Find the first three terms in the expansion of:
\((4a - 5b)^7\)
\(=16384a^7 - 143360a^6b \\+537600a^5b^2 ...\)
If £200 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 4 years. £225.47
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,5),(7,10),(-3,10)\)
(2,15)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2-4\)
\((x+2)(x-2)\)
Factorise:
\(4x^2-9x-9\)
\((4x+3)(x-3)\)
Draw a rough sketch of the graph of:
\(y=-2x+1\)
Gradient -2
y intercept 1
What is the value of:
\(3^{-2}\)
\(= \frac{1}{9}\)
Find angle ABC if AC = 3m and BC = 5m. 36.9o
Find AC if angle ABC = 61o and BC = 4.2m. 3.67m
Describe the red region.
\(y = 4x^3 - 7x^2 + 6x\)
Find \( \dfrac{dy}{dx}\)
\(12x^2 - 14x + 6\)
\(y = \dfrac{9}{x^8} - 2\sqrt[3]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{72}{x^9} - \frac{2}{3}x^{-\frac{2}{3}}\)
\(y=(9x^7+7)^8\)
Find \( \dfrac{dy}{dx}\)
\(504x^6(9x^7+7)^7\)
\(y=(2x+9)(7x-4)\)
Find \( \dfrac{dy}{dx}\)
\(28x+55\)
\(y=\frac{2x^2}{4x-1}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(8x^2-4x)}{(4x-1)^2}\)
Find the equation of the tangent to the curve:
\(y = -2x^2 - 4x + 6\)
where \(x = 3\)
\(y = 24 - 16x\)
Find the equation of the normal to the curve:
\(y = x^2 - 2x + 1\)
where \(x = 0\)
\(y = \frac{x}{2} + 1\)
\(y =9x^2 - 8x + 6\)
Find \( \int y \quad dx\)
\(3x^3 - 4x^2 + 6x+c\)
A game is played 17 times and the probability of winning is 0.2. Calculate the probability of winning exactly 3 times. 0.239
Make up a maths question using this:
\(u_n=u_1+(n-1)d\)
The nth term of an arithmetic sequence
What letter is this?
Two terms of an arithmetic sequence:
\(u_{6} = -23\)
\(u_{20} = -79\)
Find the sum of the first 25 terms.-1275
Find the equations of the asymptotes of:
\(y=5\left(\dfrac{3x}{5+x}\right)\)
\(x=-5,y=15\)
In the triangle ABC,
BC = 9.2cm.
CA = 10.4cm.
BĈA = 40.6°
Find AB to 1 dp.
6.9cm
Evaluate:
$$\sum_{n=3}^{6} 2n+1$$
40
\(f(x)=-5x^2-2x+8\)
What is the value of the discriminent and what does it indicate?
164, Two distinct roots
\(f(x)=x^2+7x-3\)
By completing the square find the coordinates of the vertex.
(-3.5, -15.25)
Solve for x:
\( \log(x) + \log(29-x) = 2\)
\(x = 4 \text{ or } x = 25 \)
Find the integral:
\(\int (x+3)\sqrt{x^2+6x+8} \;dx\)
\(\frac{1}{3}(x^2+6x+8)^{\frac32}+c\)
Find the equation of the straight line that passes through:
(-3, -1) and (4, 6)
\(y=x+2\)
Find the inverse of the function \(f\):
\(f(x)=\frac{x+6}{4}\)
\(4x-6\)
\(f(x)=x^2-1 \\[1cm] \text{Find }f \bullet f(x) \\\)
\(x^4-2x^2\)
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
\(y=2^x\)
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
$$\sin{\dfrac{13\pi}{6}}$$\(\dfrac{1}{2}\)
Solve:
\(2d+3e-4f = -5 \\ d-e-f= -5\\ 9d+2e-2f=23\)
d = 3, e = 3, f = 5
Find the perimeter of a sector with radius 5.4cm and angle \( \frac{5\pi}{6}\)
🍕
24.9cm
How many ways can five children sit in a row without the youngest being in the middle?
96
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2+3x-9}{x+2}$$x=-2,y=2x-1
The first term of a geometric sequence is 26 and the fourth term is twice this value. What is the common ratio?
\( \sqrt[3]{2} \)
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:
\(\int^{5}_{1} (x-8)^2 \; dx\)
\(105.333333333333\)
Given equal populations of Type X and Type Y bacteria, with mutation rates of 40% and 50% respectively, if a mutated bacterium is found, what's the probability it's Type Y?
\(0.556\)
Find the cartesian equation of this plane:
\( \mathbf{r} = \begin{pmatrix} -2 \\ 2 \\ 3 \end{pmatrix} \; + \; s \begin{pmatrix} 3 \\ 1 \\ 0 \end{pmatrix} \; + \; t \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix} \)
2x-6y+5z=-1
Simplify
$$ (4+3i)(2+2i) $$
\(2+14i\)
Evaluate:
\(\int 4x\sin{\left( \frac{x}{2} \right)}\; dx\)
\(-8xcos\frac{x}{2}+16sin\frac{x}{2}+c\)
Simplify:
$$\tan{x}\cot{x}$$\(1\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\frac{1}{x}\) is rotated about the x-axis for \(1 \le x \le 2\)
\(\frac{\pi}{2}\) cubic units
What is the difference between a permutation and a combination?
Permutations consider order; combinations do not.
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = (1 + x)^n\)
\(1 + nx + \frac{n(n-1)x^2}{2} + \frac{n(n-1)(n-2)x^3}{6}\)
Solve for \(z\)
$$ z^3 = - 8i $$
\(\sqrt{3}-i,2i,-\sqrt{3}-i\)
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 first \( n \) natural numbers is \( \frac{n(n + 1)}{2} \)
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.
