Find the first three terms in the expansion of:
\((4a - 3b)^9\)
\(=262144a^9 - 1769472a^8b \\+5308416a^7b^2 ...\)
If £220 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 8 years. £302.81
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,3),(8,9),(-2,7)\)
(2,13)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(12x^2+5x-2\)
\((3x+2)(4x-1)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(4^{-3}\)
\(= \frac{1}{64}\)
Find angle BCA if AB = 3.4m and BC = 4.4m. 50.6o
Find BC if angle BCA = 41o and AB = 5.2m. 7.93m
Describe the red region.
\(y = 9x^3 - 7x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 14x + 3\)
\(y = \dfrac{6}{x^{9}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{54}{x^{10}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\sqrt{6x^4-6x}\)
Find \( \dfrac{dy}{dx}\)
\((12x^3-3)(6x^4-6x)^{-\frac{1}{2}}\)
\(y=e^{9x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(9e^{9x}cosx-e^{9x}sinx\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(x = -3\)
\(y =6x^2 - 16x + 4\)
Find \( \int y \quad dx\)
\(2x^3 - 8x^2 + 4x+c\)
A game is played 12 times and the probability of winning is 0.8. Calculate the probability of winning exactly 5 times. 0.00332
Make up a maths question using this:
\( \triangle = b^2-4ac\)
Quadratic equation discriminant
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = 53\)
\(u_{20} = 123\)
Find the sum of the first 32 terms.3152
Find the equations of the asymptotes of:
\(y=\dfrac{3x-5}{6x-12}\)
\(x=2,y=\frac{1}{2}\)
In the triangle ABC,
BĈA = 50.0°.
BC = 9.8cm.
AB̂C = 55.7°.
Find CA to 1 dp.
8.4cm
Evaluate:
$$\sum_{n=1}^{5} 2^n$$
62
\(f(x)=3x^2+5x+7\)
What is the value of the discriminant and what does it indicate?
-59, No real roots
\(f(x)=x^2+8x-5\)
By completing the square find the coordinates of the vertex.
(-4, -21)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-6, 10) and (1, -11)
\(y=-3x-8\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+7}{8}\)
\(8x-7\)
\(\text{Find }f(x) \text{ if} \\ f(1-b)=3-b \\\)
\(f(x)=x+2\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^{p+q}\)
Draw a rough sketch of
\(y=2^x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{2}} \div \cos{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\(2x+y-3z= 4 \\ 3x+y+z= 37 \\ x-y+2z = 17\)
x = 9, y = 4, z = 6
Find the area of a sector with radius 3.5cm and angle \( \frac{\pi}{3}\)
🍕
6.41cm2
How many ways can fifteen children sit in a row without the youngest being in the middle?
1220496076800
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
The first term of a geometric sequence is 49 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:
\((1-\dfrac{x}{2})^{\frac13}\)
\(1-\frac{x}{6}-\frac{x^2}{36}-\frac{5x^3}{648}\)
Evaluate:
\(\int^{4}_{0} e^x dx\)
\(e^{4}- 1 \approx 53.6\)
Each afternoon the probability my cat sleeps is 0.7 and the probability that my dog sleeps is 0.5. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon.
\(0.63\)
Find the vector equation of the line:
\( \dfrac{x-8}{3} = \dfrac{3-y}{3} = \dfrac{z}{3} \)
\( \mathbf{r} = \begin{pmatrix} 8 \\ 3 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 3 \\ -3 \\ 3 \end{pmatrix} \)
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
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
\(f(x) = \sqrt{x+1}\)
\(1 + \frac{x}{2} - \frac{x^2}{8} + \frac{x^3}{16}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
A committee of 5 is chosen from 15 people by random selection. Two Londoners were amongst the group from which the selection was made. Find the probability that both Londoners are chosen for the committee.
2/21 or 9.52%
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:
$$\sqrt{18}$$
\(3\sqrt{2}\)
Simplify:
$$\dfrac{7}{2\sqrt{5}}$$\(\frac{7\sqrt{5}}{10}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$\(\frac{21 + 3\sqrt{2}}{47}\)
Calculate the standard deviation of the following numbers:
4, 2, 5, 8, 6
2
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