Find the first three terms in the expansion of:
\((3a - 4b)^8\)
\(=6561a^8 - 69984a^7b \\+326592a^6b^2 ...\)
If £120 is invested with an interest rate of 3% compounded quarterly, find the value of the investment after 6 years. £143.57
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,3),(6,8),(-4,8)\)
(1,13)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2+2x-8\)
\((x+4)(x-2)\)
Factorise:
\(8x^2-10x-3\)
\((4x+1)(2x-3)\)
Draw a rough sketch of the graph of:
\(y=x\)
Gradient 1
y intercept 0
What is the value of:
\(1^{-3}\)
\(= 1\)
Find angle BCA if AC = 4.6m and BC = 5.6m. 34.8o
Find AB if angle ABC = 65o and BC = 5.1m. 2.16m
Describe the red region.
\(y = 3x^3 - 2x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 4x + 7\)
\(y = \dfrac{2}{x^3} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{6}{x^4} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=e^{5x+6}\)
Find \( \dfrac{dy}{dx}\)
\(5e^{5x+6}\)
\(y=6x^2e^x\)
Find \( \dfrac{dy}{dx}\)
\(12xe^x+6x^2e^x\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(y = 0\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =6x^2 - 10x + 2\)
Find \( \int y \quad dx\)
\(2x^3 - 5x^2 + 2x+c\)
A game is played 12 times and the probability of winning is 0.7. Calculate the probability of winning exactly 8 times. 0.231
Make up a maths question using this:
\( A = 4\pi r^2 \)
Surface area of a sphere
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 46\)
\(u_{16} = 95\)
Find the sum of the first 29 terms.2552
Find the equations of the asymptotes of:
\(y=3\left(\dfrac{2x+3}{7-x}\right)\)
\(x=7,y=-6\)
In the triangle ABC,
BĈA = 48.8°.
BC = 8.4cm.
AB̂C = 49.9°.
Find CA to 1 dp.
6.5cm
Evaluate:
$$\sum_{n=2}^{7} n^2 - 3n$$
58
\(f(x)=-9x^2+5x-4\)
What is the value of the discriminant and what does it indicate?
-119, No real roots
\(f(x)=x^2+7x-7\)
By completing the square find the coordinates of the vertex.
(-3.5, -19.25)
Simplify:
\(\log_2(4\sqrt{16})\)
4
Find the integral:
\(\int \dfrac{\ln(x)}{x} \;dx\)
\(\dfrac{\ln(x)^2}{2}+c\)
Find the equation of the straight line that passes through:
(-2, -4) and (0, 2)
\(y=3x+2\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-8}\)
\(x²+8\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
Write in standard form:
\((a \times 10^3) \div (b\times 10^5)\)
where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)
\(\frac{a}{10b}\times10^{-1}\)
Draw a rough sketch of
\(y=x^2+7x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\(2x+y-3z= 14 \\ 3x+y+z= 25 \\ x-y+2z = 6\)
x = 7, y = 3, z = 1
Find the perimeter of a sector with radius 4.2cm and angle \( \frac{\pi}{6}\)
🍕
10.6cm
In how many ways can 11 different books be arranged on a shelf if 2 of them must be together?
7257600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
The 4th term of a geometric sequence is 54 and the sum of the first 4 terms is 80. Find the first term.
2
Find the first 4 terms in the expansion of:
\((1+2x)^{\frac12}\)
\(1+x-\frac{x^2}{2}+\frac{x^3}{2}\)
Evaluate:
\(\int^{6}_{1} (x-8)^2 \; dx\)
\(111.666666666667\)
Box A contains 3 red and 4 blue cubes, and box B contains 5 red and 7 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?
\(\dfrac{35}{71}\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 6 \\ 9 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 7 \\ -9 \\ 2 \end{pmatrix} \; \text{and} \; \begin{pmatrix} 1 \\ -18 \\ 2 \end{pmatrix} \)
59.5 square units
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^2\) is rotated about the x-axis for \(-2 \le x \le 2\)
\(\frac{64\pi}{5}\) cubic units
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
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 the sum of the squares of the first \( n \) natural numbers is \( \frac{n(n + 1)(2n + 1)}{6} \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{75}$$
\(5\sqrt{3}\)
Simplify:
$$\dfrac{6}{\sqrt{11}}$$\(\frac{6\sqrt{11}}{11}\)
Simplify
\((1 + \sqrt{2})(2 + \sqrt{2})\)
\(4 + 3\sqrt{2}\)
Simplify:
$$\dfrac{5}{3 - \sqrt{2}}$$\(\frac{15 + 5\sqrt{2}}{7}\)
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