Find the first three terms in the expansion of:
\((4a - 2b)^8\)
\(=65536a^8 - 262144a^7b \\+458752a^6b^2 ...\)
If £240 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 4 years. £281.42
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,1),(8,5),(0,5)\)
(4,9)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2+2x-8\)
\((x+4)(x-2)\)
Factorise:
\(3x^2+8x-16\)
\((x+4)(3x-4)\)
Draw a rough sketch of the graph of:
\(2y=x+4\)
Gradient 0.5
y intercept 2
What is the value of:
\(2^{1}\)
\(= 2\)
Find angle BCA if AB = 4.3m and AC = 6m. 35.6o
Find AC if angle ABC = 56o and AB = 3.6m. 5.34m
Describe the red region.
\(y = 4x^3 - 4x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 8x + 2\)
\(y = \dfrac{9}{x^6} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{54}{x^7} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=(6x^3+7)^9\)
Find \( \dfrac{dy}{dx}\)
\(162x^2(6x^3+7)^8\)
\(y=e^{2x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(2e^{2x}cosx-e^{2x}sinx\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =27x^2 - 8x + 4\)
Find \( \int y \quad dx\)
\(9x^3 - 4x^2 + 4x+c\)
A game is played 17 times and the probability of winning is 0.5. Calculate the probability of winning exactly 4 times. 0.0182
Make up a maths question using this:
\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)
Trigonometric identity
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = 68\)
\(u_{12} = 82\)
Find the sum of the first 15 terms.810
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,
BC = 9.8cm.
CA = 13.9cm.
BĈA = 39.6°
Find AB to 1 dp.
8.9cm
Evaluate:
$$\sum_{n=2}^{8} 4n+2$$
154
\(f(x)=-2x^2-8x+2\)
What is the value of the discriminant and what does it indicate?
80, Two distinct roots
\(f(x)=x^2+7x-6\)
By completing the square find the coordinates of the vertex.
(-3.5, -18.25)
Solve for x:
\(\log_3x = 2\)
9
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-7, -4) and (5, 8)
\(y=x+3\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-6\)
\((x+6)²\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
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
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\tan{5\pi}$$\(0\)
Solve:
\(2d+3e-4f = 8 \\ d-e-f= -6\\ 9d+2e-2f=47\)
d = 5, e = 6, f = 5
Find the perimeter of a sector with radius 3.4cm and angle \( \frac{\pi}{6}\)
🍕
8.58cm
A safe has a five-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
15120
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\((1-4x)^{-3}\)
\(1+12x+96x^2+640x^3\)
Evaluate:
\(\int^{4}_{1} (x-8)^2 \; dx\)
\(93\)
Tin A contains 5 red balls and 6 green balls. Tin B contains 7 red balls and 8 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.
\(\frac{154}{229}\)
Find the vector product:
\( \begin{pmatrix} 8 \\ 5 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 2 \\ -4 \\ 7 \end{pmatrix} \)
\( \begin{pmatrix} 35 \\ -56 \\ -42 \end{pmatrix} \)
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\cosec{x}\tan{x}$$\(\sec{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x\) is rotated about the x-axis for \(0 \le x \le 1\)
\(\frac{\pi}{3}\) 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
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
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 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:
$$\sqrt{50}$$
\(5\sqrt{2}\)
Simplify:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)
Simplify
\((9 + 2\sqrt{2})(9 - 2\sqrt{2})\)
\(73\)
Simplify:
$$\dfrac{8}{3 + \sqrt{6}}$$\(\frac{24 - 8\sqrt{6}}{3}\)
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