Find the first three terms in the expansion of:
\((3a - 4b)^8\)
\(=6561a^8 - 69984a^7b \\+326592a^6b^2 ...\)
If £140 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 8 years. £225.45
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,3),(7,8),(-4,9)\)
(2,14)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(x^2+2x-8\)
\((x+4)(x-2)\)
Draw a rough sketch of the graph of:
\(y=-2x+1\)
Gradient -2
y intercept 1
What is the value of:
\(2^{-3}\)
\(= \frac{1}{8}\)
Find angle BCA if AB = 6m and BC = 7m. 59.0o
Find AC if angle ABC = 62o and BC = 4.3m. 3.80m
Describe the red region.
\(y = 7x^3 - 9x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 18x + 7\)
\(y = \dfrac{5}{x^{6}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{30}{x^{7}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=8x^2e^x\)
Find \( \dfrac{dy}{dx}\)
\(16xe^x+8x^2e^x\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 2x + 3\)
Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =21x^2 - 16x + 5\)
Find \( \int y \quad dx\)
\(7x^3 - 8x^2 + 5x+c\)
A game is played 20 times and the probability of winning is 0.3. Calculate the probability of winning exactly 17 times. 0.000000505
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:
\(u_{9} = -43\)
\(u_{17} = -83\)
Find the sum of the first 49 terms.-6027
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
AB = 8.4cm.
BC = 6.7cm.
CA = 9.8cm.
Find angle CÂB.
42.3°
Evaluate:
$$\sum_{n=4}^{6} n^2 - 3n$$
32
\(f(x)=8x^2-6x+7\)
What is the value of the discriminant and what does it indicate?
-188, No real roots
\(f(x)=x^2-2x-7\)
By completing the square find the coordinates of the vertex.
(1, -8)
Simplify \(\log_{10}10^5\)
5
Find the integral:
\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)
\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-1, -1) and (9, 29)
\(y=3x+2\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-15}{12}\)
\((12x+15)²\)
\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)
\(f(x)=x+2\)
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
\(y=x^3-4x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{2}} \div \cos{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{6}}$$\(\dfrac{1}{\sqrt{3}}\)
Solve:
\( g-7h-7i=-35 \\ 2g-2h+i= 14\\ 5g+3h+i = 45\)
g = 7, h = 2, i = 4
Find the area of a sector with radius 8.3cm and angle \( \frac{\pi}{6}\)
🍕
18.0cm2
How many ways can twelve people be divided into two equal groups?
462
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
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:
\(\int^{4}_{2} (x-8)^2 \; dx\)
\(50.6666666666666\)
Given equal populations of Type X and Type Y bacteria, with mutation rates of 20% and 50% respectively, if a mutated bacterium is found, what's the probability it's Type Y?
\(0.714\)
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
$$ (5-3i)(4-2i) $$
\(14-22i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
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
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
\(f(x) = \frac{1}{1-x}\)
\(1 + x + x^2 + x^3\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
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 sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{45}$$
\(3\sqrt{5}\)
Simplify:
$$\dfrac{7}{2\sqrt{5}}$$\(\frac{7\sqrt{5}}{10}\)
Simplify
\((2 - 2\sqrt{2})^2\)
\(12 - 8\sqrt{2}\)
Simplify:
$$\dfrac{2}{5 - \sqrt{7}}$$\(\frac{10 + 2\sqrt{7}}{18}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
Find the inverse function:
\(f(x)=7-2x\)
\(f^{-1}(x)=\dfrac{7-x}{2}\)
Make \(r\) the subject:
\({\small V=\frac{\pi h}{3}(R^2+Rr+r^2),}\\{\small r>0}\)
\(r=\dfrac{\sqrt{\dfrac{12V}{\pi h}-3R^2}-R}{2}\)
Find the scalar and vector products of:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}-2\\4\\8\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}4\\0\\2\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=8,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}8\\36\\-16\end{smallmatrix}\right) } \)
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Robyn, ABCIS In Vietnam
Thursday, December 12, 2024
"Would it be possible to refreshing revision to show the same option more than once? for example, selecting 'differentiation 4' three times and so having three different questions in three different tiles on display?
Obviously I can the refresh option three times, but for the kids that can complete the first step faster than others having a second one in the same category to move onto would be great.
[Transum: Thank you very much for your comment. Feedback is always appreciated. Unfortunately that facility was not built into the code. I will have a think about it and consider putting it into the pro version of Refreshing Revision. In the meantime I guess you could use the snipping tool to snip the panels into a Word document and then refresh the page to get a new question. Snip that into the document and then you'll have control over the order of the questions and how many you have.]"