Find the first three terms in the expansion of:
\((4a - 3b)^5\)
\(=1024a^5 - 3840a^4b \\+5760a^3b^2 ...\)
If £240 is invested with an interest rate of 5% compounded quarterly, find the value of the investment after 4 years. £292.77
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,4),(7,10),(-5,10)\)
(1,16)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(12x^2-7x-12\)
\((4x+3)(3x-4)\)
Draw a rough sketch of the graph of:
\(y=2x+1\)
Gradient 2
y intercept 1
What is the value of:
\(16^{\frac{1}{2}}\)
\(= 4\)
Find angle ABC if AC = 5.4m and BC = 6.6m. 54.9o
Find BC if angle BCA = 22o and AB = 4.2m. 11.2m
Describe the red region.
\(y = 3x^3 - 6x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 12x + 6\)
\(y = \dfrac{9}{x^{7}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{63}{x^{8}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=\sqrt{7x^8-6x}\)
Find \( \dfrac{dy}{dx}\)
\((28x^7-3)(7x^8-6x)^{-\frac{1}{2}}\)
\(y=\sin x \cos x\)
Find \( \dfrac{dy}{dx}\)
\(cos^2x-sin^2x\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 6x + 3\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =21x^2 - 10x + 7\)
Find \( \int y \quad dx\)
\(7x^3 - 5x^2 + 7x+c\)
A game is played 11 times and the probability of winning is 0.8. Calculate the probability of winning exactly 3 times. 0.000216
Make up a maths question using this:
\(\log_ax=\dfrac{\log_bx}{\log_ba}\)
Logarithm changing base formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{8} = -38\)
\(u_{11} = -56\)
Find the sum of the first 44 terms.-5500
Find the equations of the asymptotes of:
\(y=10+\dfrac{9x}{5-3x}\)
\(x=\frac{5}{3},y=7\)
In the triangle ABC,
BĈA = 52.2°.
BC = 5.4cm.
AB̂C = 88.87°.
Find CA to 1 dp.
8.6cm
Evaluate:
$$\sum_{n=2}^{6} n^2 - 2n$$
50
\(f(x)=-6x^2-6x-5\)
What is the value of the discriminant and what does it indicate?
-84, No real roots
\(f(x)=x^2-3x+8\)
By completing the square find the coordinates of the vertex.
(1.5, 5.75)
Evaluate \(\log_5(625) \)
4
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:
(-4, -12) and (5, 6)
\(y=2x-4\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-5\)
\((x+5)²\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=\dfrac{5}{x}\)
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
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\(2x+y-3z= -11 \\ 3x+y+z= 32 \\ x-y+2z = 23\)
x = 7, y = 2, z = 9
Find the perimeter of a sector with radius 7.7cm and angle \( \frac{\pi}{4}\)
🍕
21.4cm
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:
$$y=\dfrac{8x^2-19x-15}{1-2x}$$x=1/2,y=15/2-4x
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
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:
\(\int^{3}_{1} x^2-2x+7 \; dx\)
\(14.7\)
The probability that it is cloudy on a particular day is 0.5. The probability that it is cloudy with a high level of pollution on a particular day is 0.2. Find the probability that there will be a high level of pollution on a day when it is cloudy.
\(0.400\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
Describe the behavior of a function at its inflection point.
The concavity of the function changes
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 \(z\)
$$ z^4 = - 16 $$
\(\sqrt{2}+i\sqrt{2},-\sqrt{2}+i\sqrt{2} \\ \sqrt{2}-i\sqrt{2},-\sqrt{2}-i\sqrt{2}\)
6 girls sit at random on 6 seats in a row. Determine the probability that the two friends Karen and Julie sit at the ends of the row.
1/15 or 6.67%
Prove by mathematical induction that \( 5^n - 1 \) is divisible by 4 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{2}{\sqrt{10}}$$\(\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}\)
Simplify
\((9 + 2\sqrt{2})(9 - 2\sqrt{2})\)
\(73\)
Simplify:
$$\dfrac{5}{3 - \sqrt{2}}$$\(\frac{15 + 5\sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
15, 19, 19, 21, 21, 25
3
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