + \frac{61x^6}{720}\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
A committee of 4 is randomly selected from 8 men and 11 women. Determine the likelihood that it consists of all men.
35/1938 or 1.81%
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
Simplify:
$$\sqrt{18}$$
\(3\sqrt{2}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{5}{3 - \sqrt{2}}$$\(\frac{15 + 5\sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
15, 19, 19, 21, 21, 25
3
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