Find the first three terms in the expansion of:
\((3a - 2b)^9\)
\(=19683a^9 - 118098a^8b \\+314928a^7b^2 ...\)
If £180 is invested with an interest rate of 2% compounded monthly, find the value of the investment after 6 years. £202.93
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,3),(8,9),(-1,6)\)
(2,12)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-x-12\)
\((x+3)(x-4)\)
Factorise:
\(8x^2+10x-3\)
\((2x+3)(4x-1)\)
Draw a rough sketch of the graph of:
\(2y=x+4\)
Gradient 0.5
y intercept 2
What is the value of:
\(27^{\frac{1}{3}}\)
\(= 3\)
Find angle BCA if AC = 5.1m and BC = 7.1m. 44.1o
Find BC if angle BCA = 44o and AC = 6m. 8.34m
Describe the red region.
\(y = 5x^3 - 7x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 14x + 3\)
\(y = \dfrac{3}{x^6} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{18}{x^7} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=(7x^2-5)^5\)
Find \( \dfrac{dy}{dx}\)
\(70x(7x^2-5)^4\)
\(y=x^8 \sin x\)
Find \( \dfrac{dy}{dx}\)
\(8x^7sinx+x^8cosx\)
\(y=\frac{x}{\sin x}\)
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 \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =9x^2 - 16x + 3\)
Find \( \int y \quad dx\)
\(3x^3 - 8x^2 + 3x+c\)
A game is played 18 times and the probability of winning is 0.8. Calculate the probability of winning exactly 2 times. 0.000000000642
Make up a maths question using this:
\(\log_ax=\dfrac{\log_bx}{\log_ba}\)
Logarithm changing base formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -12\)
\(u_{11} = -18\)
Find the sum of the first 28 terms.-602
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-{1}{5}\)
In the triangle ABC,
BC = 6.3cm.
CA = 10.1cm.
BĈA = 47.8°
Find AB to 1 dp.
7.5cm
Evaluate:
$$\sum_{n=3}^{6} 2^n$$
120
\(f(x)=3x^2+6x+6\)
What is the value of the discriminant and what does it indicate?
-36, No real roots
\(f(x)=x^2+8x-5\)
By completing the square find the coordinates of the vertex.
(-4, -21)
Solve for x:
\(\log_3x = 2\)
9
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-2, 6) and (4, -6)
\(y=-2x+2\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-9}}{8}\)
\(64x²+9\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
Draw a rough sketch of
\(x=\pm \sqrt{y}\)
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:
\( 5a+2b+c=31 \\ 3a+4b+2c= 41 \\ a+5b+c=34\)
a = 3, b = 5, c = 6
Find the perimeter of a sector with radius 5.2cm and angle \( \frac{\pi}{4}\)
🍕
14.5cm
A safe has a eight-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
907200
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{120}_{60} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
Tin A contains 5 red balls and 8 green balls. Tin B contains 9 red balls and 10 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.
\(\frac{234}{329}\)
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
$$ \dfrac{i(2-i)}{3-2i}$$
\(-\frac{1}{13}+\frac{8}{13}i\)
Evaluate:
\(\int x\tan^{-1}x\; dx\)
\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
How do you use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sec(x)\)
\(1 + \frac{x^2}{2} + \frac{5x^4}{24} + \frac{61x^6}{720}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
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
Simplify
\(4\sqrt{7} - \sqrt{63}\)
\(\sqrt{7}\)
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