Find the first three terms in the expansion of:
\((2a - 3b)^4\)
\(=16a^4 - 96a^3b \\+216a^2b^2 ...\)
If £220 is invested with an interest rate of 3% compounded quarterly, find the value of the investment after 5 years. £255.46
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,3),(8,6),(0,8)\)
(5,11)
\( X \sim N(50, 5^2)\)
Find
\( P(40\lt X \lt60) \)
\(0.955\)
Factorise:
\(x^2-1\)
\((x+1)(x-1)\)
Factorise:
\(2x^2+7x-4\)
\((x+4)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=2x\)
Gradient 2
y intercept 0
What is the value of:
\(4^{-3}\)
\(= \frac{1}{64}\)
Find angle BCA if AB = 5.6m and AC = 7m. 38.7o
Find AC if angle ABC = 65o and BC = 4.2m. 3.81m
Describe the red region.
\(y = 3x^3 - 5x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 10x + 4\)
\(y = \dfrac{6}{x^{5}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{30}{x^{6}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=e^{\cos x}\)
Find \( \dfrac{dy}{dx}\)
\(-sinxe^{cosx}\)
\(y=e^{2x} \cos (x)\)
Find \( \dfrac{dy}{dx}\)
\(2e^{2x}cosx-e^{2x}sinx\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
Find the equation of the tangent to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 17x - 2\)
Find the equation of the normal to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =15x^2 - 8x + 9\)
Find \( \int y \quad dx\)
\(5x^3 - 4x^2 + 9x+c\)
A game is played 16 times and the probability of winning is 0.8. Calculate the probability of winning exactly 12 times. 0.200
Make up a maths question using this:
\( \triangle = b^2-4ac\)
Quadratic equation discriminant
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = 13\)
\(u_{15} = 34\)
Find the sum of the first 48 terms.3000
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BC = 6.5cm.
CA = 7.7cm.
BĈA = 63.1°
Find AB to 1 dp.
7.5cm
Evaluate:
$$\sum_{n=1}^{5} 98 - n^2$$
435
\(f(x)=3x^2-5x-8\)
What is the value of the discriminant and what does it indicate?
121, Two distinct roots
\(f(x)=x^2-2x+9\)
By completing the square find the coordinates of the vertex.
(1, 8)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int \dfrac{\ln(x)}{x} \;dx\)
\(\dfrac{\ln(x)^2}{2}+c\)
Find the equation of the straight line that passes through:
(-1, -1) and (2, -7)
\(y=-2x-3\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-2}{8}}\)
\(8x²+2\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
Write in standard form:
\((a \times 10^2) \div (b\times 10^4)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{-2}\)
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
$$\tan{\frac{\pi}{6}} \times \cos{45°}$$\(\dfrac{1}{\sqrt{6}}\)
Without a calculator find the exact value of
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\(2x+y-3z= 9 \\ 3x+y+z= 38 \\ x-y+2z = 13\)
x = 9, y = 6, z = 5
Find the perimeter of a sector with radius 2.4cm and angle \( \frac{5\pi}{6}\)
🍕
11.1cm
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:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{2}_{0} (x-8)^2 \; dx\)
\(98.6666666666667\)
In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (70% of fiction, 20% of non-fiction are hardcovers), what's the probability it's non-fiction?
\(0.222\)
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
$$ \dfrac{1-4i}{1+5i}$$
\(-\frac{19}{26}-\frac{9}{26}i\)
Evaluate:
\(\int \ln{x}\; dx\)
\(x\ln|x|-x+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
Find the volume of revolution when \(y=\ln{x}\) is rotated about the y-axis for \(0 \le y \le 1\)
\(\approx 10.0\) cubic units
How do you determine if a geometric series converges?
Clue: common ratio test
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \ln(1 + x)\)
\(x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4}\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
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 \( n! > 2^n \) for all integers \( n \) greater than 4
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{27}$$
\(3\sqrt{3}\)
Simplify:
$$\dfrac{6}{\sqrt{11}}$$\(\frac{6\sqrt{11}}{11}\)
Simplify
\((2 - 2\sqrt{2})^2\)
\(12 - 8\sqrt{2}\)
Simplify:
$$\dfrac{7}{4 + \sqrt{3}}$$\(\frac{28 - 7\sqrt{3}}{13}\)
Calculate the standard deviation of the following numbers:
7, 9, 10, 11, 13
2
Find the inverse function:
\(f(x)=3x-5\)
\(f^{-1}(x)=\dfrac{x+5}{3}\)
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:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}7\\3\\-1\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}8\\8\\4\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=76,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}20\\-36\\32\end{smallmatrix}\right) } \)
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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.
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