Find the first three terms in the expansion of:
\((2a - 3b)^8\)
\(=256a^8 - 3072a^7b \\+16128a^6b^2 ...\)
If £140 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 5 years. £179.67
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,2),(5,7),(-4,6)\)
(0,11)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2+3x-4\)
\((x+4)(x-1)\)
Factorise:
\(6x^2+x-2\)
\((3x+2)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=x-1\)
Gradient 1
y intercept -1
What is the value of:
\(5^{-3}\)
\(= \frac{1}{125}\)
Find angle ABC if AC = 4.7m and BC = 6.6m. 45.4o
Find AC if angle ABC = 22o and BC = 5.2m. 1.95m
Describe the red region.
\(y = 4x^3 - 5x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 10x + 9\)
\(y = \dfrac{9}{x^6} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{54}{x^7} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=(9x^2-3)^6\)
Find \( \dfrac{dy}{dx}\)
\(108x(9x^2-3)^5\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =27x^2 - 14x + 8\)
Find \( \int y \quad dx\)
\(9x^3 - 7x^2 + 8x+c\)
A game is played 17 times and the probability of winning is 0.2. Calculate the probability of winning exactly 6 times. 0.0680
What's this?
\( \int \dfrac{1}{x} = \ln |x| + c\)
Reciprocal Integral formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = -82\)
\(u_{13} = -106\)
Find the sum of the first 23 terms.-2254
Find the equations of the asymptotes of:
\(y=\dfrac{4-7x}{3-14x}\)
\(x=\frac{3}{14},y=\frac{1}{2}\)
In the triangle ABC,
AB = 5.3cm.
BC = 7.9cm.
CÂB = 95.2°.
Find angle BĈA.
41.9°
Evaluate:
$$\sum_{n=0}^{8} 116 - n^2$$
840
\(f(x)=6x^2-5x-9\)
What is the value of the discriminent and what does it indicate?
241, Two distinct roots
\(f(x)=x^2+8x-7\)
By completing the square find the coordinates of the vertex.
(-4, -23)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
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:
(-7, 5) and (4, -17)
\(y=-2x-9\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-7\)
\((x+7)²\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
Write in standard form:
\(a \times 10^2 \times b\times 10^3\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^6\)
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
$$\sin{\frac{\pi}{2}} \div \cos{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\(2d+3e-4f = 23 \\ d-e-f= -3\\ 9d+2e-2f=71\)
d = 7, e = 7, f = 3
Find the perimeter of a sector with radius 3.2cm and angle \( \frac{\pi}{3}\)
🍕
9.75cm
How many ways can five children sit in a row without the youngest being in the middle?
96
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The 6th term of a geometric sequence is 160 and the sum of the first 6 terms is 315. Find the first term.
5
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{5}_{2} x^2-2x+7 \; dx\)
\(6\)
27 Scouts went hiking. 16 got lost, 15 got blisters, and 9 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{6}{11}\)
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
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\cosec{x}\tan{x}$$\(\sec{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
How do you solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.
55/153 or 35.9%
Prove by mathematical induction that the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
Write down a summary of your last Maths lesson focussing on what you learnt.
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