Find the first three terms in the expansion of:
\((4a - 2b)^6\)
\(=4096a^6 - 12288a^5b \\+15360a^4b^2 ...\)
If £180 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 4 years. £194.95
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,2),(11,5),(2,8)\)
(8,11)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+3x-4\)
\((x+4)(x-1)\)
Factorise:
\(4x^2+3x-1\)
\((x+1)(4x-1)\)
Draw a rough sketch of the graph of:
\(2y=x-4\)
Gradient 0.5
y intercept -2
What is the value of:
\(1^{0}\)
\(= 1\)
Find angle BCA if AB = 5.2m and BC = 6.4m. 54.3o
Find AB if angle ABC = 22o and BC = 5.3m. 4.91m
Describe the red region.
\(y = 7x^3 - 3x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(21x^2 - 6x + 9\)
\(y = \dfrac{9}{x^8} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{72}{x^9} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=\sqrt{4x^2-4x}\)
Find \( \dfrac{dy}{dx}\)
\((4x^1-2)(4x^2-4x)^{-\frac{1}{2}}\)
\(y=(3x+7)(7x-5)\)
Find \( \dfrac{dy}{dx}\)
\(42x+34\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =12x^2 - 12x + 3\)
Find \( \int y \quad dx\)
\(4x^3 - 6x^2 + 3x+c\)
A game is played 15 times and the probability of winning is 0.5. Calculate the probability of winning exactly 12 times. 0.0139
What's this?
\( \int \dfrac{1}{x} = \ln |x| + c\)
Reciprocal Integral formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 28\)
\(u_{15} = 46\)
Find the sum of the first 28 terms.1246
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-{1}{5}\)
In the triangle ABC,
AB = 9.3cm.
BC = 5.5cm.
CÂB = 23.9°.
Find angle BĈA.
43.3° or 136.7°
Evaluate:
$$\sum_{n=1}^{5} 2^n$$
62
\(f(x)=-5x^2+4x+6\)
What is the value of the discriminent and what does it indicate?
136, Two distinct roots
\(f(x)=x^2+5x+5\)
By completing the square find the coordinates of the vertex.
(-2.5, -1.25)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int \dfrac{\ln(x)}{x} \;dx\)
\(\dfrac{\ln(x)^2}{2}+c\)
Find the equation of the straight line that passes through:
(-9, -8) and (7, 8)
\(y=x+1\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-14}{14}\)
\((14x+14)²\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
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
\(y=\dfrac{5}{x}\)
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
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\( j+k+l= 11 \\ 2j-3k+9l= 31\\ -j+k-3l=-13\)
x=8, y=1, z=2
Find the perimeter of a sector with radius 4.3cm and angle \( \frac{5\pi}{6}\)
🍕
19.9cm
A safe has a four-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
2520
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
Find the first 4 terms in the expansion of:
\((1+2x)^{\frac12}\)
\(1+x-\frac{x^2}{2}+\frac{x^3}{2}\)
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