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 2% compounded quarterly, find the value of the investment after 6 years. £135.26
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,2),(8,6),(-2,8)\)
(4,12)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2-2x-3\)
\((x+1)(x-3)\)
Factorise:
\(2x^2-x-6\)
\((2x+3)(x-2)\)
Draw a rough sketch of the graph of:
\(y=-2x-1\)
Gradient -2
y intercept -1
What is the value of:
\(3^{-2}\)
\(= \frac{1}{9}\)
Find angle BCA if AB = 3.7m and BC = 5.4m. 43.3o
Find BC if angle BCA = 22o and AC = 4.2m. 4.53m
Describe the red region.
\(y = 7x^3 - 9x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 18x + 6\)
\(y = \dfrac{9}{x^{5}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{45}{x^{6}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=e^{5x+6}\)
Find \( \dfrac{dy}{dx}\)
\(5e^{5x+6}\)
\(y=x^2 \sin x\)
Find \( \dfrac{dy}{dx}\)
\(2x^1sinx+x^2cosx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =18x^2 - 8x + 9\)
Find \( \int y \quad dx\)
\(6x^3 - 4x^2 + 9x+c\)
A game is played 13 times and the probability of winning is 0.7. Calculate the probability of winning exactly 6 times. 0.0442
Make up a maths question using this:
\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)
The sum of a geometric sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -24\)
\(u_{18} = -74\)
Find the sum of the first 26 terms.-1339
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 7.3cm.
BC = 5.4cm.
CA = 6.8cm.
Find angle CÂB.
44.9°
Evaluate:
$$\sum_{n=3}^{7} 87 - n^2$$
300
\(f(x)=2x^2+6x+3\)
What is the value of the discriminant and what does it indicate?
12, Two distinct roots
\(f(x)=x^2+7x-2\)
By completing the square find the coordinates of the vertex.
(-3.5, -14.25)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int x\sqrt{x^2+3} \;dx\)
\(\frac{1}{3}(x^2+3)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-7, -12) and (3, 8)
\(y=2x+2\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+8}{2}\)
\(2x-8\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
Draw a rough sketch of
\(y=\dfrac{5}{x}\)
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
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\( 5a+2b+c=38 \\ 3a+4b+2c= 34 \\ a+5b+c=20\)
a = 6, b = 2, c = 4
Find the perimeter of a sector with radius 6.9cm and angle \( \frac{2\pi}{3}\)
🍕
28.3cm
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
201600
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\((1-4x)^{-3}\)
\(1+12x+96x^2+640x^3\)
Evaluate:
\(\int^{5}_{0} e^x dx\)
\(e^{5}- 1 \approx 147\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.14. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.538\)
Find the parametric equation of the line:
\( \dfrac{x-7}{8} = \dfrac{8-y}{7} = \dfrac{z}{8} \)
\( x=7+8\lambda \quad y = 8 -7\lambda \quad z=8 \lambda \)
Simplify
$$ \dfrac{i(2-i)}{3-2i}$$
\(-\frac{1}{13}+\frac{8}{13}i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\dfrac{\sin^2{x}-1}{\cos{x}}$$\(-\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
What is the inverse of a function?
Clue: swaps the roles of x and y
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = x^3\)
\(x^3 \text{ only 1 term}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
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 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:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
Calculate the standard deviation of the following numbers:
4, 2, 5, 8, 6
2
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