Find the first three terms in the expansion of:
\((3a - 4b)^9\)
\(=19683a^9 - 236196a^8b \\+1259712a^7b^2 ...\)
If £240 is invested with an interest rate of 2% compounded quarterly, find the value of the investment after 9 years. £287.20
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((4,4),(7,9),(-1,7)\)
(2,12)
\( X \sim N(50, 5^2)\)
Find
\( P(40\lt X \lt60) \)
\(0.955\)
Factorise:
\(x^2-x-12\)
\((x+3)(x-4)\)
Factorise:
\(2x^2+3x-9\)
\((x+3)(2x-3)\)
Draw a rough sketch of the graph of:
\(y=x+1\)
Gradient 1
y intercept 1
What is the value of:
\(2^{0}\)
\(= 1\)
Find angle ABC if AB = 3.3m and BC = 4.4m. 41.4o
Find AC if angle ABC = 49o and AB = 5.1m. 5.87m
Describe the red region.
\(y = 5x^3 - 2x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 4x + 9\)
\(y = \dfrac{4}{x^{8}} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{32}{x^{9}} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=\sqrt{2x^4+3}\)
Find \( \dfrac{dy}{dx}\)
\(4x^3(2x^4+3)^{-\frac{1}{2}}\)
\(y=x(2x^2+3)^6\)
Find \( \dfrac{dy}{dx}\)
\((2x^2+3)^6+24x^2(2x^2+3)^5\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
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:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = \frac{x}{16} - \frac{387}{16}\)
\(y =15x^2 - 16x + 6\)
Find \( \int y \quad dx\)
\(5x^3 - 8x^2 + 6x+c\)
A game is played 13 times and the probability of winning is 0.5. Calculate the probability of winning exactly 8 times. 0.157
Make up a maths question using this:
\( P(A|B) = \dfrac{P(A \cap B)}{P(B)} \)
Conditional probability formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 69\)
\(u_{18} = 150\)
Find the sum of the first 48 terms.10008
Find the equations of the asymptotes of:
\(y=\dfrac{2x-7}{6-2x}-5\)
\(x=3,y=-6\)
In the triangle ABC,
AB = 5.7cm.
BC = 5.1cm.
CÂB = 47.2°.
Find angle BĈA.
55.0° or 125°
Evaluate:
$$\sum_{n=4}^{6} 4n+5$$
75
\(f(x)=3x^2+2x-5\)
What is the value of the discriminant and what does it indicate?
64, Two distinct roots
\(f(x)=x^2+8x-5\)
By completing the square find the coordinates of the vertex.
(-4, -21)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
Find the integral:
\(\int \dfrac{5x}{x^2-3} \;dx\)
\(\frac{5}{2} \ln(x^2-3)+c\)
Find the equation of the straight line that passes through:
(-4, -5) and (3, 9)
\(y=2x+3\)
Find the inverse of the function \(f\):
\(f(x)=\frac{\sqrt{x}-14}{15}\)
\((15x+14)²\)
\(f(x)=3x+2 \\ g(x)=2x^2 \\[1cm] \text{Find }gf(x)\)
\(18x^2+24x+8\)
Write in standard form:
\((a \times 10^p) \div (b\times 10^q)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{p-q}\)
Draw a rough sketch of
\(y=x^3-4x\)
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
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\( j+k+l= 10 \\ 2j-3k+9l= 24\\ -j+k-3l=-10\)
j = 6, k = 2, l = 2
Find the area of a sector with radius 8.5cm and angle \( \frac{\pi}{3}\)
🍕
37.8cm2
How many ways can twenty people be divided into two equal groups?
92378
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
-109230
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt{4+x}}\)
\(\frac{1}{2}-\frac{x}{16}+\frac{3x^2}{256}-\frac{5x^3}{2048}\)
Evaluate:
\(\int^{\pi/3}_{\pi/6} \sin{x} \; dx\)
\(\dfrac{\sqrt{3}-1}{2}\)
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 15% chance of breaking down on any given day?
\(0.638\)
Find the angle between two unit vectors \(u\) and \(v\) such that the vectors \(2u-3v\) and \(5u+2v\) are perpendicular. Give you answer correct to the nearest degree.
\( 69^o \)
Simplify
$$ \dfrac{i(2-i)}{3-2i}$$
\(-\frac{1}{13}+\frac{8}{13}i\)
Evaluate:
\(\int xe^x\; dx\)
\(xe^x-e^x+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=x(4-x)\) is rotated about the x-axis for \(0 \le x \le 4\)
\(\frac{512\pi}{15}\) cubic units
Describe the behavior of a function at its asymptote.
Clue: approaches but never reaches
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \sec(x)\)
\(1 + \frac{x^2}{2} + \frac{5x^4}{24} + \frac{61x^6}{720}\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
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 \( 5^n - 1 \) is divisible by 4 for all natural numbers \( n \)
Show true for n=1, assume true for n=k, prove for n=k+1
Simplify:
$$\sqrt{20}$$
\(2\sqrt{5}\)
Simplify:
$$\dfrac{7}{\sqrt{5}}$$\(\frac{7\sqrt{5}}{5}\)
Simplify
\((9 + 2\sqrt{2})(9 - 2\sqrt{2})\)
\(73\)
Simplify:
$$\dfrac{8}{3 + \sqrt{6}}$$\(\frac{24 - 8\sqrt{6}}{3}\)
Calculate the standard deviation of the following numbers:
43, 45, 49, 51, 55, 57
5
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.
