Find the first three terms in the expansion of:
\((2a - 4b)^7\)
\(=128a^7 - 1792a^6b \\+10752a^5b^2 ...\)
If £160 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 5 years. £176.78
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,3),(6,6),(-1,7)\)
(3,10)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2-2x-8\)
\((x+2)(x-4)\)
Factorise:
\(5x^2+8x-4\)
\((x+2)(5x-2)\)
Draw a rough sketch of the graph of:
\(y=2x\)
Gradient 2
y intercept 0
What is the value of:
\(3^{-2}\)
\(= \frac{1}{9}\)
Find angle ABC if AB = 3.9m and BC = 5.6m. 45.9o
Find AC if angle ABC = 38o and AB = 5.4m. 4.22m
Describe the red region.
\(y = 5x^3 - 3x^2 + 5x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 6x + 5\)
\(y = \dfrac{5}{x^{2}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{10}{x^{3}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\frac{1}{(4x+5)^4}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{16}{(4x+5)^5}\)
\(y=(2x+8)(9x-2)\)
Find \( \dfrac{dy}{dx}\)
\(36x+68\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
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:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =15x^2 - 18x + 7\)
Find \( \int y \quad dx\)
\(5x^3 - 9x^2 + 7x+c\)
A game is played 16 times and the probability of winning is 0.1. Calculate the probability of winning exactly 12 times. 0.00000000119
Make up a maths question using this:
\(S_n = \dfrac{u_1(r^n-1)}{r-1}\)
The sum of a geometric sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{6} = -26\)
\(u_{12} = -50\)
Find the sum of the first 40 terms.-3360
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
BC = 6.6cm.
CA = 12.8cm.
BĈA = 44.3°
Find AB to 1 dp.
9.3cm
Evaluate:
$$\sum_{n=1}^{8} n^2 - 8n$$
-84
\(f(x)=-3x^2+6x-2\)
What is the value of the discriminant and what does it indicate?
12, Two distinct roots
\(f(x)=x^2+7x-6\)
By completing the square find the coordinates of the vertex.
(-3.5, -18.25)
Evaluate \(\log_5(625) \)
4
Find the integral:
\(\int x\sqrt{x^2+3} \;dx\)
\(\frac{1}{3}(x^2+3)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-8, 23) and (4, -13)
\(y=-3x-1\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-18}{16}\)
\((16x+18)²\)
\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)
\(16x^2+48x+39\)
Write in standard form:
\((a \times 10^2) \div (b\times 10^4)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{-2}\)
Draw a rough sketch of
\(y=3-\dfrac{10}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( g-7h-7i=-59 \\ 2g-2h+i= 8\\ 5g+3h+i = 35\)
g = 4, h = 3, i = 6
Find the perimeter of a sector with radius 5.1cm and angle \( \frac{\pi}{4}\)
🍕
14.2cm
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:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The sum of the first 4 terms of a geometric sequence is 312 and the sum of the first 5 terms is 1562. What is the first term?
2
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{8}_{0} e^x dx\)
\(e^{8}- 1 \approx 2980\)
Tin A contains 7 red balls and 9 green balls. Tin B contains 10 red balls and 12 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.
\(\frac{160}{237}\)
There are eight different ways that three planes can relate in three dimensions. One is where they all intersect at a point. How many of the other seven ways can you sketch or describe?
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
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 \( 2^n > n^2 \) for all integers \( n \) greater
than four
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
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)
Calculate the standard deviation of the following numbers:
6, 10, 12, 14, 18
4
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