Find the first three terms in the expansion of:
\((2a - 3b)^7\)
\(=128a^7 - 1344a^6b \\+6048a^5b^2 ...\)
If £160 is invested with an interest rate of 1% compounded quarterly, find the value of the investment after 6 years. £169.88
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,5),(5,11),(-4,8)\)
(-1,14)
\( X \sim N(100, 7^2)\)
Find
\( P(93\lt X \lt107) \)
\(0.683\)
Factorise:
\(x^2-16\)
\((x+4)(x-4)\)
Factorise:
\(9x^2-6x-8\)
\((3x+2)(3x-4)\)
Draw a rough sketch of the graph of:
\(y=-2x+1\)
Gradient -2
y intercept 1
What is the value of:
\(2^{-3}\)
\(= \frac{1}{8}\)
Find angle BCA if AC = 4.5m and BC = 6.3m. 44.4o
Find BC if angle BCA = 54o and AC = 5.8m. 9.87m
Describe the red region.
\(y = 8x^3 - 9x^2 + 9x\)
Find \( \dfrac{dy}{dx}\)
\(24x^2 - 18x + 9\)
\(y = \dfrac{8}{x^6} - 6\sqrt[7]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{48}{x^7} - \frac{6}{7}x^{-\frac{6}{7}}\)
\(y=(6x+5)^3\)
Find \( \dfrac{dy}{dx}\)
\(18(6x+5)^2\)
\(y=x^7 \ln x\)
Find \( \dfrac{dy}{dx}\)
\(7x^6lnx+x^6\)
\(y=\frac{x+5}{x-5}\)
Find \( \dfrac{dy}{dx}\)
\(-\frac{10}{(x-5)^2}\)
Find the equation of the tangent to the curve:
\(y = 4x^2 + 2x - 1\)
where \(x = -2\)
\(y = -14x - 17\)
Find the equation of the normal to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = -\frac{x}{16} - \frac{273}{16}\)
\(y =18x^2 - 8x + 4\)
Find \( \int y \quad dx\)
\(6x^3 - 4x^2 + 4x+c\)
A game is played 14 times and the probability of winning is 0.3. Calculate the probability of winning exactly 13 times. 0.00000156
Make up a maths question using this:
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{5} = -28\)
\(u_{13} = -68\)
Find the sum of the first 17 terms.-816
Find the equations of the asymptotes of:
\(y=12-\dfrac{4x+3}{7-2x}\)
\(x=\frac{7}{2},y=14\)
In the triangle ABC,
BĈA = 42.3°.
BC = 8.9cm.
AB̂C = 94.27°.
Find CA to 1 dp.
12.9cm
Evaluate:
$$\sum_{n=3}^{8} 3n+2$$
111
\(f(x)=4x^2+6x-8\)
What is the value of the discriminant and what does it indicate?
164, Two distinct roots
\(f(x)=x^2+5x+1\)
By completing the square find the coordinates of the vertex.
(-2.5, -5.25)
Simplify \(\log_{10}10^5\)
5
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:
(-2, -10) and (4, 2)
\(y=2x-6\)
Find the inverse of the function \(f\):
\(f(x)= \sqrt{x+16}\)
\(x²-16\)
\(f(x)=2x-3 \\[1cm] \text{Find }f \bullet f(1-\sqrt{m}) \\\)
\(-5-4\sqrt{m}\)
Write in standard form:
\((a \times 10^3) \div (b\times 10^5)\)
where \(a \div b \) is a two digit number \((10 \le \frac{a}{b} \lt 100)\)
\(\frac{a}{10b}\times10^{-1}\)
Draw a rough sketch of
\(x=\pm \sqrt{y}\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\sin{\frac{\pi}{2}} \div \cos{45°}$$\(\sqrt{2}\)
Without a calculator find the exact value of
$$\sin{5\pi}$$\(0\)
Solve:
\( g-7h-7i=-106 \\ 2g-2h+i= 4\\ 5g+3h+i = 62\)
g = 6, h = 8, i = 8
Find the perimeter of a sector with radius 4.4cm and angle \( \frac{\pi}{6}\)
🍕
11.1cm
Ansh is with five people in a queue. How many ways can they line up without Ansh being at the back?
600
Find the equations of the asymptotes of:
$$y=\dfrac{2x^2-8x+8}{x-3}$$x=3, y=2x-2
The fourth term of a geometric sequence is \(-16\) and the sum to infinity is \(32\). What is the common ratio?
-0.669
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:
\(\int^{120}_{60} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
Every family in Happyland has either has a car or a motor scooter or both. 61% of the families have a car. 77% of the families have a scooter. A family is selected at random and it is found that they have a car. Find the probability they also have a scooter.
\(\dfrac{38}{61}\)
Find the vector product:
\( \begin{pmatrix} 3 \\ 8 \\ 0 \end{pmatrix} \; \times \; \begin{pmatrix} 9 \\ -2 \\ 9 \end{pmatrix} \)
\( \begin{pmatrix} 72 \\ -27 \\ -78 \end{pmatrix} \)
Simplify
$$ \dfrac{2-i}{1+3i}$$
\(-\frac{1}{10}-\frac{7}{10}i\)
Evaluate:
\(\int x\cos{x}\; dx\)
\(xsinx+cosx+c\)
Simplify:
$$\dfrac{\tan{x}}{\sec{x}}$$\(\sin{x}\)
$$ \DeclareMathOperator{cosec}{cosec} $$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
How do you determine if a geometric series converges?
Clue: common ratio test
Show how the first four terms of the Maclaurin series are obtained for
\(f(x) = \cos(x)\)
\(1 - \frac{x^2}{2} + \frac{x^4}{24} - \frac{x^6}{720}\)
Expand and simplify:
$$ (\sqrt{3}+i)^8 $$
\(-128-128\sqrt{3}i \\ \text{or } 128(-1-\sqrt{3}i)\)
6 children, three boys and three girls, are randomly seated on a row of 6 chairs. Determine the likelihood that the three boys are seated together.
1/5 or 20%
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
Simplify:
$$\sqrt{12}$$
\(2\sqrt{3}\)
Simplify:
$$\dfrac{2}{\sqrt{10}}$$\(\frac{2\sqrt{10}}{10} = \frac{\sqrt{10}}{5}\)
Simplify
\((3 + \sqrt{5})(3 - \sqrt{5})\)
\(4\)
Simplify:
$$\dfrac{6}{5 + \sqrt{2}}$$\(\frac{30 - 6\sqrt{2}}{23}\)
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.
