Find the first three terms in the expansion of:
\((3a - 4b)^4\)
\(=81a^4 - 432a^3b \\+864a^2b^2 ...\)
If £120 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 9 years. £171.90
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,2),(5,6),(-3,6)\)
(1,10)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2-9\)
\((x+3)(x-3)\)
Factorise:
\(5x^2+11x-12\)
\((x+3)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=-x+1\)
Gradient -1
y intercept 1
What is the value of:
\(25^{\frac{1}{2}}\)
\(= 5\)
Find angle ABC if AC = 5.9m and BC = 6.9m. 58.8o
Find AC if angle ABC = 48o and AB = 3.9m. 4.33m
Describe the red region.
\(y = 6x^3 - 3x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(18x^2 - 6x + 9\)
\(y = \dfrac{9}{x^4} - 4\sqrt[5]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{36}{x^5} - \frac{4}{5}x^{-\frac{4}{5}}\)
\(y=(4x+2)^4\)
Find \( \dfrac{dy}{dx}\)
\(16(4x+2)^3\)
\(y=x \tan x\)
Find \( \dfrac{dy}{dx}\)
\(tanx+\frac{x}{cos^2x}\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = 1 - 5x\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =27x^2 - 8x + 3\)
Find \( \int y \quad dx\)
\(9x^3 - 4x^2 + 3x+c\)
A game is played 18 times and the probability of winning is 0.2. Calculate the probability of winning exactly 16 times. 0.000000000642
Make up a maths question using this:
\( \int \dfrac{1}{x} = \ln |x| + c\)
Reciprocal Integral formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{7} = 44\)
\(u_{17} = 134\)
Find the sum of the first 25 terms.2450
Find the equations of the asymptotes of:
\(y=\dfrac{4-7x}{3-14x}\)
\(x=\frac{3}{14},y=\frac{1}{2}\)
In the triangle ABC,
BC = 9.2cm.
CA = 12.4cm.
BĈA = 25.5°
Find AB to 1 dp.
5.7cm
Evaluate:
$$\sum_{n=0}^{8} n^2 - 6n$$
-12
\(f(x)=9x^2-4x+9\)
What is the value of the discriminent and what does it indicate?
-308, No real roots
\(f(x)=x^2+9x+1\)
By completing the square find the coordinates of the vertex.
(-4.5, -19.25)
Evaluate \(\log_2(32) \)
5
Find the integral:
\(\int \dfrac{\ln(x)}{x} \;dx\)
\(\dfrac{\ln(x)^2}{2}+c\)
Find the equation of the straight line that passes through:
(-8, 18) and (9, -33)
\(y=-3x-6\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x-9}\)
\(x²+9\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
Write in standard form:
\((a \times 10^3) \div (b\times 10^5)\)
where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)
\(\frac{a}{10b}\times10^{-1}\)
Draw a rough sketch of
\(y=x^2-8\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)
Without a calculator find the exact value of
$$\tan{4\pi}$$\(0\)
Solve:
\( 5a+2b+c=30 \\ 3a+4b+2c= 39 \\ a+5b+c=33\)
a = 3, b = 5, c = 5
Find the perimeter of a sector with radius 8.8cm and angle \( \frac{5\pi}{6}\)
🍕
40.6cm
In how many ways can 10 different books be arranged on a shelf if 4 of them must be together?
120960
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
The first term of a geometric sequence is 42 and the fourth term is twice this value. What is the common ratio?
\( \sqrt[3]{2} \)
Find the first 4 terms in the expansion of:
\(\dfrac{1}{2-x}\)
\(\frac{1}{2}+\frac{x}{4}+\frac{x^2}{8}+\frac{x^3}{16}\)
Evaluate:
\(\int^{4}_{0} (x-8)^2 \; dx\)
\(149.333333333333\)
Tin A contains 4 red balls and 5 green balls. Tin B contains 6 red balls and 7 green balls. A dice is thrown and if the score is less than 3 a ball is selected from tin A; otherwise a ball is selected from tin B. Given that the ball selected was red, calculate the probability that it came from tin B.
\(\frac{27}{40}\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
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 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
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Expand and simplify:
$$ (i-\sqrt{3})^5 $$
\(16\sqrt{3} + 16i \\ \text{or } 16(\sqrt{3} + i)\)
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 \( n \) even numbers is \( n(n + 1) \)
Show true for n=1, assume true for n=k, prove for n=k+1
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