Find the first three terms in the expansion of:
\((4a - 2b)^9\)
\(=262144a^9 - 1179648a^8b \\+2359296a^7b^2 ...\)
If £240 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 9 years. £287.20
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,5),(8,9),(1,8)\)
(4,12)
\( X \sim N(-25, 3^2)\)
Find
\( P(-20\lt X \lt-10) \)
\(0.0478\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(3x^2+8x-3\)
\((x+3)(3x-1)\)
Draw a rough sketch of the graph of:
\(y=2x-1\)
Gradient 2
y intercept -1
What is the value of:
\(5^{0}\)
\(= 1\)
Find angle BCA if AB = 3.3m and AC = 4.5m. 36.3o
Find BC if angle BCA = 46o and AC = 5.1m. 7.34m
Describe the red region.
\(y = 8x^3 - 8x^2 + 5x\)
Find \( \dfrac{dy}{dx}\)
\(24x^2 - 16x + 5\)
\(y = \dfrac{7}{x^{7}} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{49}{x^{8}} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=(5x^4+5)^9\)
Find \( \dfrac{dy}{dx}\)
\(180x^3(5x^4+5)^8\)
\(y=x^6 \sin x\)
Find \( \dfrac{dy}{dx}\)
\(6x^5sinx+x^6cosx\)
\(y=\frac{x+3}{x-5}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{8}{(x-5)^2}\)
Find the equation of the tangent to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 2x + 3\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =24x^2 - 4x + 9\)
Find \( \int y \quad dx\)
\(8x^3 - 2x^2 + 9x+c\)
A game is played 18 times and the probability of winning is 0.6. Calculate the probability of winning exactly 14 times. 0.0614
Make up a maths question using this:
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -30\)
\(u_{16} = -129\)
Find the sum of the first 35 terms.-5145
Find the equations of the asymptotes of:
\(y=10+\dfrac{9x}{5-3x}\)
\(x=\frac{5}{3},y=7\)
In the triangle ABC,
BC = 6.1cm.
CA = 8.1cm.
BĈA = 54.1°
Find AB to 1 dp.
6.7cm
Evaluate:
$$\sum_{n=2}^{8} 2n+1$$
77
\(f(x)=5x^2-5x+8\)
What is the value of the discriminant and what does it indicate?
-135, No real roots
\(f(x)=x^2+2x+6\)
By completing the square find the coordinates of the vertex.
(-1, 5)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-1, 8) and (1, 2)
\(y=-3x+5\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-5\)
\((x+5)²\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
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
\(y=x(5-x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{30°} \div \sin{\frac{\pi}{3}}$$\(1\)
Without a calculator find the exact value of
$$\cos{7\pi}$$\(-1\)
Solve:
\( g-7h-7i=-89 \\ 2g-2h+i= -4\\ 5g+3h+i = 37\)
g = 2, h = 7, i = 6
Find the area of a sector with radius 7.1cm and angle \( \frac{5\pi}{6}\)
🍕
66.0cm2
In how many ways can 9 different books be arranged on a shelf if 2 of them must be together?
80640
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:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{40}_{20} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
Box A contains 7 red and 10 blue cubes, and box B contains 12 red and 14 blue cubes. Finn selects a box at random and takes a cube from that box. Given that the cube is red, what is the probability that it came from box B?
\(\dfrac{102}{193}\)
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
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)
\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)
Solve for \(z\)
$$ z^4 = - 16 $$
\(\sqrt{2}+i\sqrt{2},-\sqrt{2}+i\sqrt{2} \\ \sqrt{2}-i\sqrt{2},-\sqrt{2}-i\sqrt{2}\)
6 girls sit at random on 6 seats in a row. Determine the probability that the two friends Karen and Julie sit at the ends of the row.
1/15 or 6.67%
Prove by mathematical induction that the sum of the first \( n \) natural numbers is \( \frac{n(n + 1)}{2} \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{48}$$
\(4\sqrt{3}\)
Simplify:
$$\dfrac{3}{4\sqrt{2}}$$\(\frac{3\sqrt{2}}{8}\)
Simplify
\((2 - 2\sqrt{2})^2\)
\(12 - 8\sqrt{2}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
Calculate the standard deviation of the following numbers:
11, 17, 20, 23, 29
6
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