Find the first three terms in the expansion of:
\((2a - 3b)^4\)
\(=16a^4 - 96a^3b \\+216a^2b^2 ...\)
If £180 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 4 years. £211.06
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,1),(8,5),(-2,7)\)
(4,11)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
Factorise:
\(5x^2+16x-16\)
\((x+4)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=-2x+1\)
Gradient -2
y intercept 1
What is the value of:
\(1^{1}\)
\(= 1\)
Find angle ABC if AC = 3.7m and AB = 4.7m. 38.2o
Find AC if angle ABC = 42o and BC = 4.4m. 2.94m
Describe the red region.
\(y = 6x^3 - 8x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 16x + 7\)
\(y = \dfrac{2}{x^{8}} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{16}{x^{9}} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=(7x^4+9)^7\)
Find \( \dfrac{dy}{dx}\)
\(196x^3(7x^4+9)^6\)
\(y=e^{2x} \cos (x)\)
Find \( \dfrac{dy}{dx}\)
\(2e^{2x}cosx-e^{2x}sinx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =24x^2 - 12x + 8\)
Find \( \int y \quad dx\)
\(8x^3 - 6x^2 + 8x+c\)
A game is played 15 times and the probability of winning is 0.8. Calculate the probability of winning exactly 4 times. 0.0000115
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:
\(u_{10} = -73\)
\(u_{20} = -163\)
Find the sum of the first 44 terms.-8162
Find the equations of the asymptotes of:
\(y=12-\dfrac{4x+3}{7-2x}\)
\(x=\frac{7}{2},y=14\)
In the triangle ABC,
AB = 6.8cm.
BC = 5.6cm.
CÂB = 34.9°.
Find angle BĈA.
44.0° or 136°
Evaluate:
$$\sum_{n=4}^{5} n^2 - 7n$$
-22
\(f(x)=-6x^2+5x-5\)
What is the value of the discriminant and what does it indicate?
-95, No real roots
\(f(x)=x^2-8x+2\)
By completing the square find the coordinates of the vertex.
(4, -14)
Simplify:
\(\log_2(4\sqrt{16})\)
4
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:
(-8, 24) and (9, -10)
\(y=-2x+8\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-7}\)
\(x²+7\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(x=\pm \sqrt{y}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\( j+k+l= 26 \\ 2j-3k+9l= 70\\ -j+k-3l=-26\)
j = 8, k = 9, l = 9
Find the area of a sector with radius 5.7cm and angle \( \frac{5\pi}{6}\)
🍕
42.5cm2
Ansh is with eight people in a queue. How many ways can they line up without Ansh being at the back?
322560
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
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:
\(\int^{4}_{0} x^2-2x+7 \; dx\)
\(33.3\)
Every family in Happyland has either has a car or a motor scooter or both. 54% of the families have a car. 59% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.
\(\dfrac{13}{54}\)
Find the point of intersection of these planes:
\(\Pi_1: \quad 2x + y - 3z = -5\)
\(\Pi_2: \quad x - 3y + 2z = 1\)
\(\Pi_3: \quad 3x - 2y + z = 2\)
\( (1,2,3) \)
Simplify
$$ \dfrac{1-4i}{1+5i}$$
\(-\frac{19}{26}-\frac{9}{26}i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\cos^3{x}+\sin^2{x}\cos{x}$$\(\cos{x}\)
Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) cubic units
Describe the behavior of a function at its inflection point.
The concavity of the function changes
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Given |z| = 8, find:
$$ |(3+4i)z| $$
\(40\)
A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.
55/153 or 35.9%
Prove by mathematical induction that the sum of the first \( n \) natural numbers is \( \frac{n(n + 1)}{2} \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{18}$$
\(3\sqrt{2}\)
Simplify:
$$\dfrac{5}{2\sqrt{3}}$$\(\frac{5\sqrt{3}}{6}\)
Simplify
\(7\sqrt{13} - 9\sqrt{13}\)
\(-2\sqrt{13}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
Calculate the standard deviation of the following numbers:
7, 9, 10, 11, 13
2
Find the inverse function:
\(f(x)=\ln(x+2)\)
\(f^{-1}(x)=e^x-2\)
Make \(v\) the subject:
\(s=\sqrt{\dfrac{u+v}{u-v}}\)
\(v=\dfrac{u(s^2-1)}{s^2+1}\)
Find the scalar and vector products of:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}3\\3\\6\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}8\\8\\1\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=54,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}-45\\45\\0\end{smallmatrix}\right) } \)
Write down a summary of your last Maths lesson focussing on what you learnt.
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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.]"