Find the first three terms in the expansion of:
\((3a - 4b)^9\)
\(=19683a^9 - 236196a^8b \\+1259712a^7b^2 ...\)
If £120 is invested with an interest rate of 1% compounded quarterly, find the value of the investment after 9 years. £131.29
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,4),(8,9),(-1,8)\)
(3,13)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(3x^2-2x-8\)
\((3x+4)(x-2)\)
Draw a rough sketch of the graph of:
\(y=x-2\)
Gradient 1
y intercept -2
What is the value of:
\(1^{0}\)
\(= 1\)
Find angle BCA if AC = 5.2m and BC = 6.4m. 35.7o
Find AB if angle ABC = 39o and BC = 3.6m. 2.80m
Describe the red region.
\(y = 8x^3 - 8x^2 + 5x\)
Find \( \dfrac{dy}{dx}\)
\(24x^2 - 16x + 5\)
\(y = \dfrac{8}{x^{3}} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{24}{x^{4}} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\sqrt{6x^8-6x}\)
Find \( \dfrac{dy}{dx}\)
\((24x^7-3)(6x^8-6x)^{-\frac{1}{2}}\)
\(y=x(5x^2+6)^7\)
Find \( \dfrac{dy}{dx}\)
\((5x^2+6)^7+70x^2(5x^2+6)^6\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
Find the equation of the tangent to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)
Find the equation of the normal to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =15x^2 - 16x + 8\)
Find \( \int y \quad dx\)
\(5x^3 - 8x^2 + 8x+c\)
A game is played 13 times and the probability of winning is 0.2. Calculate the probability of winning exactly 6 times. 0.0230
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:
\(u_{9} = 103\)
\(u_{13} = 151\)
Find the sum of the first 40 terms.9640
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
BĈA = 83.4°.
BC = 5.6cm.
AB̂C = 59.9°.
Find CA to 1 dp.
8.1cm
Evaluate:
$$\sum_{n=2}^{5} 2^n$$
60
\(f(x)=-4x^2+2x+8\)
What is the value of the discriminant and what does it indicate?
132, Two distinct roots
\(f(x)=x^2-4x-3\)
By completing the square find the coordinates of the vertex.
(2, -7)
What is the value of \(\ln{e^3}\) ?
3
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:
(-5, -7) and (2, 14)
\(y=3x+8\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-2}\)
\(x²+2\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
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
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\(2x+y-3z= 0 \\ 3x+y+z= 29 \\ x-y+2z = 9\)
x = 5, y = 8, z = 6
Find the area of a sector with radius 5.6cm and angle \( \frac{\pi}{4}\)
🍕
12.3cm2
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 4th term of a geometric sequence is 625 and the sum of the first 4 terms is 780. Find \(u_1\) if \(r > 1\).
5
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{140}_{70} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.08. 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?
\(0.521\)
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
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\sin{x}\cot{x}$$\(\cos{x}\)
Find the volume of revolution when \(y=x^2\) is rotated about the y-axis for \(0 \le y \le 4\)
\(8\pi\) 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
\(f(x) = \frac{1}{x^2 + 1}\)
\(1 - x^2 + x^4 - x^6\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
6 children, three boys and three girls, are randomly seated on a row of 6 chairs. Determine the likelihood that the three boys are seated together.
1/5 or 20%
Prove by mathematical induction that the sum of the first \( n \) even numbers is \( n(n + 1) \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\(4\sqrt{7} - \sqrt{63}\)
\(\sqrt{7}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
Calculate the standard deviation of the following numbers:
9, 13, 15, 17, 21
4
Find the inverse function:
\(f(x)=(x-2)^2+1,\quad x\geq2\)
\(f^{-1}(x)=2+\sqrt{x-1},x\geq1\)
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:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}-3\\5\\1\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}-1\\9\\9\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=57,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}36\\26\\-22\end{smallmatrix}\right) } \)
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?
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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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