Find the first three terms in the expansion of:
\((2a - 3b)^7\)
\(=128a^7 - 1344a^6b \\+6048a^5b^2 ...\)
If £140 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 5 years. £170.94
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,4),(7,8),(-1,8)\)
(3,12)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Draw a rough sketch of the graph of:
\(y=x-2\)
Gradient 1
y intercept -2
What is the value of:
\(4^{1}\)
\(= 4\)
Find angle BCA if AB = 5.4m and AC = 7m. 37.6o
Find AC if angle BCA = 62o and AB = 4.3m. 2.29m
Describe the red region.
\(y = 7x^3 - 8x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 16x + 4\)
\(y = \dfrac{7}{x^3} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{21}{x^4} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=(2x^2-3)^6\)
Find \( \dfrac{dy}{dx}\)
\(24x(2x^2-3)^5\)
\(y=\sin x \sqrt{ x^2 + 8}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+8}+\frac{xsinx}{\sqrt{x^2+8}}\)
\(y=\frac{x+2}{x-3}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{5}{(x-3)^2}\)
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:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =27x^2 - 18x + 3\)
Find \( \int y \quad dx\)
\(9x^3 - 9x^2 + 3x+c\)
A game is played 19 times and the probability of winning is 0.4. Calculate the probability of winning exactly 8 times. 0.180
Make up a maths question using this:
\(u_n=u_1+(n-1)d\)
The nth term of an arithmetic sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = 44\)
\(u_{11} = 62\)
Find the sum of the first 15 terms.660
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 7.3cm.
BC = 7.7cm.
CA = 8.1cm.
Find angle CÂB.
59.7°
Evaluate:
$$\sum_{n=0}^{6} 74 - n^2$$
427
\(f(x)=3x^2+6x+3\)
What is the value of the discriminant and what does it indicate?
0, One repeated root
\(f(x)=x^2-5x-6\)
By completing the square find the coordinates of the vertex.
(2.5, -12.25)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-2, 15) and (2, 3)
\(y=-3x+9\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-4}}{9}\)
\(81x²+4\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=x(5-x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)
Without a calculator find the exact value of
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\(2x+y-3z= -9 \\ 3x+y+z= 32 \\ x-y+2z = 15\)
x = 5, y = 8, z = 9
Find the perimeter of a sector with radius 3.6cm and angle \( \frac{\pi}{3}\)
🍕
11.0cm
How many ways can seven children sit in a row without the youngest being in the middle?
4320
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
The 7th term of a geometric sequence is 320 and the sum of the first 7 terms is 635. Find the first term.
5
Find the first 4 terms in the expansion of:
\((1-\dfrac{x}{2})^{\frac13}\)
\(1-\frac{x}{6}-\frac{x^2}{36}-\frac{5x^3}{648}\)
Evaluate:
\(\int^{60}_{30} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
Given equal populations of Type X and Type Y bacteria, with mutation rates of 50% and 70% respectively, if a mutated bacterium is found, what's the probability it's Type Y?
\(0.583\)
Find the angle between two unit vectors \(u\) and \(v\) such that the vectors \(2u-3v\) and \(5u+2v\) are perpendicular. Give you answer correct to the nearest degree.
\( 69^o \)
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=e^x\) is rotated about the x-axis for \(0 \le x \le 3\)
\(\frac{\pi}{2}(e^6-1)\) cubic units
What is the difference between a rational and an irrational number?
Rational can be expressed as a fraction with integer numerator and denominator
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sqrt{x+1}\)
\(1 + \frac{x}{2} - \frac{x^2}{8} + \frac{x^3}{16}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
A committee of 4 is randomly selected from 8 men and 11 women. Determine the likelihood that it consists of all men.
35/1938 or 1.81%
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:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$\(\frac{21 + 3\sqrt{2}}{47}\)
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