Find the first three terms in the expansion of:
\((4a - 2b)^5\)
\(=1024a^5 - 2560a^4b \\+2560a^3b^2 ...\)
If £160 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 9 years. £229.20
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,3),(11,8),(0,9)\)
(6,14)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
Factorise:
\(15x^2-4x-3\)
\((3x+1)(5x-3)\)
Draw a rough sketch of the graph of:
\(y=-2x-2\)
Gradient -2
y intercept -2
What is the value of:
\(16^{\frac{1}{2}}\)
\(= 4\)
Find angle ABC if AB = 3.3m and BC = 5m. 48.7o
Find AB if angle ABC = 35o and BC = 3.6m. 2.95m
Describe the red region.
\(y = 3x^3 - 6x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 12x + 4\)
\(y = \dfrac{8}{x^{6}} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{48}{x^{7}} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\sin (5x^2+6)\)
Find \( \dfrac{dy}{dx}\)
\(10xcos(5x^2+6)\)
\(y=x(2x^2+3)^6\)
Find \( \dfrac{dy}{dx}\)
\((2x^2+3)^6+24x^2(2x^2+3)^5\)
\(y=\frac{x+2}{x-2}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{4}{(x-2)^2}\)
Find the equation of the tangent to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 17x - 2\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =15x^2 - 14x + 9\)
Find \( \int y \quad dx\)
\(5x^3 - 7x^2 + 9x+c\)
A game is played 14 times and the probability of winning is 0.2. Calculate the probability of winning exactly 11 times. 0.00000382
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:
\(u_{9} = 68\)
\(u_{14} = 113\)
Find the sum of the first 16 terms.1016
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BC = 9.9cm.
CA = 11.8cm.
BĈA = 40.4°
Find AB to 1 dp.
7.7cm
Evaluate:
$$\sum_{n=3}^{5} 2n+1$$
27
\(f(x)=6x^2+9x-4\)
What is the value of the discriminant and what does it indicate?
177, Two distinct roots
\(f(x)=x^2+2x-6\)
By completing the square find the coordinates of the vertex.
(-1, -7)
Solve for x:
\(\log_3x = 2\)
9
Find the integral:
\(\int 3xe^{x^2} \;dx\)
\(\frac{3}{2}e^{x^2}+c\)
Find the equation of the straight line that passes through:
(-8, -13) and (0, 3)
\(y=2x+3\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-6}{7}}\)
\(7x²+6\)
\(\text{Find }f(x) \text{ if} \\ f(a^3)=2a^6 \\\)
\(f(x)=2x^2\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
Draw a rough sketch of
\(x=\pm \sqrt{y}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{4}} + \sin{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\( 5a+2b+c=18 \\ 3a+4b+2c= 22 \\ a+5b+c=16\)
a = 2, b = 2, c = 4
Find the perimeter of a sector with radius 3.9cm and angle \( \frac{\pi}{6}\)
🍕
9.84cm
How many ways can seven children sit in a row without the youngest being in the middle?
4320
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
The 7th term of a geometric sequence is 20480 and the sum of the first 7 terms is 27305. Find the first term.
5
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:
\(\int^{6}_{0} e^x dx\)
\(e^{6}- 1 \approx 402\)
Box A contains 6 red and 8 blue cubes, and box B contains 11 red and 13 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B?
\(\dfrac{77}{149}\)
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
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int e^x\sin{x}\; dx\)
\(\frac{e^x}{2}(sinx-cosx)+c\)
Simplify:
$$\dfrac{\sin^2{x}-1}{\cos{x}}$$\(-\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt{x}\) is rotated about the y-axis for \(1 \le y \le 4\)
\(\frac{1023\pi}{5}\) 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
\(f(x) = \frac{1}{1-x}\)
\(1 + x + x^2 + x^3\)
Given |z| = 8, find:
$$ |(3+4i)z| $$
\(40\)
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 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:
$$\sqrt{50}$$
\(5\sqrt{2}\)
Simplify:
$$\dfrac{6}{\sqrt{11}}$$\(\frac{6\sqrt{11}}{11}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{7}{4 + \sqrt{3}}$$\(\frac{28 - 7\sqrt{3}}{13}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
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