Find the first three terms in the expansion of:
\((5a - 3b)^7\)
\(=78125a^7 - 328125a^6b \\+590625a^5b^2 ...\)
If £120 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 4 years. £135.28
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,1),(4,4),(-2,4)\)
(1,7)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(12x^2-5x-3\)
\((3x+1)(4x-3)\)
Draw a rough sketch of the graph of:
\(y=-x+2\)
Gradient -1
y intercept 2
What is the value of:
\(3^{1}\)
\(= 3\)
Find angle ABC if AC = 4.4m and BC = 6.3m. 44.3o
Find BC if angle BCA = 56o and AB = 4.7m. 5.67m
Describe the red region.
\(y = 2x^3 - 9x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 18x + 2\)
\(y = \dfrac{5}{x^9} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{45}{x^10} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=(2x^6+4)^8\)
Find \( \dfrac{dy}{dx}\)
\(96x^5(2x^6+4)^7\)
\(y=x(3x+5)^3\)
Find \( \dfrac{dy}{dx}\)
\((3x+5)^3+9x(3x+5)^2\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =24x^2 - 14x + 4\)
Find \( \int y \quad dx\)
\(8x^3 - 7x^2 + 4x+c\)
A game is played 17 times and the probability of winning is 0.1. Calculate the probability of winning exactly 10 times. 0.000000930
What's this?
\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)
Trigonometric identity
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 59\)
\(u_{19} = 129\)
Find the sum of the first 23 terms.1840
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
BC = 9.3cm.
CA = 12.9cm.
BĈA = 26.6°
Find AB to 1 dp.
6.2cm
Evaluate:
$$\sum_{n=1}^{8} 2n+6$$
120
\(f(x)=7x^2-5x+4\)
What is the value of the discriminent and what does it indicate?
-87, No real roots
\(f(x)=x^2+9x-1\)
By completing the square find the coordinates of the vertex.
(-4.5, -21.25)
Simplify \(\log_{10}10^5\)
5
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-7, -12) and (0, 2)
\(y=2x+2\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x+13}\)
\(x²-13\)
\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)
\(16x^2+48x+39\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
Draw a rough sketch of
\(y=x^2-8\)
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
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( 5a+2b+c=25 \\ 3a+4b+2c= 29 \\ a+5b+c=19\)
x=3, y=2, z=6
Find the perimeter of a sector with radius 4.6cm and angle \( \frac{\pi}{6}\)
🍕
11.6cm
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:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
The sum of the first 7 terms of a geometric sequence is 58593 and the sum of the first 8 terms is 292968. What is the first term?
3
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{4}_{0} e^x dx\)
\(e^{4}- 1 \approx 53.6\)
What is the probability that it was machine B that broke down if at least one of the machines broke down today, given machine A has a 8% chance and machine B has a 13% chance of breaking down on any given day?
\(0.651\)
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