Find the first three terms in the expansion of:
\((3a - 2b)^9\)
\(=19683a^9 - 118098a^8b \\+314928a^7b^2 ...\)
If £140 is invested with an interest rate of 1% compounded quarterly, find the value of the investment after 9 years. £153.17
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,3),(4,6),(-2,6)\)
(1,9)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+x-2\)
\((x+2)(x-1)\)
Factorise:
\(2x^2-5x-12\)
\((2x+3)(x-4)\)
Draw a rough sketch of the graph of:
\(y=-2x+1\)
Gradient -2
y intercept 1
What is the value of:
\(3^{-1}\)
\(= \frac{1}{3}\)
Find angle ABC if AC = 3m and BC = 5m. 36.9o
Find AC if angle ABC = 26o and BC = 5.7m. 2.50m
Describe the red region.
\(y = 5x^3 - 4x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 8x + 2\)
\(y = \dfrac{9}{x^3} - 7\sqrt[8]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{27}{x^4} - \frac{7}{8}x^{-\frac{7}{8}}\)
\(y=(4x^4+9)^8\)
Find \( \dfrac{dy}{dx}\)
\(128x^3(4x^4+9)^7\)
\(y=9x^2e^x\)
Find \( \dfrac{dy}{dx}\)
\(18xe^x+9x^2e^x\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = 17 - 13x\)
Find the equation of the normal to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 5\frac{1}{2} - \frac{x}{2}\)
\(y =24x^2 - 14x + 9\)
Find \( \int y \quad dx\)
\(8x^3 - 7x^2 + 9x+c\)
A game is played 20 times and the probability of winning is 0.4. Calculate the probability of winning exactly 9 times. 0.160
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:
\(u_{7} = -13\)
\(u_{20} = -65\)
Find the sum of the first 25 terms.-925
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BĈA = 74.0°.
BC = 5.7cm.
AB̂C = 57.41°.
Find CA to 1 dp.
6.4cm
Evaluate:
$$\sum_{n=0}^{6} 2n+2$$
56
\(f(x)=-4x^2+9x+3\)
What is the value of the discriminant and what does it indicate?
129, Two distinct roots
\(f(x)=x^2-4x-1\)
By completing the square find the coordinates of the vertex.
(2, -5)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int 3xe^{x^2} \;dx\)
\(\frac{3}{2}e^{x^2}+c\)
Find the equation of the straight line that passes through:
(-5, -17) and (3, -1)
\(y=2x-7\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-16}{19}\)
\((19x+16)²\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\(a \times 10^p \times b\times 10^q\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^{p+q+1}\)
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
$$\cos{\frac{\pi}{6}} \times \sin{45°}$$\(\dfrac{\sqrt{6}}{4}\)
Without a calculator find the exact value of
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\(2x+y-3z= 0 \\ 3x+y+z= 25 \\ x-y+2z = 10\)
x = 5, y = 5, z = 5
Find the area of a sector with radius 5.3cm and angle \( \frac{2\pi}{3}\)
🍕
29.4cm2
How many ways can nine children sit in a row without the youngest being in the middle?
322560
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{10} 3 \times 2^{k-1} $$
3069
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:
\(\int^{3}_{1} x^2-2x+7 \; dx\)
\(14.7\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.05. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.513\)
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
$$ (4-5i)(3-4i) $$
\(-8-31i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\cos^3{x}+\sin^2{x}\cos{x}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x^3\) is rotated about the y-axis for \(1 \le y \le 2\)
\(\approx 4.10\) cubic units
How do you determine the domain of a function?
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sqrt{x+1}\)
\(1 + \frac{x}{2} - \frac{x^2}{8} + \frac{x^3}{16}\)
Find the five 5th roots of 1
\(1, cis\frac{2\pi}{5}, cis\frac{4\pi}{5},\\ cis\frac{-2\pi}{5}, cis\frac{-4\pi}{5}\)
Of the 22 people on boat, 3 are professional singers. If 4 people get sea sick, determine the chance that all three singers do not.
204/385 or 53.0%
Prove by mathematical induction that \( 2^n > n^2 \) for all integers \( n \) greater
than four
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{32}$$
\(4\sqrt{2}\)
Simplify:
$$\dfrac{5}{2\sqrt{3}}$$\(\frac{5\sqrt{3}}{6}\)
Simplify
\(4\sqrt{7} - \sqrt{63}\)
\(\sqrt{7}\)
Simplify:
$$\dfrac{4}{6 - \sqrt{5}}$$\(\frac{24 + 4\sqrt{5}}{31}\)
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