Find the first three terms in the expansion of:
\((4a - 3b)^9\)
\(=262144a^9 - 1769472a^8b \\+5308416a^7b^2 ...\)
If £140 is invested with an interest rate of 1% compounded quarterly, find the value of the investment after 9 years. £153.17
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,2),(5,5),(-1,5)\)
(2,8)
\( X \sim N(300, 10^2)\)
Find
\( P(270\lt X \lt330) \)
\(0.997\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
Factorise:
\(3x^2+8x-3\)
\((x+3)(3x-1)\)
Draw a rough sketch of the graph of:
\(y=x+2\)
Gradient 1
y intercept 2
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle ABC if AB = 6m and BC = 7.5m. 36.9o
Find AC if angle ABC = 45o and AB = 5.3m. 5.30m
Describe the red region.
\(y = 4x^3 - 8x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 16x + 3\)
\(y = \dfrac{3}{x^{4}} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{12}{x^{5}} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=(8x+6)^4\)
Find \( \dfrac{dy}{dx}\)
\(32(8x+6)^3\)
\(y=x \tan x\)
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:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(x = -3\)
\(y =21x^2 - 18x + 2\)
Find \( \int y \quad dx\)
\(7x^3 - 9x^2 + 2x+c\)
A game is played 10 times and the probability of winning is 0.4. Calculate the probability of winning exactly 2 times. 0.121
Make up a maths question using this:
\( \int \dfrac{1}{x} = \ln |x| + c\)
Reciprocal Integral formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 75\)
\(u_{11} = 91\)
Find the sum of the first 39 terms.6357
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
BC = 7.3cm.
CA = 7.1cm.
BĈA = 45.7°
Find AB to 1 dp.
5.6cm
Evaluate:
$$\sum_{n=3}^{6} 101 - n^2$$
318
\(f(x)=-9x^2+2x-2\)
What is the value of the discriminant and what does it indicate?
-68, No real roots
\(f(x)=x^2+2x+1\)
By completing the square find the coordinates of the vertex.
(-1, 0)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int \dfrac{x^2}{x^3-1} \;dx\)
\(\frac{1}{3} \ln(x^3-1)+c\)
Find the equation of the straight line that passes through:
(-4, 5) and (4, -11)
\(y=-2x-3\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-8}{3}}\)
\(3x²+8\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
$$\tan{\frac{\pi}{6}} \times \cos{45°}$$\(\dfrac{1}{\sqrt{6}}\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{6}}$$\(\dfrac{1}{\sqrt{3}}\)
Solve:
\( 5a+2b+c=38 \\ 3a+4b+2c= 34 \\ a+5b+c=20\)
a = 6, b = 2, c = 4
Find the perimeter of a sector with radius 3.8cm and angle \( \frac{\pi}{3}\)
🍕
11.6cm
In how many ways can 8 different books be arranged on a shelf if 2 of them must be together?
10080
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:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{5}_{0} e^x dx\)
\(e^{5}- 1 \approx 147\)
Each afternoon the probability my cat sleeps is 0.7 and the probability that my dog sleeps is 0.8. The probability that the dog sleeps given that the cat is sleeping is 0.9. Find the probability that both sleep in the afternoon.
\(0.63\)
Find the angle between the plane and the line:
\(\Pi: \quad 4x+4y-2z=7\)
\(L: \quad x+1= \dfrac{4-y}{2} = 3-z \)
\( \approx 7.82^o \)
Simplify
$$ (3-5i)(3-2i) $$
\(-1-21i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\sin{x}\cot{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
What is the difference between a rational and an irrational number?
Rational can be expressed as a fraction with integer numerator and denominator
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \frac{1}{1-x}\)
\(1 + x + x^2 + x^3\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
5 alphabet blocks A, E, P, R and S are placed at random in a row. What is the likelihood that they spell out either SPEAR or PARSE?
1/60 or 1.67%
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:
$$\sqrt{8}$$
\(2\sqrt{2}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
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:
11, 17, 20, 23, 29
6
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