Find the first three terms in the expansion of:
\((4a - 2b)^6\)
\(=4096a^6 - 12288a^5b \\+15360a^4b^2 ...\)
If £140 is invested with an interest rate of 4% compounded quarterly, find the value of the investment after 8 years. £192.49
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((1,1),(5,7),(-5,5)\)
(-1,11)
\( X \sim N(65, 9^2)\)
Find
\( P(36\lt X \lt48) \)
\(0.0288\)
Factorise:
\(x^2-3x-4\)
\((x+1)(x-4)\)
Factorise:
\(4x^2+11x-3\)
\((x+3)(4x-1)\)
Draw a rough sketch of the graph of:
\(2y=x\)
Gradient 0.5
y intercept 0
What is the value of:
\(3^{1}\)
\(= 3\)
Find angle ABC if AB = 4.2m and BC = 5.4m. 38.9o
Find AC if angle BCA = 42o and AB = 5.1m. 5.66m
Describe the red region.
\(y = 9x^3 - 2x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(27x^2 - 4x + 9\)
\(y = \dfrac{7}{x^{5}} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{35}{x^{6}} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=(7x^5+7)^9\)
Find \( \dfrac{dy}{dx}\)
\(315x^4(7x^5+7)^8\)
\(y=x(5x+6)^3\)
Find \( \dfrac{dy}{dx}\)
\((5x+6)^3+15x(5x+6)^2\)
\(y=\frac{e^{3x}}{ \cos 4x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)
Find the equation of the tangent to the curve:
\(y = -x^2 + 4x + 2\)
where \(x = 1\)
\(y = 2x + 3\)
Find the equation of the normal to the curve:
\(y = 5x^2 + 7x + 3\)
where \(x = 1\)
\(y = 15\frac{1}{17} - \frac{x}{17}\)
\(y =18x^2 - 8x + 2\)
Find \( \int y \quad dx\)
\(6x^3 - 4x^2 + 2x+c\)
A game is played 15 times and the probability of winning is 0.3. Calculate the probability of winning exactly 2 times. 0.0916
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:
\(u_{7} = 48\)
\(u_{18} = 114\)
Find the sum of the first 49 terms.7644
Find the equations of the asymptotes of:
\(y=\dfrac{10-2x}{10x}\)
\(x=0,y=-\frac{1}{5}\)
In the triangle ABC,
AB = 5.1cm.
BC = 5.2cm.
CÂB = 43.0°.
Find angle BĈA.
41.9°
Evaluate:
$$\sum_{n=0}^{6} n^2 - 4n$$
7
\(f(x)=6x^2+5x+3\)
What is the value of the discriminant and what does it indicate?
-47, No real roots
\(f(x)=x^2+2x-9\)
By completing the square find the coordinates of the vertex.
(-1, -10)
Solve for x:
\(\log_2(x) = 4\)
16
Find the integral:
\(\int \dfrac{\ln(x)}{x} \;dx\)
\(\dfrac{\ln(x)^2}{2}+c\)
Find the equation of the straight line that passes through:
(-7, -12) and (7, 16)
\(y=2x+2\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x}-2\)
\((x+2)²\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
Write in standard form:
\((a \times 10^2) \div (b\times 10^4)\)
where \(a \div b \) is a single digit number \((1 \le \frac{a}{b} \lt 10)\)
\(\frac{a}{b}\times10^{-2}\)
Draw a rough sketch of
\(y=x^2-8\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\tan{45°} - \sin{\frac{\pi}{6}} - \cos{\frac{\pi}{3}}$$\(0\)
Without a calculator find the exact value of
$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)
Solve:
\(2d+3e-4f = 11 \\ d-e-f= -4\\ 9d+2e-2f=40\)
d = 4, e = 5, f = 3
Find the perimeter of a sector with radius 6.4cm and angle \( \frac{\pi}{4}\)
🍕
17.8cm
A safe has a nine-digit code. How many possibilities are there if no digit can be repeated and the code must be odd?
201600
Find the equations of the asymptotes of:
$$y=\dfrac{8x^2-19x-15}{1-2x}$$x=1/2,y=15/2-4x
The sum of the first 7 terms of a geometric sequence is 254 and the sum of the first 8 terms is 510. What is the first term?
2
Find the first 4 terms in the expansion of:
\((1-4x)^{-3}\)
\(1+12x+96x^2+640x^3\)
Evaluate:
\(\int^{160}_{80} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
24 Scouts went hiking. 12 got lost, 11 got blisters, and 6 got both lost and blisters. Find the probability that a randomly selected Scout got blisters, given that they were not lost.
\(\dfrac{5}{12}\)
Find the vector equation of the line:
\( \dfrac{x-2}{4} = \dfrac{3-y}{6} = \dfrac{z}{5} \)
\( \mathbf{r} = \begin{pmatrix} 2 \\ 3 \\ 0 \end{pmatrix} \quad + \quad t \begin{pmatrix} 4 \\ -6 \\ 5 \end{pmatrix} \)
Simplify
$$ \sqrt{5-12i} $$
\(3-2i \; \text{ or } -3+2i\)
Evaluate:
\(\int (2x+1)e^{-x}\; dx\)
\(-\frac{2x+3}{e^x}+c\)
Simplify:
$$\cosec{x}\tan{x}$$\(\sec{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$Find the volume of revolution when \(y=\sqrt{x}\) is rotated about the y-axis for \(1 \le y \le 4\)
\(\frac{1023\pi}{5}\) 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
\(f(x) = \frac{1}{1-x}\)
\(1 + x + x^2 + x^3\)
Solve for \(z\)
$$ z^4 = \sqrt{3}+i $$
\(\sqrt[4]{2} cis \frac{\pi}{24},\sqrt[4]{2} cis \frac{13\pi}{24} \\ \sqrt[4]{2} cis \frac{-11\pi}{24}, \sqrt[4]{2} cis \frac{-23\pi}{24}\)
6 girls sit at random on 6 seats in a row. Determine the probability that the two friends Karen and Julie sit at the ends of the row.
1/15 or 6.67%
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:
$$\sqrt{50}$$
\(5\sqrt{2}\)
Simplify:
$$\dfrac{5}{\sqrt{8}}$$\(\frac{5\sqrt{8}}{8} = \frac{5\sqrt{2}}{4}\)
Simplify
\(8\sqrt{3}(1 - \sqrt{3})\)
\(8\sqrt{3} - 24\)
Simplify:
$$\dfrac{9}{2 + \sqrt{5}}$$\(\frac{18 - 9\sqrt{5}}{-1} = -18 + 9\sqrt{5}\)
Calculate the standard deviation of the following numbers:
27, 29, 30, 31, 33
2
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.
