Find the first three terms in the expansion of:
\((4a - 3b)^9\)
\(=262144a^9 - 1769472a^8b \\+5308416a^7b^2 ...\)
If £100 is invested with an interest rate of 3% compounded quarterly, find the value of the investment after 5 years. £116.12
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,4),(8,8),(-1,9)\)
(4,13)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Factorise:
\(3x^2+10x-8\)
\((x+4)(3x-2)\)
Draw a rough sketch of the graph of:
\(y=-x\)
Gradient -1
y intercept 0
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle ABC if AC = 4.2m and AB = 5.6m. 36.9o
Find AB if angle ABC = 66o and BC = 4m. 1.63m
Describe the red region.
\(y = 3x^3 - 8x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 16x + 3\)
\(y = \dfrac{6}{x^{2}} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{12}{x^{3}} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\sqrt{4x^4-2x}\)
Find \( \dfrac{dy}{dx}\)
\((8x^3-1)(4x^4-2x)^{-\frac{1}{2}}\)
\(y=e^{8x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(8e^{8x}cosx-e^{8x}sinx\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(y = 0\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =18x^2 - 4x + 7\)
Find \( \int y \quad dx\)
\(6x^3 - 2x^2 + 7x+c\)
A game is played 17 times and the probability of winning is 0.8. Calculate the probability of winning exactly 10 times. 0.0267
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:
\(u_{8} = 57\)
\(u_{11} = 78\)
Find the sum of the first 50 terms.8975
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 8.5cm.
BC = 8.1cm.
CA = 12.7cm.
Find angle CÂB.
38.9°
Evaluate:
$$\sum_{n=3}^{7} n^2 - 3n$$
60
\(f(x)=8x^2+8x-8\)
What is the value of the discriminant and what does it indicate?
320, Two distinct roots
\(f(x)=x^2+2x+4\)
By completing the square find the coordinates of the vertex.
(-1, 3)
Simplify:
\(\log_2(4\sqrt{16})\)
4
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, -24) and (4, 0)
\(y=2x-8\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-9}}{4}\)
\(16x²+9\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(y=3-\dfrac{10}{x}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\(2x+y-3z= -2 \\ 3x+y+z= 26 \\ x-y+2z = 8\)
x = 4, y = 8, z = 6
Find the perimeter of a sector with radius 8.1cm and angle \( \frac{\pi}{4}\)
🍕
22.6cm
How many ways can nine children sit in a row without the youngest being in the middle?
322560
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
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:
\(\int^{5}_{1} x^2-2x+7 \; dx\)
\(45.3\)
Box A contains 6 red and 8 blue cubes, and box B contains 11 red and 12 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?
\(\dfrac{77}{146}\)
Find the vector equation of the line:
\( \dfrac{x-6}{6} = \dfrac{9-y}{2} = \dfrac{z}{9} \)
\( \mathbf{r} = \begin{pmatrix} 6 \\ 9 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 6 \\ -2 \\ 9 \end{pmatrix} \)
Simplify
$$ (5-6i)(5-5i) $$
\(-5-55i\)
Evaluate:
\(\int x\tan^{-1}x\; dx\)
\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)
Simplify:
$$\cos^3{x}+\sin^2{x}\cos{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)
\(\frac{65\pi}{4}\) 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
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
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 the product of \( n \) consecutive integers is divisible by \( n! \) (n factorial)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{18}$$
\(3\sqrt{2}\)
Simplify:
$$\dfrac{2}{\sqrt{10}}$$\(\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}\)
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:
9, 13, 15, 17, 21
4
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