Find the first three terms in the expansion of:
\((2a - 3b)^7\)
\(=128a^7 - 1344a^6b \\+6048a^5b^2 ...\)
If £160 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 4 years. £173.29
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,1),(10,5),(0,7)\)
(6,11)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(16x^2-8x-3\)
\((4x+1)(4x-3)\)
Draw a rough sketch of the graph of:
\(y=-x+1\)
Gradient -1
y intercept 1
What is the value of:
\(2^{0}\)
\(= 1\)
Find angle ABC if AC = 5.2m and BC = 6.4m. 54.3o
Find AC if angle BCA = 25o and AB = 5.2m. 11.2m
Describe the red region.
\(y = 4x^3 - 4x^2 + 5x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 8x + 5\)
\(y = \dfrac{6}{x^9} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{54}{x^10} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=\sqrt{2x^4-2x}\)
Find \( \dfrac{dy}{dx}\)
\((4x^3-1)(2x^4-2x)^{-\frac{1}{2}}\)
\(y=(3x+6)(8x-5)\)
Find \( \dfrac{dy}{dx}\)
\(48x+33\)
\(y=\frac{x+5}{x-5}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{10}{(x-5)^2}\)
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:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(x = -3\)
\(y =24x^2 - 10x + 6\)
Find \( \int y \quad dx\)
\(8x^3 - 5x^2 + 6x+c\)
A game is played 13 times and the probability of winning is 0.4. Calculate the probability of winning exactly 5 times. 0.221
Make up a maths question using this:
\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)
Trigonometric identity
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -60\)
\(u_{17} = -132\)
Find the sum of the first 35 terms.-4900
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 8.8cm.
BC = 6.7cm.
CA = 10.6cm.
Find angle CÂB.
39.0°
Evaluate:
$$\sum_{n=2}^{8} 5n+0$$
175
\(f(x)=3x^2+8x-3\)
What is the value of the discriminant and what does it indicate?
100, Two distinct roots
\(f(x)=x^2-9x-7\)
By completing the square find the coordinates of the vertex.
(4.5, -27.25)
Evaluate \(\log_5(625) \)
4
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:
(-3, -9) and (5, 7)
\(y=2x-3\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+8}{9}\)
\(9x-8\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
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
\(y=x^2-8\)
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
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\( g-7h-7i=-63 \\ 2g-2h+i= 15\\ 5g+3h+i = 51\)
g = 7, h = 3, i = 7
Find the area of a sector with radius 8.4cm and angle \( \frac{\pi}{4}\)
🍕
27.7cm2
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
1814400
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
The 6th term of a geometric sequence is 3072 and the sum of the first 6 terms is 4095. Find the first term.
3
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 10% chance and machine B has a 12% chance of breaking down on any given day?
\(0.577\)
Find the point of intersection of these planes:
\(\Pi_1: \quad 2x + y - 3z = -5\)
\(\Pi_2: \quad x - 3y + 2z = 1\)
\(\Pi_3: \quad 3x - 2y + z = 2\)
\( (1,2,3) \)
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) 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
\(f(x) = \sqrt{x+1}\)
\(1 + \frac{x}{2} - \frac{x^2}{8} + \frac{x^3}{16}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
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:
$$\sqrt{45}$$
\(3\sqrt{5}\)
Simplify:
$$\dfrac{8}{3\sqrt{7}}$$\(\frac{8\sqrt{7}}{21}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{5}{2 - \sqrt{3}}$$\(\frac{10 + 5\sqrt{3}}{1} = 10 + 5\sqrt{3}\)
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