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 2% compounded monthly, find the value of the investment after 6 years. £157.83
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,2),(10,6),(1,7)\)
(6,11)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(4x^2-1\)
\((2x+1)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle BCA if AB = 4.6m and BC = 6m. 50.1o
Find AC if angle BCA = 58o and AB = 3.3m. 2.06m
Describe the red region.
\(y = 7x^3 - 3x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 6x + 8\)
\(y = \dfrac{5}{x^5} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{25}{x^6} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\sqrt{5x^2-2x}\)
Find \( \dfrac{dy}{dx}\)
\((5x^1-1)(5x^2-2x)^{-\frac{1}{2}}\)
\(y=x \tan x\)
Find \( \dfrac{dy}{dx}\)
\(tanx+\frac{x}{cos^2x}\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =21x^2 - 10x + 7\)
Find \( \int y \quad dx\)
\(7x^3 - 5x^2 + 7x+c\)
A game is played 12 times and the probability of winning is 0.9. Calculate the probability of winning exactly 5 times. 0.0000468
Make up a maths question using this:
\(z=\dfrac{x-\mu}{\sigma}\)
Standardised Normal Variable
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -10\)
\(u_{19} = -21\)
Find the sum of the first 36 terms.-738
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,
BĈA = 46.3°.
BC = 8.7cm.
AB̂C = 46.33°.
Find CA to 1 dp.
6.3cm
Evaluate:
$$\sum_{n=3}^{7} n^2 - 3n$$
60
\(f(x)=-4x^2-2x+9\)
What is the value of the discriminent and what does it indicate?
148, Two distinct roots
\(f(x)=x^2+7x+1\)
By completing the square find the coordinates of the vertex.
(-3.5, -11.25)
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:
(-4, -16) and (9, 10)
\(y=2x-8\)
Find the inverse of the function \(f\):
\(f(x)=\frac{2+ x}{5}\)
\(5x-2\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\((a \times 10^2) \div (b\times 10^4)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{-2}\)
Draw a rough sketch of
\(y+x=2\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$\(0\)
Without a calculator find the exact value of
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\( j+k+l= 14 \\ 2j-3k+9l= 27\\ -j+k-3l=-12\)
j = 9, k = 3, l = 2
Find the perimeter of a sector with radius 6.7cm and angle \( \frac{\pi}{4}\)
🍕
18.7cm
In how many ways can 7 different books be arranged on a shelf if 2 of them must be together?
1440
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The fourth term of a geometric sequence is \(-16\) and the sum to infinity is \(32\). What is the common ratio?
-0.669
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{3}_{1} (x-8)^2 \; dx\)
\(72.6666666666667\)
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 9% chance and machine B has a 14% chance of breaking down on any given day?
\(0.644\)
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
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt{x}\) is rotated about the y-axis for \(1 \le y \le 4\)
\(\frac{1023\pi}{5}\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \frac{1}{1-x}\)
\(1 + x + x^2 + x^3\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
A committee of 5 is chosen from 15 people by random selection. Two Londoners were amongst the group from which the selection was made. Find the probability that both Londoners are chosen for the committee.
2/21 or 9.52%
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
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