Find the first three terms in the expansion of:
\((3a - 4b)^9\)
\(=19683a^9 - 236196a^8b \\+1259712a^7b^2 ...\)
If £240 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 6 years. £343.08
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,2),(6,8),(-5,7)\)
(0,13)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(3x^2+4x-4\)
\((x+2)(3x-2)\)
Draw a rough sketch of the graph of:
\(2y=x-2\)
Gradient 0.5
y intercept -1
What is the value of:
\(4^{1}\)
\(= 4\)
Find angle BCA if AC = 3.2m and BC = 5.1m. 51.1o
Find AC if angle BCA = 36o and AB = 4.9m. 6.74m
Describe the red region.
\(y = 2x^3 - 8x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 16x + 4\)
\(y = \dfrac{4}{x^9} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{36}{x^10} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=\sqrt{2x^8-4x}\)
Find \( \dfrac{dy}{dx}\)
\((8x^7-2)(2x^8-4x)^{-\frac{1}{2}}\)
\(y=x(5x^2+6)^6\)
Find \( \dfrac{dy}{dx}\)
\((5x^2+6)^6+60x^2(5x^2+6)^5\)
\(y=\frac{x^2+5}{3x-7}\)
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:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =18x^2 - 4x + 7\)
Find \( \int y \quad dx\)
\(6x^3 - 2x^2 + 7x+c\)
A game is played 18 times and the probability of winning is 0.6. Calculate the probability of winning exactly 9 times. 0.128
Make up a maths question using this:
\(u_n=u_1+(n-1)d\)
The nth term of an arithmetic sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{6} = -45\)
\(u_{18} = -165\)
Find the sum of the first 19 terms.-1615
Find the equations of the asymptotes of:
\(y=10+\dfrac{9x}{5-3x}\)
\(x=\frac{5}{3},y=7\)
In the triangle ABC,
AB = 9.1cm.
BC = 6.8cm.
CA = 7.3cm.
Find angle CÂB.
47.4°
Evaluate:
$$\sum_{n=2}^{5} 2^n$$
60
\(f(x)=2x^2-7x+7\)
What is the value of the discriminant and what does it indicate?
-7, No real roots
\(f(x)=x^2+3x+5\)
By completing the square find the coordinates of the vertex.
(-1.5, 2.75)
Solve for x:
\(\log_2(x) = 4\)
16
Find the integral:
\(\int \dfrac{x^2}{x^3-1} \;dx\)
\(\frac{1}{3} \ln(x^3-1)+c\)
Find the equation of the straight line that passes through:
(-4, -18) and (1, -3)
\(y=3x-6\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-18}{15}\)
\((15x+18)²\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
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
\(y=\dfrac{5}{x}\)
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
$$\cos{720°}$$\(1\)
Solve:
\(2d+3e-4f = 2 \\ d-e-f= -4\\ 9d+2e-2f=43\)
d = 5, e = 4, f = 5
Find the perimeter of a sector with radius 9.1cm and angle \( \frac{2\pi}{3}\)
🍕
37.3cm
In how many ways can 12 different books be arranged on a shelf if 4 of them must be together?
8709120
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The 6th term of a geometric sequence is 4096 and the sum of the first 6 terms is 5460. Find the first term.
4
Find the first 4 terms in the expansion of:
\((1+4x)^{\frac{3}{2}}\)
\(1+6x+6x^2-4x^3\)
Evaluate:
\(\int^{7}_{0} (x-8)^2 \; dx\)
\(170.333333333333\)
Every family in Happyland has either has a car or a motor scooter or both. 51% of the families have a car. 59% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.
\(\dfrac{10}{51}\)
Find the vector product:
\( \begin{pmatrix} 5 \\ 3 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 6 \\ -5 \\ 5 \end{pmatrix} \)
\( \begin{pmatrix} 15 \\ -25 \\ -43 \end{pmatrix} \)
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int x\tan^{-1}x\; dx\)
\((\frac{x^2+1}{2})tan^{-1}x-\frac{x}{2}+c\)
Simplify:
$$\sec{x}-\tan{x}\sin{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x\) is rotated about the x-axis for \(0 \le x \le 1\)
\(\frac{\pi}{3}\) cubic units
What is the binomial theorem?
Clue: Expand \( (a + b)^n \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sin(x)\)
\(x - \frac{x^3}{6} + \frac{x^5}{120} - \frac{x^7}{5040}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
Prove by mathematical induction that \( 5^n - 1 \) is divisible by 4 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{75}$$
\(5\sqrt{3}\)
Simplify:
$$\dfrac{9}{\sqrt{6}}$$\(\frac{9\sqrt{6}}{6} = \frac{3\sqrt{6}}{2}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{3}{7 - \sqrt{2}}$$\(\frac{21 + 3\sqrt{2}}{47}\)
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