Find the first three terms in the expansion of:
\((4a - 3b)^8\)
\(=65536a^8 - 393216a^7b \\+1032192a^6b^2 ...\)
If £240 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 8 years. £281.53
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,4),(6,8),(-2,8)\)
(2,12)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-x-2\)
\((x+1)(x-2)\)
Factorise:
\(10x^2-3x-4\)
\((2x+1)(5x-4)\)
Draw a rough sketch of the graph of:
\(2y=x-2\)
Gradient 0.5
y intercept -1
What is the value of:
\(5^{0}\)
\(= 1\)
Find angle ABC if AC = 5m and BC = 7m. 45.6o
Find AC if angle ABC = 29o and BC = 3.3m. 1.60m
Describe the red region.
\(y = 2x^3 - 6x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 12x + 8\)
\(y = \dfrac{5}{x^{8}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{40}{x^{9}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=\frac{1}{(6x+7)^3}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{18}{(6x+7)^4}\)
\(y=\sin (x) \sqrt{ x^2 + 7}\)
Find \( \dfrac{dy}{dx}\)
\(cosx \sqrt{x^2+7}+\frac{xsinx}{\sqrt{x^2+7}}\)
\(y=\frac{x+4}{x-3}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{7}{(x-3)^2}\)
Find the equation of the tangent to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)
Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =18x^2 - 12x + 8\)
Find \( \int y \quad dx\)
\(6x^3 - 6x^2 + 8x+c\)
A game is played 18 times and the probability of winning is 0.4. Calculate the probability of winning exactly 9 times. 0.128
Make up a maths question using this:
\( \triangle = b^2-4ac\)
Quadratic equation discriminant
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = -78\)
\(u_{14} = -110\)
Find the sum of the first 45 terms.-8190
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,
AB = 5.1cm.
BC = 6.6cm.
CÂB = 77.8°.
Find angle BĈA.
49.1°
Evaluate:
$$\sum_{n=3}^{4} 2^n$$
24
\(f(x)=5x^2+2x-7\)
What is the value of the discriminant and what does it indicate?
144, Two distinct roots
\(f(x)=x^2-7x-8\)
By completing the square find the coordinates of the vertex.
(3.5, -20.25)
Solve for x:
\(\log_2(x) = 4\)
16
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:
(-3, 4) and (5, -4)
\(y=-x+1\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-17}{19}\)
\((19x+17)²\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
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
\(y=x^2+7x\)
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
$$\sin{5\pi}$$\(0\)
Solve:
\( g-7h-7i=-70 \\ 2g-2h+i= 4\\ 5g+3h+i = 60\)
g = 7, h = 7, i = 4
Find the area of a sector with radius 5.1cm and angle \( \frac{\pi}{4}\)
🍕
10.2cm2
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:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
The 8th term of a geometric sequence is 6561 and the sum of the first 8 terms is 9840. Find \(u_1\) if \(r > 1\).
3
Find the first 4 terms in the expansion of:
\((1+2x)^{\frac12}\)
\(1+x-\frac{x^2}{2}+\frac{x^3}{2}\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.06. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.515\)
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
$$ (5-5i)(5-6i) $$
\(-5-55i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)
\(\frac{65\pi}{4}\) 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
\(f(x) = \sqrt{x+1}\)
\(1 + \frac{x}{2} - \frac{x^2}{8} + \frac{x^3}{16}\)
Expand and simplify:
$$ (i-\sqrt{3})^5 $$
\(16\sqrt{3} + 16i \\ \text{or } 16(\sqrt{3} + i)\)
Of the 22 people on boat, 3 are professional singers. If 4 people get sea sick, determine the chance that all three singers do not.
204/385 or 53.0%
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:
$$\sqrt{8}$$
\(2\sqrt{2}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)
Calculate the standard deviation of the following numbers:
15, 19, 19, 21, 21, 25
3
Find the inverse function:
\(f(x)=2^x+1\)
\(f^{-1}(x)=\log_2(x-1), x>1\)
Make \(n\) the subject:
\(m=n^2-10n+17 \\\)
\(n=5\pm\sqrt{m+8}\)
Find the scalar and vector products of:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}-2\\2\\-2\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}3\\-1\\4\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=-16,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}6\\2\\-4\end{smallmatrix}\right) } \)
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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.]"