Find the first three terms in the expansion of:
\((2a - 3b)^4\)
\(=16a^4 - 96a^3b \\+216a^2b^2 ...\)
If £240 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 9 years. £343.79
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,4),(7,10),(-5,10)\)
(1,16)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(5x^2+11x-12\)
\((x+3)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=2x+1\)
Gradient 2
y intercept 1
What is the value of:
\(3^{0}\)
\(= 1\)
Find angle BCA if AB = 6m and BC = 7.3m. 55.3o
Find AB if angle ABC = 25o and BC = 4.3m. 3.90m
Describe the red region.
\(y = 7x^3 - 4x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 8x + 9\)
\(y = \dfrac{7}{x^{9}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{63}{x^{10}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\sqrt{4x^2-2x}\)
Find \( \dfrac{dy}{dx}\)
\((4x^1-1)(4x^2-2x)^{-\frac{1}{2}}\)
\(y=x(2x+5)^3\)
Find \( \dfrac{dy}{dx}\)
\((2x+5)^3+6x(2x+5)^2\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 17x - 2\)
Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =15x^2 - 12x + 4\)
Find \( \int y \quad dx\)
\(5x^3 - 6x^2 + 4x+c\)
A game is played 13 times and the probability of winning is 0.3. Calculate the probability of winning exactly 10 times. 0.000579
Make up a maths question using this:
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 88\)
\(u_{18} = 196\)
Find the sum of the first 28 terms.4312
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
AB = 5.7cm.
BC = 7.5cm.
CA = 10.9cm.
Find angle CÂB.
40.1°
Evaluate:
$$\sum_{n=1}^{7} n^2 - 9n$$
-112
\(f(x)=8x^2+7x+8\)
What is the value of the discriminant and what does it indicate?
-207, No real roots
\(f(x)=x^2+4x-4\)
By completing the square find the coordinates of the vertex.
(-2, -8)
Solve for x:
\(\log_3x = 2\)
9
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-5, 0) and (0, -5)
\(y=-x-5\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-9}\)
\(x²+9\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
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
$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$\(0\)
Without a calculator find the exact value of
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\(2d+3e-4f = 10 \\ d-e-f= -1\\ 9d+2e-2f=63\)
d = 7, e = 4, f = 4
Find the area of a sector with radius 3.3cm and angle \( \frac{\pi}{4}\)
🍕
4.28cm2
How many ways can nine children sit in a row without the youngest being in the middle?
322560
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{7}_{0} e^x dx\)
\(e^{7}- 1 \approx 1100\)
29 Scouts went hiking. 11 got lost, 15 got blisters, and 6 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{1}{2}\)
Find the parametric equation of the line:
\( \dfrac{x-9}{4} = \dfrac{6-y}{9} = \dfrac{z}{7} \)
\( x=9+4\lambda \quad y = 6 -9\lambda \quad z=7 \lambda \)
Simplify
$$ (2-i)^{-2} $$
\(\frac{3}{25}+\frac{4}{25}i\)
Evaluate:
\(\int \ln{x}\; dx\)
\(x\ln|x|-x+c\)
Simplify:
$$\sin{x}\cot{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\ln{x}\) is rotated about the y-axis for \(0 \le y \le 1\)
\(\approx 10.0\) cubic units
What is the binomial theorem?
Clue: Expand \( (a + b)^n \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sin(x)\)
\(x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040}\)
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 first \( n \) odd numbers is \( n^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{48}$$
\(4\sqrt{3}\)
Simplify:
$$\dfrac{8}{3\sqrt{7}}$$\(\frac{8\sqrt{7}}{21}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$\(\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}\)
Calculate the standard deviation of the following numbers:
7, 9, 10, 11, 13
2
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