Find the first three terms in the expansion of:
\((5a - 2b)^6\)
\(=15625a^6 - 37500a^5b \\+37500a^4b^2 ...\)
If £180 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 5 years. £219.78
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,4),(7,7),(-1,9)\)
(4,12)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
Factorise:
\(x^2+x-12\)
\((x+4)(x-3)\)
Draw a rough sketch of the graph of:
\(y=x+2\)
Gradient 1
y intercept 2
What is the value of:
\(125^{\frac{1}{3}}\)
\(= 5\)
Find angle ABC if AB = 5.5m and BC = 6.5m. 32.2o
Find AC if angle ABC = 53o and BC = 3.7m. 2.95m
Describe the red region.
\(y = 4x^3 - 5x^2 + 3x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 10x + 3\)
\(y = \dfrac{8}{x^7} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{56}{x^8} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\sqrt{8x^8-2x}\)
Find \( \dfrac{dy}{dx}\)
\((32x^7-1)(8x^8-2x)^{-\frac{1}{2}}\)
\(y=x(4x^2+5)^7\)
Find \( \dfrac{dy}{dx}\)
\((4x^2+5)^7+56x^2(4x^2+5)^6\)
\(y=\frac{ \ln x}{x^2}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(1-2lnx)}{x^3}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =15x^2 - 14x + 6\)
Find \( \int y \quad dx\)
\(5x^3 - 7x^2 + 6x+c\)
A game is played 13 times and the probability of winning is 0.4. Calculate the probability of winning exactly 4 times. 0.184
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:
\(u_{7} = 40\)
\(u_{20} = 131\)
Find the sum of the first 32 terms.3408
Find the equations of the asymptotes of:
\(y=\dfrac{2x+5}{2x+3}\)
\(x=-\frac{3}{2},y=1\)
In the triangle ABC,
BC = 8.7cm.
CA = 11.5cm.
BĈA = 44.7°
Find AB to 1 dp.
8.1cm
Evaluate:
$$\sum_{n=0}^{5} 2^n$$
63
\(f(x)=3x^2+2x+6\)
What is the value of the discriminent and what does it indicate?
-68, No real roots
\(f(x)=x^2-8x+4\)
By completing the square find the coordinates of the vertex.
(4, -12)
Write the following in terms of logs to base 10:
\(\log_a(z)\)
\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)
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:
(-9, -11) and (8, 23)
\(y=2x+7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-16}{15}\)
\((15x+16)²\)
\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)
\(147x^2-126x+27\)
Write in standard form:
\(a \times 10^2 \times b\times 10^3\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^6\)
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
$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\( 5a+2b+c=19 \\ 3a+4b+2c= 24 \\ a+5b+c=20\)
x=2, y=3, z=3
Find the perimeter of a sector with radius 9.4cm and angle \( \frac{2\pi}{3}\)
🍕
38.5cm
How many ways can fourteen people be divided into two equal groups?
1716
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$
7.97
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