Find the first three terms in the expansion of:
\((3a - 4b)^4\)
\(=81a^4 - 432a^3b \\+864a^2b^2 ...\)
If £240 is invested with an interest rate of 6% compounded monthly, find the value of the investment after 8 years. £387.39
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,3),(7,9),(-2,6)\)
(1,12)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2-2x-3\)
\((x+1)(x-3)\)
Factorise:
\(5x^2+19x-4\)
\((x+4)(5x-1)\)
Draw a rough sketch of the graph of:
\(y=2x\)
Gradient 2
y intercept 0
What is the value of:
\(5^{1}\)
\(= 5\)
Find angle ABC if AB = 5.1m and BC = 6.4m. 37.2o
Find AB if angle ABC = 52o and BC = 5.1m. 3.14m
Describe the red region.
\(y = 5x^3 - 4x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 8x + 6\)
\(y = \dfrac{3}{x^5} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{15}{x^6} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\sqrt{3x^8+4}\)
Find \( \dfrac{dy}{dx}\)
\(12x^7(3x^8+4)^{-\frac{1}{2}}\)
\(y=x^5 \sin x\)
Find \( \dfrac{dy}{dx}\)
\(5x^4sinx+x^5cosx\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =24x^2 - 16x + 8\)
Find \( \int y \quad dx\)
\(8x^3 - 8x^2 + 8x+c\)
A game is played 16 times and the probability of winning is 0.9. Calculate the probability of winning exactly 11 times. 0.0137
Make up a maths question using this:
\( A = 4\pi r^2 \)
Surface area of a sphere
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -26\)
\(u_{17} = -110\)
Find the sum of the first 45 terms.-6840
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
AB = 5.4cm.
BC = 6.1cm.
CA = 7.2cm.
Find angle CÂB.
55.7°
Evaluate:
$$\sum_{n=1}^{6} 2n+0$$
42
\(f(x)=-3x^2-6x-1\)
What is the value of the discriminent and what does it indicate?
24, Two distinct roots
\(f(x)=x^2+2x+6\)
By completing the square find the coordinates of the vertex.
(-1, 5)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-2, -1) and (4, -19)
\(y=-3x-7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-15}{17}\)
\((17x+15)²\)
\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)
\(16x^2+48x+39\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^{p+q}\)
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
$$\cos{\frac{\pi}{4}} + \sin{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( j+k+l= 17 \\ 2j-3k+9l= 24\\ -j+k-3l=-9\)
j = 3, k = 9, l = 5
Find the perimeter of a sector with radius 4.2cm and angle \( \frac{2\pi}{3}\)
🍕
17.2cm
In how many ways can 12 different books be arranged on a shelf if 3 of them must be together?
21772800
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\((1+x)^{-8}\)
\(1-8x-36x^2-120x^3\)
Evaluate:
\(\int^{140}_{70} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
27 Scouts went hiking. 14 got lost, 11 got blisters, and 6 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{5}{13}\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 9 \\ 4 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 8 \\ -3 \\ 3 \end{pmatrix} \; \text{and} \; \begin{pmatrix} -1 \\ -7 \\ 3 \end{pmatrix} \)
33.0 square units
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) cubic units
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)
\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)
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
Write down a summary of your last Maths lesson focussing on what you learnt.
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