Find the first three terms in the expansion of:
\((3a - 2b)^5\)
\(=243a^5 - 810a^4b \\+1080a^3b^2 ...\)
If £200 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 5 years. £232.32
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,1),(6,4),(-1,5)\)
(3,8)
\( X \sim N(4.5, 0.35^2)\)
Find
\( P(4.1\lt X \lt4.5) \)
\(0.373\)
Factorise:
\(x^2-1\)
\((x+1)(x-1)\)
Factorise:
\(5x^2+16x-16\)
\((x+4)(5x-4)\)
Draw a rough sketch of the graph of:
\(y=-2x+1\)
Gradient -2
y intercept 1
What is the value of:
\(1^{\frac{1}{3}}\)
\(= 1\)
Find angle ABC if AC = 3.5m and AB = 5.4m. 32.9o
Find AC if angle BCA = 47o and AB = 5m. 4.66m
Describe the red region.
\(y = 8x^3 - 3x^2 + 5x\)
Find \( \dfrac{dy}{dx}\)
\(24x^2 - 6x + 5\)
\(y = \dfrac{2}{x^{4}} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{8}{x^{5}} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=(7x^7+5)^8\)
Find \( \dfrac{dy}{dx}\)
\(392x^6(7x^7+5)^7\)
\(y=x \tan x\)
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:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = \frac{x}{14} + 11\frac{1}{7}\)
\(y =27x^2 - 18x + 6\)
Find \( \int y \quad dx\)
\(9x^3 - 9x^2 + 6x+c\)
A game is played 16 times and the probability of winning is 0.2. Calculate the probability of winning exactly 4 times. 0.200
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:
\(u_{6} = 71\)
\(u_{19} = 240\)
Find the sum of the first 50 terms.16225
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
BC = 6.5cm.
CA = 9.3cm.
BĈA = 55.8°
Find AB to 1 dp.
7.8cm
Evaluate:
$$\sum_{n=1}^{6} 2^n$$
126
\(f(x)=2x^2+4x-2\)
What is the value of the discriminant and what does it indicate?
32, Two distinct roots
\(f(x)=x^2+7x-5\)
By completing the square find the coordinates of the vertex.
(-3.5, -17.25)
Simplify:
\(\log_2(4\sqrt{16})\)
4
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:
(-8, -12) and (5, 14)
\(y=2x+4\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-4\)
\((x+4)²\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(y+x=2\)
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
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\( g-7h-7i=-48 \\ 2g-2h+i= 12\\ 5g+3h+i = 56\)
g = 8, h = 4, i = 4
Find the perimeter of a sector with radius 4.1cm and angle \( \frac{\pi}{6}\)
🍕
10.3cm
Ansh is with six people in a queue. How many ways can they line up without Ansh being at the back?
4320
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
The first term of a geometric sequence is 30 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:
\(\int^{5}_{2} (x-8)^2 \; dx\)
\(63\)
What is the probability that it was machine B that broke down if at least one of the independent machines broke down today, given machine A has a 8% chance and machine B has a 11% chance of breaking down on any given day?
\(0.607\)
Find the point of intersection of these planes:
\(\Pi_1: \quad 2x + y - 3z = -5\)
\(\Pi_2: \quad x - 3y + 2z = 1\)
\(\Pi_3: \quad 3x - 2y + z = 2\)
\( (1,2,3) \)
Simplify
$$ (6+5i)(3+5i) $$
\(-7+45i\)
Evaluate:
\(\int x^2 \ln{x}\; dx\)
\(\frac{x^3}{9}(3\ln x-1)+c\)
Simplify:
$$\sin{x}\cot{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=e^x\) is rotated about the x-axis for \(0 \le x \le 3\)
\(\frac{\pi}{2}(e^6-1)\) cubic units
How do you solve a quadratic inequality?
Factorise the quadratic, then analyze the sign of each factor over its domain.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Find the four 4th roots of 1
\(1, i, -1, -i\)
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 first \( n \) even numbers is \( n(n + 1) \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{8}$$
\(2\sqrt{2}\)
Simplify:
$$\dfrac{2}{\sqrt{10}}$$\(\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}\)
Simplify
\(7\sqrt{7} - 3\sqrt{7}\)
\(4\sqrt{7}\)
Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$\(\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}\)
Calculate the standard deviation of the following numbers:
21, 21, 21, 29, 29, 29
4
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