Find the first three terms in the expansion of:
\((4a - 3b)^6\)
\(=4096a^6 - 18432a^5b \\+34560a^4b^2 ...\)
If £200 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 8 years. £254.17
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,5),(9,10),(-2,11)\)
(4,16)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
Factorise:
\(5x^2+8x-4\)
\((x+2)(5x-2)\)
Draw a rough sketch of the graph of:
\(2y=x+2\)
Gradient 0.5
y intercept 1
What is the value of:
\(125^{\frac{1}{3}}\)
\(= 5\)
Find angle ABC if AB = 4m and BC = 5.1m. 38.3o
Find AC if angle ABC = 56o and AB = 3.8m. 5.63m
Describe the red region.
\(y = 7x^3 - 3x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 6x + 6\)
\(y = \dfrac{9}{x^{3}} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{27}{x^{4}} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=(2x+7)(7x-2)\)
Find \( \dfrac{dy}{dx}\)
\(28x+45\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
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:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =21x^2 - 16x + 4\)
Find \( \int y \quad dx\)
\(7x^3 - 8x^2 + 4x+c\)
A game is played 15 times and the probability of winning is 0.5. Calculate the probability of winning exactly 10 times. 0.0916
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:
\(u_{10} = 37\)
\(u_{19} = 64\)
Find the sum of the first 39 terms.2613
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
AB = 9.1cm.
BC = 6.4cm.
CÂB = 34.1°.
Find angle BĈA.
52.9° or 127.1°
Evaluate:
$$\sum_{n=0}^{9} n^2 - 7n$$
-30
\(f(x)=4x^2+5x-6\)
What is the value of the discriminant and what does it indicate?
121, Two distinct roots
\(f(x)=x^2-7x+2\)
By completing the square find the coordinates of the vertex.
(3.5, -10.25)
Solve for x:
\(\log_2(x) = 4\)
16
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:
(-6, -25) and (8, 17)
\(y=3x-7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-5}}{9}\)
\(81x²+5\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
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
\(x=\pm \sqrt{y}\)
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
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( j+k+l= 22 \\ 2j-3k+9l= 65\\ -j+k-3l=-24\)
j = 7, k = 7, l = 8
Find the perimeter of a sector with radius 8.5cm and angle \( \frac{\pi}{3}\)
🍕
25.9cm
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:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The sum of the first 5 terms of a geometric sequence is 242 and the sum of the first 6 terms is 728. What is the first term?
2
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{7}_{0} e^x dx\)
\(e^{7}- 1 \approx 1100\)
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 7% chance and machine B has a 11% chance of breaking down on any given day?
\(0.638\)
Find the vector equation of the line:
\( \dfrac{x-8}{7} = \dfrac{6-y}{3} = \dfrac{z}{9} \)
\( \mathbf{r} = \begin{pmatrix} 8 \\ 6 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 7 \\ -3 \\ 9 \end{pmatrix} \)
Simplify
$$ (4-3i)(5-5i) $$
\(5-35i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\cos^3{x}+\sin^2{x}\cos{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
How do you use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)
\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
Prove by mathematical induction that the product of \( n \) consecutive integers is divisible by \( n! \) (n factorial)
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
\(7\sqrt{13} - 9\sqrt{13}\)
\(-2\sqrt{13}\)
Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$\(\frac{21 + 3\sqrt{2}}{47}\)
Calculate the standard deviation of the following numbers:
4, 2, 5, 8, 6
2
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