Find the first three terms in the expansion of:
\((3a - 4b)^7\)
\(=2187a^7 - 20412a^6b \\+81648a^5b^2 ...\)
If £240 is invested with an interest rate of 1% compounded quarterly, find the value of the investment after 5 years. £252.29
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,2),(6,5),(-1,6)\)
(3,9)
\( X \sim N(43, 7^2)\)
Find
\( P(32\lt X \lt45) \)
\(0.554\)
Factorise:
\(x^2+x-6\)
\((x+3)(x-2)\)
Factorise:
\(4x^2+5x-6\)
\((x+2)(4x-3)\)
Draw a rough sketch of the graph of:
\(y=x+2\)
Gradient 1
y intercept 2
What is the value of:
\(5^{-1}\)
\(= \frac{1}{5}\)
Find angle BCA if AB = 3.6m and AC = 5.4m. 33.7o
Find AC if angle BCA = 50o and AB = 3.2m. 2.69m
Describe the red region.
\(y = 3x^3 - 3x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(9x^2 - 6x + 2\)
\(y = \dfrac{5}{x^5} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{25}{x^6} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=\sin (6x^2+7)\)
Find \( \dfrac{dy}{dx}\)
\(12xcos(6x^2+7)\)
\(y=(2x+7)(6x-3)\)
Find \( \dfrac{dy}{dx}\)
\(24x+36\)
\(y=\frac{x^2+5}{3x-7}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3x^2-14x-15)}{(3x-7)^2}\)
Find the equation of the tangent to the curve:
\(y = 3x^2 - 6x + 9\)
where \(x = 2\)
\(y = 6x + 3\)
Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =9x^2 - 14x + 6\)
Find \( \int y \quad dx\)
\(3x^3 - 7x^2 + 6x+c\)
A game is played 15 times and the probability of winning is 0.4. Calculate the probability of winning exactly 13 times. 0.000254
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:
\(u_{8} = 50\)
\(u_{19} = 127\)
Find the sum of the first 26 terms.2301
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 5.5cm.
BC = 9.9cm.
CÂB = 115°.
Find angle BĈA.
30.1°
Evaluate:
$$\sum_{n=3}^{8} 82 - n^2$$
293
\(f(x)=-9x^2+2x-2\)
What is the value of the discriminant and what does it indicate?
-68, No real roots
\(f(x)=x^2+6x+5\)
By completing the square find the coordinates of the vertex.
(-3, -4)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-4, 0) and (5, 9)
\(y=x+4\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-18}{17}\)
\((17x+18)²\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
Write in standard form:
\(a \times 10^2 \times b\times 10^3\)
where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)
\(\frac{ab}{10}\times10^6\)
Draw a rough sketch of
\(y=x(5-x)\)
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
$$\tan{\dfrac{19\pi}{6}}$$\(\dfrac{1}{\sqrt{3}}\)
Solve:
\(2d+3e-4f = 21 \\ d-e-f= -5\\ 9d+2e-2f=46\)
d = 4, e = 7, f = 2
Find the perimeter of a sector with radius 7.1cm and angle \( \frac{\pi}{4}\)
🍕
19.8cm
A safe has a six-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
75600
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\(\dfrac{1}{(1+3x)^3}\)
\(1-9x+54x^2-270x^3\)
Evaluate:
\(\int^{2}_{0} x^2-2x+7 \; dx\)
\(12.7\)
In a bookstore with equally sized fiction and non-fiction sections, if a hardcover book is selected (30% of fiction, 60% of non-fiction are hardcovers), what's the probability it's non-fiction?
\(0.667\)
Find the area of the triangle with sides:
\( \begin{pmatrix} 5 \\ 7 \\ 0 \end{pmatrix}, \; \begin{pmatrix} 7 \\ -3 \\ 9 \end{pmatrix} \; \text{and} \; \begin{pmatrix} 2 \\ -10 \\ 9 \end{pmatrix} \)
50.2 square units
Simplify
$$ \dfrac{3+2i}{4-i}$$
\(\frac{10}{17}+\frac{11}{17}i\)
Evaluate:
\(\int x\sec^2x\; dx\)
\(xtanx+\ln|cosx|+c\)
Simplify:
$$5\sin{x}+3\cos{x}\tan{x}$$\(8\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt[3]{x^2}\) is rotated about the y-axis for \(2 \le y \le 3\)
\(\frac{65\pi}{4}\) 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
\(f(x) = e^x\)
\(1 + x + \frac{x^2}{2} + \frac{x^3}{6}\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
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:
$$\sqrt{48}$$
\(4\sqrt{3}\)
Simplify:
$$\dfrac{9}{\sqrt{6}}$$\(\frac{9\sqrt{6}}{6} = \frac{3\sqrt{6}}{2}\)
Simplify
\(\sqrt{50} - 3\sqrt{2}\)
\(2\sqrt{2}\)
Simplify:
$$\dfrac{5}{2 - \sqrt{3}}$$\(\frac{10 + 5\sqrt{3}}{1} = 10 + 5\sqrt{3}\)
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