Find the first three terms in the expansion of:
\((4a - 2b)^9\)
\(=262144a^9 - 1179648a^8b \\+2359296a^7b^2 ...\)
If £180 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 5 years. £242.43
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,1),(8,7),(-4,7)\)
(2,13)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2+3x-4\)
\((x+4)(x-1)\)
Factorise:
\(5x^2+11x-12\)
\((x+3)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=-2x-2\)
Gradient -2
y intercept -2
What is the value of:
\(1^{0}\)
\(= 1\)
Find angle ABC if AB = 3m and BC = 4.6m. 49.3o
Find AC if angle ABC = 21o and BC = 4.4m. 1.58m
Describe the red region.
\(y = 9x^3 - 4x^2 + 8x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 8x + 8\)
\(y = \dfrac{6}{x^5} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{30}{x^6} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=(4x^5+2)^8\)
Find \( \dfrac{dy}{dx}\)
\(160x^4(4x^5+2)^7\)
\(y=\sin x \cos x\)
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:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)
Find the equation of the normal to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 9\frac{1}{3} - \frac{x}{6}\)
\(y =18x^2 - 6x + 3\)
Find \( \int y \quad dx\)
\(6x^3 - 3x^2 + 3x+c\)
A game is played 10 times and the probability of winning is 0.2. Calculate the probability of winning exactly 5 times. 0.0264
Make up a maths question using this:
\( P(A|B) = \dfrac{P(A \cap B)}{P(B)} \)
Conditional probability formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -25\)
\(u_{19} = -81\)
Find the sum of the first 40 terms.-3480
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
AB = 6.8cm.
BC = 8.4cm.
CA = 11.7cm.
Find angle CÂB.
45.0°
Evaluate:
$$\sum_{n=1}^{6} n^2 - 4n$$
7
\(f(x)=6x^2+6x-5\)
What is the value of the discriminent and what does it indicate?
156, Two distinct roots
\(f(x)=x^2-2x+7\)
By completing the square find the coordinates of the vertex.
(1, 6)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-1, -2) and (2, 1)
\(y=x-1\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-6}\)
\(x²+6\)
\(\text{Find }f(x) \text{ if} \\ ff(2a-3)=\\18a-27 \\\)
\(f(x)=3x\)
Write in standard form:
\(a \times 10^{-1} \times b\times 10^{-1}\)
where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)
\(\frac{ab}{100}\times10^0\)
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
$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$\(0\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\(2x+y-3z= 5 \\ 3x+y+z= 11 \\ x-y+2z = 0\)
x = 2, y = 4, z = 1
Find the perimeter of a sector with radius 4.6cm and angle \( \frac{5\pi}{6}\)
🍕
21.2cm
In how many ways can 9 different books be arranged on a shelf if 4 of them must be together?
17280
Find the equations of the asymptotes of:
$$y=\dfrac{8x^2-19x-15}{1-2z}$$x=1/2,y=15/2-4x
The fourth term of a geometric sequence is \(-16\) and the sum to infinity is \(32\). What is the common ratio?
-0.669, 1.25
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(3+x)^2}\)
\(\frac{1}{9}-\frac{2x}{27}+\frac{x^2}{27}-\frac{4x^3}{243}\)
Evaluate:
\(\int^{4}_{1} (x-8)^2 \; dx\)
\(93\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.09. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.524\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 5 \\ 6 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 2 \\ -3 \\ 8 \end{pmatrix} \; \text{and} \; \begin{pmatrix} -3 \\ -9 \\ 8 \end{pmatrix} \)
34.0 square units
Simplify
$$ (4-3i)(3-5i) $$
\(-3-29i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\dfrac{\sin^2{x}-1}{\cos{x}}$$\(-\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\frac{1}{x}\) is rotated about the x-axis for \(1 \le x \le 2\)
\(\frac{\pi}{2}\) cubic units
What is the binomial theorem?
Clue: Expand \( (a + b)^n \)
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 4 is randomly selected from 8 men and 11 women. Determine the likelihood that it consists of all men.
35/1938 or 1.81%
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
Write down a summary of your last Maths lesson focussing on what you learnt.
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