Find the first three terms in the expansion of:
\((3a - 2b)^8\)
\(=6561a^8 - 34992a^7b \\+81648a^6b^2 ...\)
If £180 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 4 years. £219.76
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,5),(7,8),(-2,11)\)
(4,14)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2+2x-8\)
\((x+4)(x-2)\)
Factorise:
\(5x^2+x-4\)
\((x+1)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=-x-1\)
Gradient -1
y intercept -1
What is the value of:
\(2^{0}\)
\(= 1\)
Find angle BCA if AB = 4.6m and AC = 6.2m. 36.6o
Find AC if angle ABC = 46o and BC = 4.8m. 3.45m
Describe the red region.
\(y = 3x^3 - 4x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 8x + 8\)
\(y = \dfrac{4}{x^{9}} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{36}{x^{10}} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=e^{8x+9}\)
Find \( \dfrac{dy}{dx}\)
\(8e^{8x+9}\)
\(y=x(3x+5)^3\)
Find \( \dfrac{dy}{dx}\)
\((3x+5)^3+9x(3x+5)^2\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
Find the equation of the tangent to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(y = 0\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =21x^2 - 12x + 5\)
Find \( \int y \quad dx\)
\(7x^3 - 6x^2 + 5x+c\)
A game is played 11 times and the probability of winning is 0.6. Calculate the probability of winning exactly 8 times. 0.177
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:
\(u_{7} = 10\)
\(u_{16} = 28\)
Find the sum of the first 44 terms.1804
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 = 5.9cm.
BC = 5.1cm.
CA = 6.9cm.
Find angle CÂB.
46.1°
Evaluate:
$$\sum_{n=1}^{6} 87 - n^2$$
431
\(f(x)=7x^2+8x+3\)
What is the value of the discriminant and what does it indicate?
-20, No real roots
\(f(x)=x^2-7x+9\)
By completing the square find the coordinates of the vertex.
(3.5, -3.25)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-1, 7) and (2, -2)
\(y=-3x+4\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-7}{2}}\)
\(2x²+7\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
Write in standard form:
\((a \times 10^4) \div (b\times 10^{-2})\)
where \(a \div b \) is a decimal number \((0.1 \le \frac{a}{b} \lt 1)\)
\(\frac{10a}{b}\times10^5\)
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
$$\cos{30°} \div \sin{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\cos{720°}$$\(1\)
Solve:
\( 5a+2b+c=38 \\ 3a+4b+2c= 34 \\ a+5b+c=23\)
a = 6, b = 3, c = 2
Find the perimeter of a sector with radius 7.5cm and angle \( \frac{\pi}{4}\)
🍕
20.9cm
In how many ways can 8 different books be arranged on a shelf if 4 of them must be together?
2880
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
The fourth term of a geometric sequence is \(-16\) and the sum to infinity is \(32\). What is the common ratio?
-0.669
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{5}_{0} x^2-2x+7 \; dx\)
\(51.7\)
In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (60% of fiction, 80% of non-fiction are hardcovers), what's the probability it's non-fiction?
\(0.571\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 5 \\ 6 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 4 \\ -8 \\ 5 \end{pmatrix} \; \text{and} \; \begin{pmatrix} -1 \\ -14 \\ 5 \end{pmatrix} \)
37.5 square units
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
Find the volume of revolution when \(y=x^2\) is rotated about the x-axis for \(-2 \le x \le 2\)
\(\frac{64\pi}{5}\) cubic units
How do you solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \frac{1}{x^2 + 1}\)
\(1 - x^2 + x^4 - x^6\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
A committee of 4 is randomly selected from 8 men and 11 women. Determine the likelihood that it consists of all men.
35/1938 or 1.81%
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:
$$\sqrt{50}$$
\(5\sqrt{2}\)
Simplify:
$$\dfrac{5}{\sqrt{8}}$$\(\frac{5\sqrt{8}}{8} = \frac{5\sqrt{2}}{4}\)
Simplify
\(4\sqrt{7} - \sqrt{63}\)
\(\sqrt{7}\)
Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$\(\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
Find the inverse function:
\(f(x)=3x-5\)
\(f^{-1}(x)=\dfrac{x+5}{3}\)
Make \(x\) the subject:
\(q=\log_a\left(\dfrac{x-b}{x+b}\right)\)
\(x=\dfrac{b(1+a^q)}{1-a^q}\)
Find the scalar and vector products of:
\({\scriptsize\mathbf a=\left(\begin{smallmatrix}3\\5\\5\end{smallmatrix}\right)\text{ and }\mathbf b=\left(\begin{smallmatrix}3\\4\\0\end{smallmatrix}\right)}\)
\( {\scriptsize \mathbf a\cdot\mathbf b=29,\quad \mathbf a\times\mathbf b=\left(\begin{smallmatrix}-20\\15\\-3\end{smallmatrix}\right) } \)
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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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