Find the first three terms in the expansion of:
\((4a - 3b)^8\)
\(=65536a^8 - 393216a^7b \\+1032192a^6b^2 ...\)
If £140 is invested with an interest rate of 6% compounded monthly, find the value of the investment after 7 years. £212.85
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,5),(9,10),(-1,10)\)
(4,15)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(4x^2+3x-1\)
\((x+1)(4x-1)\)
Draw a rough sketch of the graph of:
\(y=-2x+2\)
Gradient -2
y intercept 2
What is the value of:
\(9^{\frac{1}{2}}\)
\(= 3\)
Find angle BCA if AB = 5.1m and BC = 6.9m. 47.7o
Find AC if angle ABC = 54o and AB = 3.8m. 5.23m
Describe the red region.
\(y = 5x^3 - 3x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 6x + 8\)
\(y = \dfrac{4}{x^7} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{28}{x^8} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=x^4 \ln x\)
Find \( \dfrac{dy}{dx}\)
\(4x^3lnx+x^3\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
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:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =12x^2 - 18x + 4\)
Find \( \int y \quad dx\)
\(4x^3 - 9x^2 + 4x+c\)
A game is played 11 times and the probability of winning is 0.2. Calculate the probability of winning exactly 7 times. 0.00173
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:
\(u_{9} = -89\)
\(u_{11} = -109\)
Find the sum of the first 17 terms.-1513
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
BC = 8.3cm.
CA = 7.7cm.
BĈA = 37.7°
Find AB to 1 dp.
5.2cm
Evaluate:
$$\sum_{n=3}^{6} n^2 - 3n$$
32
\(f(x)=-9x^2-9x+7\)
What is the value of the discriminent and what does it indicate?
333, Two distinct roots
\(f(x)=x^2+3x-8\)
By completing the square find the coordinates of the vertex.
(-1.5, -10.25)
Simplify:
\(\log_2(4\sqrt{16})\)
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:
(-9, -23) and (8, 11)
\(y=2x-5\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x+13}\)
\(x²-13\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
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
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\tan{5\pi}$$\(0\)
Solve:
\( g-7h-7i=-70 \\ 2g-2h+i= 10\\ 5g+3h+i = 56\)
g = 7, h = 5, i = 6
Find the area of a sector with radius 3.3cm and angle \( \frac{\pi}{4}\)
🍕
4.28cm2
In how many ways can 8 different books be arranged on a shelf if 4 of them must be together?
2880
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
Box A contains 5 red and 8 blue cubes, and box B contains 11 red and 12 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?
\(\dfrac{143}{258}\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ (2-i)^{-2} $$
\(\frac{3}{25}+\frac{4}{25}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
What is the formula for compound interest?
\( A = P(1 + \frac{r}{n})^{nt} \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
Prove by mathematical induction that the sum of the first \( n \) even numbers is \( n(n + 1) \)
Show true for n=1, assume true for n=k, prove for n=k+1
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