Find the first three terms in the expansion of:
\((3a - 2b)^9\)
\(=19683a^9 - 118098a^8b \\+314928a^7b^2 ...\)
If £100 is invested with an interest rate of 6% compounded monthly, find the value of the investment after 4 years. £127.05
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((5,2),(10,7),(0,7)\)
(5,12)
\( X \sim N(9.03, 0.89^2)\)
Find
\( P(7.15\lt X \lt9.01) \)
\(0.474\)
Factorise:
\(x^2+2x-8\)
\((x+4)(x-2)\)
Factorise:
\(15x^2-4x-3\)
\((3x+1)(5x-3)\)
Draw a rough sketch of the graph of:
\(y=-x-1\)
Gradient -1
y intercept -1
What is the value of:
\(4^{0}\)
\(= 1\)
Find angle ABC if AB = 5.8m and BC = 7.2m. 36.3o
Find AC if angle ABC = 45o and BC = 5m. 3.54m
Describe the red region.
\(y = 6x^3 - 5x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 10x + 9\)
\(y = \dfrac{9}{x^2} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{18}{x^3} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=3\ln (4x^2+5)\)
Find \( \dfrac{dy}{dx}\)
\(24x(4x^2+5)^{-1}\)
\(y=x(5x^2+6)^6\)
Find \( \dfrac{dy}{dx}\)
\((5x^2+6)^6+60x^2(5x^2+6)^5\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
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:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =21x^2 - 4x + 7\)
Find \( \int y \quad dx\)
\(7x^3 - 2x^2 + 7x+c\)
A game is played 11 times and the probability of winning is 0.7. Calculate the probability of winning exactly 10 times. 0.0932
Make up a maths question using this:
\(z=\dfrac{x-\mu}{\sigma}\)
Standardised Normal Variable
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = 90\)
\(u_{17} = 160\)
Find the sum of the first 34 terms.5610
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
BĈA = 66.5°.
BC = 7.8cm.
AB̂C = 63.88°.
Find CA to 1 dp.
9.2cm
Evaluate:
$$\sum_{n=3}^{7} 76 - n^2$$
245
\(f(x)=5x^2+9x+8\)
What is the value of the discriminent and what does it indicate?
-79, No real roots
\(f(x)=x^2-4x-2\)
By completing the square find the coordinates of the vertex.
(2, -6)
Simplify:
\(\log_2(4\sqrt{16})\)
4
Find the integral:
\(\int \sin(x)\cos^2(x) \;dx\)
\(-\frac{1}{3} \cos^3(x)+c\)
Find the equation of the straight line that passes through:
(-4, 9) and (9, -4)
\(y=-x+5\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-2}\)
\(x²+2\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
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
\(y=x^3-4x\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{4}} \times \cos{45°}$$\(\dfrac{1}{2}\)
Without a calculator find the exact value of
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\(2d+3e-4f = 4 \\ d-e-f= 0\\ 9d+2e-2f=43\)
d = 5, e = 2, f = 3
Find the perimeter of a sector with radius 4.2cm and angle \( \frac{\pi}{4}\)
🍕
11.7cm
Ansh is with eight people in a queue. How many ways can they line up without Ansh being at the back?
322560
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The 8th term of a geometric sequence is 312500 and the sum of the first 8 terms is 390624. Find the first term.
4
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:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
Box A contains 5 red and 6 blue cubes, and box B contains 7 red and 8 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?
\(\dfrac{77}{152}\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 8 \\ 8 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 2 \\ -3 \\ 2 \end{pmatrix} \; \text{and} \; \begin{pmatrix} -6 \\ -11 \\ 2 \end{pmatrix} \)
23.0 square units
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x(4-x)\) is rotated about the x-axis for \(0 \le x \le 4\)
\(\frac{512\pi}{15}\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Expand and simplify:
$$ (i-\sqrt{3})^5 $$
\(16\sqrt{3} + 16i \\ \text{or } 16(\sqrt{3} + i)\)
A team of 11 is randomly chosen from a squad of 18 including the club captain and vice captain. Determine the probability that both the captain and vice-captain are chosen.
55/153 or 35.9%
Prove by mathematical induction that the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
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