Find the first three terms in the expansion of:
\((3a - 2b)^9\)
\(=19683a^9 - 118098a^8b \\+314928a^7b^2 ...\)
If £180 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 8 years. £247.75
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,3),(7,9),(-4,8)\)
(1,14)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2-1\)
\((x+1)(x-1)\)
Factorise:
\(20x^2-11x-4\)
\((4x+1)(5x-4)\)
Draw a rough sketch of the graph of:
\(2y=x-2\)
Gradient 0.5
y intercept -1
What is the value of:
\(1^{\frac{1}{3}}\)
\(= 1\)
Find angle ABC if AB = 4.6m and BC = 5.7m. 36.2o
Find AC if angle BCA = 42o and AB = 5.7m. 6.33m
Describe the red region.
\(y = 5x^3 - 3x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 6x + 4\)
\(y = \dfrac{8}{x^9} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{72}{x^10} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=\sqrt{6x^8-2x}\)
Find \( \dfrac{dy}{dx}\)
\((24x^7-1)(6x^8-2x)^{-\frac{1}{2}}\)
\(y=(3x+7)(9x-2)\)
Find \( \dfrac{dy}{dx}\)
\(54x+57\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
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:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =6x^2 - 18x + 3\)
Find \( \int y \quad dx\)
\(2x^3 - 9x^2 + 3x+c\)
A game is played 13 times and the probability of winning is 0.1. Calculate the probability of winning exactly 7 times. 0.0000912
What's this?
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 43\)
\(u_{17} = 83\)
Find the sum of the first 43 terms.4644
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 8.9cm.
BC = 6.7cm.
CÂB = 40.4°.
Find angle BĈA.
59.3° or 120.7°
Evaluate:
$$\sum_{n=2}^{8} 72 - n^2$$
301
\(f(x)=4x^2+7x+7\)
What is the value of the discriminent and what does it indicate?
-63, No real roots
\(f(x)=x^2+4x-7\)
By completing the square find the coordinates of the vertex.
(-2, -11)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)
\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-8, -25) and (2, 5)
\(y=3x-1\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-9}{8}}\)
\(8x²+9\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
Write in standard form:
\((a \times 10^4) \div (b\times 10^{-2})\)
where \(a \div b \) is a decimal number \((0.1 \le \frac{a}{b} \lt 1)\)
\(\frac{10a}{b}\times10^5\)
Draw a rough sketch of
\(y=\sin(x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\(2x+y-3z= 19 \\ 3x+y+z= 35 \\ x-y+2z = 3\)
x=8, y=9, z=2
Find the area of a sector with radius 3.5cm and angle \( \frac{\pi}{4}\)
🍕
4.81cm2
How many ways can ten people be divided into two equal groups?
126
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
10
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt[3]{1+x}}\)
\(1 - \frac{x}{3} + \frac{2x^2}{9} - \frac{14x^3}{81}\)
Evaluate:
\(\int^{140}_{70} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.05. 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?
\(0.513\)
Find the parametric equation of the line:
\( \dfrac{x-5}{8} = \dfrac{8-y}{7} = \dfrac{z}{5} \)
\( x=5+8\lambda \quad y = 8 -7\lambda \quad z=5 \lambda \)
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
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