Find the first three terms in the expansion of:
\((2a - 3b)^4\)
\(=16a^4 - 96a^3b \\+216a^2b^2 ...\)
If £100 is invested with an interest rate of 5% compounded monthly, find the value of the investment after 6 years. £134.90
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,4),(6,7),(-1,8)\)
(3,11)
\( X \sim N(27.1, 1.8^2)\)
Find
\( P(28.1\lt X \lt29.1) \)
\(0.156\)
Factorise:
\(x^2-x-6\)
\((x+2)(x-3)\)
Factorise:
\(3x^2+x-2\)
\((x+1)(3x-2)\)
Draw a rough sketch of the graph of:
\(y=2x+1\)
Gradient 2
y intercept 1
What is the value of:
\(1^{\frac{1}{2}}\)
\(= 1\)
Find angle ABC if AB = 4.2m and BC = 5.2m. 36.1o
Find AC if angle ABC = 38o and AB = 4m. 3.13m
Describe the red region.
\(y = 2x^3 - 2x^2 + 7x\)
Find \( \dfrac{dy}{dx}\)
\(6x^2 - 4x + 7\)
\(y = \dfrac{6}{x^7} - 3\sqrt[4]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{42}{x^8} - \frac{3}{4}x^{-\frac{3}{4}}\)
\(y=\sqrt{7x^2+8}\)
Find \( \dfrac{dy}{dx}\)
\(7x^1(7x^2+8)^{-\frac{1}{2}}\)
\(y=e^{7x} \cos x\)
Find \( \dfrac{dy}{dx}\)
\(7e^{7x}cosx-e^{7x}sinx\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = x^2 + 6x + 9\)
where \(x = -3\)
\(y = 0\)
Find the equation of the normal to the curve:
\(y = -5x^2 + 7x - 3\)
where \(x = 2\)
\(y = \frac{x}{13} - \frac{119}{13}\)
\(y =15x^2 - 4x + 5\)
Find \( \int y \quad dx\)
\(5x^3 - 2x^2 + 5x+c\)
A game is played 12 times and the probability of winning is 0.2. Calculate the probability of winning exactly 10 times. 0.00000433
Make up a maths question using this:
\(\log_ax=\dfrac{\log_bx}{\log_ba}\)
Logarithm changing base formula
What letter is this?
Two terms of an arithmetic sequence:
\(u_{6} = 37\)
\(u_{13} = 86\)
Find the sum of the first 39 terms.5265
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BC = 9.1cm.
CA = 12.8cm.
BĈA = 29.3°
Find AB to 1 dp.
6.6cm
Evaluate:
$$\sum_{n=0}^{6} 2^n$$
127
\(f(x)=-8x^2+3x-2\)
What is the value of the discriminent and what does it indicate?
-55, No real roots
\(f(x)=x^2+3x+9\)
By completing the square find the coordinates of the vertex.
(-1.5, 6.75)
Solve for x:
\(\log_2(x) = 4\)
16
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:
(-5, -1) and (5, 19)
\(y=2x+9\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-9\)
\((x+9)²\)
\(f(x)=5x+1 \\ g(x)=x^2 \\[1cm] \text{Find }gf(3x)\)
\(225x^2+30x+1\)
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
\(y=3-\dfrac{10}{x}\)
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
$$\cos{720°}$$\(1\)
Solve:
\( 5a+2b+c=42 \\ 3a+4b+2c= 42 \\ a+5b+c=27\)
a = 6, b = 3, c = 6
Find the perimeter of a sector with radius 4.2cm and angle \( \frac{2\pi}{3}\)
🍕
17.2cm
In how many ways can 8 different books be arranged on a shelf if 4 of them must be together?
2880
Find the equations of the asymptotes of:
$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2
The 6th term of a geometric sequence is 9375 and the sum of the first 6 terms is 11718. Find the first term.
3
Find the first 4 terms in the expansion of:
\((1-\dfrac{x}{2})^{\frac13}\)
\(1-\frac{x}{6}-\frac{x^2}{36}-\frac{5x^3}{648}\)
Evaluate:
\(\int^{9}_{2} (x-8)^2 \; dx\)
\(72.3333333333333\)
30 Scouts went hiking. 10 got lost, 15 got blisters, and 5 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{1}{2}\)
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
$$ (3-5i)(3-6i) $$
\(-21-33i\)
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
What is the binomial theorem?
Clue: Expand \( (a + b)^n \)
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
A school committee of 8 is chosen at random from 12 senior students and 4 junior students. Find the probability that all four junior students are chosen.
1/26 or 3.85%
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
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.
