Find the first three terms in the expansion of:
\((3a - 4b)^4\)
\(=81a^4 - 432a^3b \\+864a^2b^2 ...\)
If £160 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 9 years. £273.46
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,5),(6,9),(-2,9)\)
(2,13)
\( X \sim N(100, 7^2)\)
Find
\( P(93\lt X \lt107) \)
\(0.683\)
Factorise:
\(x^2+3x-4\)
\((x+4)(x-1)\)
Factorise:
\(3x^2+2x-8\)
\((x+2)(3x-4)\)
Draw a rough sketch of the graph of:
\(2y=x\)
Gradient 0.5
y intercept 0
What is the value of:
\(4^{0}\)
\(= 1\)
Find angle ABC if AC = 3.2m and BC = 4.3m. 48.1o
Find BC if angle BCA = 61o and AB = 4.4m. 5.03m
Describe the red region.
\(y = 5x^3 - 6x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 12x + 6\)
\(y = \dfrac{3}{x^{4}} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{12}{x^{5}} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=\frac{1}{(2x+3)^6}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{12}{(2x+3)^7}\)
\(y=\sin x \sqrt{ x^2 + 3}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+3}+\frac{xsinx}{\sqrt{x^2+3}}\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 6x + 3\)
Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =27x^2 - 18x + 7\)
Find \( \int y \quad dx\)
\(9x^3 - 9x^2 + 7x+c\)
A game is played 13 times and the probability of winning is 0.5. Calculate the probability of winning exactly 11 times. 0.00952
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:
\(u_{9} = 96\)
\(u_{20} = 228\)
Find the sum of the first 43 terms.10836
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 = 9.1cm.
CA = 13.4cm.
BĈA = 47.6°
Find AB to 1 dp.
9.9cm
Evaluate:
$$\sum_{n=1}^{8} n^2 - 5n$$
24
\(f(x)=-9x^2+4x+9\)
What is the value of the discriminant and what does it indicate?
340, Two distinct roots
\(f(x)=x^2+3x-4\)
By completing the square find the coordinates of the vertex.
(-1.5, -6.25)
What is the value of \(\ln{e^3}\) ?
3
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, -8) and (4, 10)
\(y=3x-2\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-3}\)
\(x²+3\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(y=3-\dfrac{10}{x}\)
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
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( j+k+l= 13 \\ 2j-3k+9l= 37\\ -j+k-3l=-15\)
j = 8, k = 2, l = 3
Find the perimeter of a sector with radius 5.9cm and angle \( \frac{\pi}{3}\)
🍕
18.0cm
Ansh is with six people in a queue. How many ways can they line up without Ansh being at the back?
4320
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{7}_{2} x^2-2x+7 \; dx\)
\(102\)
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 4% chance and machine B has a 9% chance of breaking down on any given day?
\(0.712\)
Find the point of intersection of \(L_1\) and \(L_2\) if:
\(L_1: \quad \dfrac{x+4}{3} = y-2 = \dfrac{z+1}{2} \)
\(L_2: \quad x = \dfrac{y-5}{2} = \dfrac{-z-1}{2} \)
\( (-1,3,1) \)
Simplify
$$ (1+i)^{4} $$
\(-4\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\dfrac{\sin^2{x}-1}{\cos{x}}$$\(-\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
Describe the graph of an exponential function.
Clue: grow or decay rapidly, horizontal asymptote
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
5 alphabet blocks A, E, P, R and S are placed at random in a row. What is the likelihood that they spell out either SPEAR or PARSE?
1/60 or 1.67%
Prove by mathematical induction that \( 2^n > n^2 \) for all integers \( n \) greater
than four
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{12}$$
\(2\sqrt{3}\)
Simplify:
$$\dfrac{4}{5\sqrt{3}}$$\(\frac{4\sqrt{3}}{15}\)
Simplify
\((1 + \sqrt{2})(2 + \sqrt{2})\)
\(4 + 3\sqrt{2}\)
Simplify:
$$\dfrac{5}{3 - \sqrt{2}}$$\(\frac{15 + 5\sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
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