Find the first three terms in the expansion of:
\((2a - 3b)^8\)
\(=256a^8 - 3072a^7b \\+16128a^6b^2 ...\)
If £200 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 6 years. £269.47
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,2),(5,6),(-3,6)\)
(1,10)
\( X \sim N(43, 7^2)\)
Find
\( P(32\lt X \lt45) \)
\(0.554\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Draw a rough sketch of the graph of:
\(y=-2x\)
Gradient -2
y intercept 0
What is the value of:
\(4^{-2}\)
\(= \frac{1}{16}\)
Find angle ABC if AB = 5.5m and BC = 6.6m. 33.6o
Find BC if angle BCA = 55o and AB = 4m. 4.88m
Describe the red region.
\(y = 7x^3 - 9x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 18x + 3\)
\(y = \dfrac{9}{x^{2}} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{18}{x^{3}} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=\frac{1}{(2x+3)^5}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{10}{(2x+3)^6}\)
\(y=x^5 \sin x\)
Find \( \dfrac{dy}{dx}\)
\(5x^4sinx+x^5cosx\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 6x + 3\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =15x^2 - 8x + 5\)
Find \( \int y \quad dx\)
\(5x^3 - 4x^2 + 5x+c\)
A game is played 14 times and the probability of winning is 0.2. Calculate the probability of winning exactly 11 times. 0.00000382
Make up a maths question using this:
\(z=\dfrac{x-\mu}{\sigma}\)
Standardised Normal Variable
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -65\)
\(u_{11} = -89\)
Find the sum of the first 39 terms.-6279
Find the equations of the asymptotes of:
\(y=12-\dfrac{4x+3}{7-2x}\)
\(x=\frac{7}{2},y=14\)
In the triangle ABC,
BC = 9.9cm.
CA = 10.6cm.
BĈA = 38.0°
Find AB to 1 dp.
6.7cm
Evaluate:
$$\sum_{n=3}^{5} 2^n$$
56
\(f(x)=-9x^2+3x+6\)
What is the value of the discriminant and what does it indicate?
225, Two distinct roots
\(f(x)=x^2-3x-4\)
By completing the square find the coordinates of the vertex.
(1.5, -6.25)
What is the value of \(\ln{e^3}\) ?
3
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, 3) and (4, 11)
\(y=x+7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-19}{13}\)
\((13x+19)²\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=\dfrac{5}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\tan{5\pi}$$\(0\)
Solve:
\( g-7h-7i=-78 \\ 2g-2h+i= 0\\ 5g+3h+i = 58\)
g = 6, h = 8, i = 4
Find the area of a sector with radius 3.9cm and angle \( \frac{2\pi}{3}\)
🍕
15.9cm2
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
201600
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt[3]{1+x}}\)
\(1 - \frac{x}{3} + \frac{2x^2}{9} - \frac{14x^3}{81}\)
Evaluate:
\(\int^{3}_{0} e^x dx\)
\(e^{3}- 1 \approx 19.1\)
Box A contains 5 red and 7 blue cubes, and box B contains 10 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?
\(\dfrac{8}{15}\)
Find the angle between the plane and the line:
\(\Pi: \quad 4x+4y-2z=7\)
\(L: \quad x+1= \dfrac{4-y}{2} = 3-z \)
\( \approx 7.82^o \)
Simplify
$$ (1+i)^{4} $$
\(-4\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
Find the volume of revolution when \(y=x(4-x)\) is rotated about the x-axis for \(0 \le x \le 4\)
\(\frac{512\pi}{15}\) 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
\(f(x) = \frac{1}{x^2 + 1}\)
\(1 - x^2 + x^4 - x^6\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
A committee of 5 is chosen from 15 people by random selection. Two Londoners were amongst the group from which the selection was made. Find the probability that both Londoners are chosen for the committee.
2/21 or 9.52%
Prove by mathematical induction that \( 11^n - 6 \) is divisible by 5 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{12}$$
\(2\sqrt{3}\)
Simplify:
$$\dfrac{5}{2\sqrt{3}}$$\(\frac{5\sqrt{3}}{6}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$\(\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}\)
Calculate the standard deviation of the following numbers:
43, 45, 49, 51, 55, 57
5
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