Find the first three terms in the expansion of:
\((2a - 4b)^7\)
\(=128a^7 - 1792a^6b \\+10752a^5b^2 ...\)
If £240 is invested with an interest rate of 1% compounded monthly, find the value of the investment after 5 years. £252.30
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((3,2),(7,6),(-1,6)\)
(3,10)
\( X \sim N(100, 7^2)\)
Find
\( P(93\lt X \lt107) \)
\(0.683\)
Factorise:
\(x^2-1\)
\((x+1)(x-1)\)
Factorise:
\(2x^2+5x-3\)
\((x+3)(2x-1)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(3^{0}\)
\(= 1\)
Find angle ABC if AC = 3.3m and AB = 4.6m. 35.7o
Find AC if angle ABC = 28o and AB = 4.8m. 2.55m
Describe the red region.
\(y = 8x^3 - 5x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(24x^2 - 10x + 3\)
\(y = \dfrac{5}{x^{2}} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{10}{x^{3}} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=\sin (3x^2+4)\)
Find \( \dfrac{dy}{dx}\)
\(6xcos(3x^2+4)\)
\(y=x \tan x\)
Find \( \dfrac{dy}{dx}\)
\(tanx+\frac{x}{cos^2x}\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =9x^2 - 16x + 4\)
Find \( \int y \quad dx\)
\(3x^3 - 8x^2 + 4x+c\)
A game is played 16 times and the probability of winning is 0.8. Calculate the probability of winning exactly 2 times. 0.0000000126
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:
\(u_{7} = -30\)
\(u_{19} = -114\)
Find the sum of the first 26 terms.-1963
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
AB = 6.2cm.
BC = 9.3cm.
CA = 11.9cm.
Find angle CÂB.
50.6°
Evaluate:
$$\sum_{n=1}^{5} n^2 - 2n$$
25
\(f(x)=6x^2-7x-1\)
What is the value of the discriminant and what does it indicate?
73, Two distinct roots
\(f(x)=x^2-6x+5\)
By completing the square find the coordinates of the vertex.
(3, -4)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)
\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-3, 0) and (3, 6)
\(y=x+3\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-3\)
\((x+3)²\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\(a \times 10^3 \times b\times 10^5\)
where \(a \times b \) is a single digit number \((1 \le ab \lt 10)\)
\(ab\times10^8\)
Draw a rough sketch of
\(y=x^2-8\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\( 5a+2b+c=22 \\ 3a+4b+2c= 30 \\ a+5b+c=29\)
a = 2, b = 5, c = 2
Find the area of a sector with radius 9.7cm and angle \( \frac{\pi}{4}\)
🍕
36.9cm2
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:
$$y=\dfrac{-6x^2+5x}{2x+1}$$x=-1/2,y=4-3x
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:
\(\int^{6}_{0} e^x dx\)
\(e^{6}- 1 \approx 402\)
Each afternoon the probability my cat sleeps is 0.6 and the probability that my dog sleeps is 0.7. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon.
\(0.54\)
Find the angle between two unit vectors \(u\) and \(v\) such that the vectors \(2u-3v\) and \(5u+2v\) are perpendicular. Give you answer correct to the nearest degree.
\( 69^o \)
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\ln{x}\) is rotated about the y-axis for \(0 \le y \le 1\)
\(\approx 10.0\) cubic units
How do you use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
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
\(1, i, -1, -i\)
Of the 22 people on boat, 3 are professional singers. If 4 people get sea sick, determine the chance that all three singers do not.
204/385 or 53.0%
Prove by mathematical induction that the sum of the squares of the first \( n \) natural numbers is \( \frac{n(n + 1)(2n + 1)}{6} \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{27}$$
\(3\sqrt{3}\)
Simplify:
$$\dfrac{8}{3\sqrt{7}}$$\(\frac{8\sqrt{7}}{21}\)
Simplify
\((1 + \sqrt{2})(2 + \sqrt{2})\)
\(4 + 3\sqrt{2}\)
Simplify:
$$\dfrac{3}{4 + \sqrt{2}}$$\(\frac{12 - 3\sqrt{2}}{14} = \frac{6 - \sqrt{2}}{7}\)
Calculate the standard deviation of the following numbers:
15, 19, 19, 21, 21, 25
3
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