Find the first three terms in the expansion of:
\((2a - 4b)^8\)
\(=256a^8 - 4096a^7b \\+28672a^6b^2 ...\)
If £220 is invested with an interest rate of 6% compounded quarterly, find the value of the investment after 8 years. £354.27
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,5),(4,10),(-4,8)\)
(-1,13)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2+2x-3\)
\((x+3)(x-1)\)
Factorise:
\(3x^2+2x-1\)
\((x+1)(3x-1)\)
Draw a rough sketch of the graph of:
\(y=-x-1\)
Gradient -1
y intercept -1
What is the value of:
\(64^{\frac{1}{3}}\)
\(= 4\)
Find angle BCA if AC = 3.2m and BC = 5.2m. 52.0o
Find BC if angle BCA = 49o and AB = 3.4m. 4.51m
Describe the red region.
\(y = 9x^3 - 2x^2 + 2x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 4x + 2\)
\(y = \dfrac{4}{x^2} - 5\sqrt[6]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{8}{x^3} - \frac{5}{6}x^{-\frac{5}{6}}\)
\(y=\sin (2x^2+3)\)
Find \( \dfrac{dy}{dx}\)
\(4xcos(2x^2+3)\)
\(y=e^{3x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(3e^{3x}cosx-e^{3x}sinx\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = 1 - 2x\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =15x^2 - 14x + 6\)
Find \( \int y \quad dx\)
\(5x^3 - 7x^2 + 6x+c\)
A game is played 13 times and the probability of winning is 0.6. Calculate the probability of winning exactly 6 times. 0.131
Make up a maths question using this:
\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)
Trigonometric identity
What letter is this?
Two terms of an arithmetic sequence:
\(u_{10} = 43\)
\(u_{13} = 58\)
Find the sum of the first 38 terms.3439
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
BC = 9.6cm.
CA = 7.6cm.
BĈA = 56.3°
Find AB to 1 dp.
8.3cm
Evaluate:
$$\sum_{n=1}^{9} n^2 - 6n$$
15
\(f(x)=7x^2+4x+8\)
What is the value of the discriminent and what does it indicate?
-208, No real roots
\(f(x)=x^2+5x-6\)
By completing the square find the coordinates of the vertex.
(-2.5, -12.25)
What is the value of \(\ln{e^3}\) ?
3
Find the integral:
\(\int \cos(x)e^{\sin(x)} \;dx\)
\(e^{\sin(x)}+c\)
Find the equation of the straight line that passes through:
(-9, -22) and (4, 4)
\(y=2x-4\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x-7}}{4}\)
\(16x²+7\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(y=x^2+7x\)
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
$$\cos{\dfrac{16\pi}{3}}$$\(-\dfrac{1}{2}\)
Solve:
\( 5a+2b+c=29 \\ 3a+4b+2c= 37 \\ a+5b+c=29\)
a = 3, b = 4, c = 6
Find the perimeter of a sector with radius 6.7cm and angle \( \frac{2\pi}{3}\)
🍕
27.4cm
In how many ways can 8 different books be arranged on a shelf if 3 of them must be together?
4320
Find the equations of the asymptotes of:
$$y=\dfrac{-6x^2-4x-1}{3x+2}$$x=-2/3, y=-2x
The sum of the first 3 terms of a geometric sequence is 62 and the sum of the first 4 terms is 312. What is the first term?
2
Find the first 4 terms in the expansion of:
\((1+x)^{-8}\)
\(1-8x-36x^2-120x^3\)
Evaluate:
\(\int^{120}_{60} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
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 10% chance and machine B has a 14% chance of breaking down on any given day?
\(0.619\)
Find the angle between the plane and the line:
\(\Pi: \quad 4x+4y-2z=7\)
\(L: \quad x+1= \dfrac{4-y}{2} = 3-z \)
\( \approx 7.82^o \)
Simplify
$$ \dfrac{i(2-i)}{3-2i}$$
\(-\frac{1}{13}+\frac{8}{13}i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\dfrac{\cot{x}}{\cosec{x}}$$\(\cos{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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 use the discriminant to determine the nature of roots?
Clue: positive, negative or zero: \( b^2 - 4ac \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)
\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)
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 the sum of the cubes of the first \( n \) natural numbers is \( \left(\frac{n(n + 1)}{2}\right)^2 \)
Show true for n=1, assume true for n=k, prove for n=k+1
Write down a summary of your last Maths lesson focussing on what you learnt.
?
Tick (or untick) the boxes above to select the concepts you want to be included in this Starter [untick all]. The display at the top of this page will change instantly to show your choices. You can also drag the panels above so that the questions are ordered to meet your needs.
* Topics shown with an asterix are on the IB Higher Level syllabus but not included in the Standard Level syllabus.
This Starter is called Refreshing Revision because every time you refresh the page you get different revision questions.
Regularly use this Starter to keep that important learning from being forgotten. Here is the web address (URL) for the version of this page with your currently selected concepts:
Copy and paste the URL above into your lesson plan or scheme of work.
For more ideas on revision there are plenty of tips, suggestions and links on the Mathematics Revision page.
Answers appear here for Transum subscribers.
Try this Uniqueness Game with your class.
Transum.org/Maths/Game/Uniqueness/Game.asp?Level=8
Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.
Teacher:
Scroll down the
page to see how
this Starter can be customised so that it
is just right for
your class.
