Find the first three terms in the expansion of:
\((2a - 4b)^9\)
\(=512a^9 - 9216a^8b \\+73728a^7b^2 ...\)
If £160 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 5 years. £195.36
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,1),(10,6),(0,6)\)
(5,11)
\( X \sim N(43, 7^2)\)
Find
\( P(32\lt X \lt45) \)
\(0.554\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Factorise:
\(4x^2-4x-3\)
\((2x+1)(2x-3)\)
Draw a rough sketch of the graph of:
\(2y=x+4\)
Gradient 0.5
y intercept 2
What is the value of:
\(2^{0}\)
\(= 1\)
Find angle BCA if AB = 4.6m and BC = 6.3m. 46.9o
Find AC if angle ABC = 31o and BC = 5.6m. 2.88m
Describe the red region.
\(y = 3x^3 - 9x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 18x + 2\)
\(y = \dfrac{7}{x^{2}} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{14}{x^{3}} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=(7x^3+7)^8\)
Find \( \dfrac{dy}{dx}\)
\(168x^2(7x^3+7)^7\)
\(y=x \tan (x)\)
Find \( \dfrac{dy}{dx}\)
\(tanx+\frac{x}{cos^2x}\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =12x^2 - 18x + 4\)
Find \( \int y \quad dx\)
\(4x^3 - 9x^2 + 4x+c\)
A game is played 10 times and the probability of winning is 0.4. Calculate the probability of winning exactly 4 times. 0.251
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:
\(u_{9} = -39\)
\(u_{14} = -69\)
Find the sum of the first 20 terms.-960
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,
BC = 7.1cm.
CA = 11.4cm.
BĈA = 36.6°
Find AB to 1 dp.
7.1cm
Evaluate:
$$\sum_{n=2}^{5} 4n+1$$
60
\(f(x)=3x^2-2x+5\)
What is the value of the discriminant and what does it indicate?
-56, No real roots
\(f(x)=x^2-2x+7\)
By completing the square find the coordinates of the vertex.
(1, 6)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-3, 14) and (3, -4)
\(y=-3x+5\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+6}{2}\)
\(2x-6\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
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
$$\tan{\frac{\pi}{6}} \times \cos{45°}$$\(\dfrac{1}{\sqrt{6}}\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( j+k+l= 19 \\ 2j-3k+9l= 36\\ -j+k-3l=-15\)
j = 9, k = 6, l = 4
Find the area of a sector with radius 7.8cm and angle \( \frac{\pi}{4}\)
🍕
23.9cm2
In how many ways can 11 different books be arranged on a shelf if 2 of them must be together?
7257600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The first term of a geometric sequence is 33 and the fourth term is twice this value. What is the common ratio?
\( \sqrt[3]{2} \)
Find the first 4 terms in the expansion of:
\(\dfrac{1}{2-x}\)
\(\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{16}\)
Evaluate:
\(\int^{6}_{2} x^2-2x+7 \; dx\)
\(65.3\)
The probability that it is cloudy on a particular day is 0.3. The probability that it is cloudy with a high level of pollution on a particular day is 0.1. Find the probability that there will be a high level of pollution on a day when it is cloudy.
\(0.333\)
Find the vector equation of the line:
\( \dfrac{x-4}{3} = \dfrac{3-y}{7} = \dfrac{z}{3} \)
\( \mathbf{r} = \begin{pmatrix} 4 \\ 3 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 3 \\ -7 \\ 3 \end{pmatrix} \)
Simplify
$$ \dfrac{1-4i}{1+5i}$$
\(-\frac{19}{26}-\frac{9}{26}i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
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
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
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
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 first \( n \) even numbers is \( n(n + 1) \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{20}$$
\(2\sqrt{5}\)
Simplify:
$$\dfrac{8}{3\sqrt{7}}$$\(\frac{8\sqrt{7}}{21}\)
Simplify
\((1 + \sqrt{2})(2 + \sqrt{2})\)
\(4 + 3\sqrt{2}\)
Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$\(\frac{21 + 3\sqrt{2}}{47}\)
Calculate the standard deviation of the following numbers:
7, 9, 10, 11, 13
2
Find the inverse function:
\(f(x)=\sqrt{x+4}\)
\(f^{-1}(x)=x^2-4,\quad x\geq0\)
Make \(x\) the subject:
\(y=a\ln(bx+c)+d \\\)
\(x=\dfrac{e^{(y-d)/a}-c}{b}\)
Find the scalar and vector products of:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}-1\\-2\\4\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}5\\6\\-2\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=-25,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}-20\\18\\4\end{smallmatrix}\right) } \)
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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.
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