Find the first three terms in the expansion of:
\((3a - 2b)^9\)
\(=19683a^9 - 118098a^8b \\+314928a^7b^2 ...\)
If £180 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 8 years. £247.75
Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?
\((2,3),(7,9),(-4,8)\)
(1,14)
\( X \sim N(33, 6^2)\)
Find
\( P(31\lt X \lt37) \)
\(0.378\)
Factorise:
\(x^2-1\)
\((x+1)(x-1)\)
Factorise:
\(20x^2-11x-4\)
\((4x+1)(5x-4)\)
Draw a rough sketch of the graph of:
\(2y=x-2\)
Gradient 0.5
y intercept -1
What is the value of:
\(1^{\frac{1}{3}}\)
\(= 1\)
Find angle ABC if AB = 4.6m and BC = 5.7m. 36.2o
Find AC if angle BCA = 42o and AB = 5.7m. 6.33m
Describe the red region.
\(y = 5x^3 - 3x^2 + 4x\)
Find \( \dfrac{dy}{dx}\)
\(15x^2 - 6x + 4\)
\(y = \dfrac{8}{x^9} - 8\sqrt[9]{x}\)
Find \( \frac{dy}{dx}\)
\(-\frac{72}{x^10} - \frac{8}{9}x^{-\frac{8}{9}}\)
\(y=\sqrt{6x^8-2x}\)
Find \( \dfrac{dy}{dx}\)
\((24x^7-1)(6x^8-2x)^{-\frac{1}{2}}\)
\(y=(3x+7)(9x-2)\)
Find \( \dfrac{dy}{dx}\)
\(54x+57\)
\(y=\frac{x}{\sin x}\)
Find \( \dfrac{dy}{dx}\)
\(\frac{(sinx-xcosx)}{sin^2x}\)
Find the equation of the tangent to the curve:
\(y = -4x^2 + 8x - 5\)
where \(x = -1\)
\(y = 16x - 1\)
Find the equation of the normal to the curve:
\(y = 2x^2 - x + 3\)
where \(x = -1\)
\(y = \frac{x}{5} + 6\frac{1}{5}\)
\(y =6x^2 - 18x + 3\)
Find \( \int y \quad dx\)
\(2x^3 - 9x^2 + 3x+c\)
A game is played 13 times and the probability of winning is 0.1. Calculate the probability of winning exactly 7 times. 0.0000912
What's this?
\(^nC_r=\dfrac{n!}{r!(n-r)!}\)
Combinations
(from n choose r)
What letter is this?
Two terms of an arithmetic sequence:
\(u_{9} = 43\)
\(u_{17} = 83\)
Find the sum of the first 43 terms.4644
Find the equations of the asymptotes of:
\(y=\dfrac{5x}{2-x}+3\)
\(x=2,y=-2\)
In the triangle ABC,
AB = 8.9cm.
BC = 6.7cm.
CÂB = 40.4°.
Find angle BĈA.
59.3° or 120.7°
Evaluate:
$$\sum_{n=2}^{8} 72 - n^2$$
301
\(f(x)=4x^2+7x+7\)
What is the value of the discriminent and what does it indicate?
-63, No real roots
\(f(x)=x^2+4x-7\)
By completing the square find the coordinates of the vertex.
(-2, -11)
Express \(\log_2(32)\) in terms of a log to base 4.
\( 10\log_4(2) \text{ or } \log_4(1024) \)
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:
(-8, -25) and (2, 5)
\(y=3x-1\)
Find the inverse of the function \(f\):
\(f(x)=\sqrt{\frac{x-9}{8}}\)
\(8x²+9\)
\(g(x)=5x-4 \\[1cm] \text{Find }g \circ g(x) \\\)
\(25x-24\)
Write in standard form:
\((a \times 10^4) \div (b\times 10^{-2})\)
where \(a \div b \) is a decimal number \((0.1 \le \frac{a}{b} \lt 1)\)
\(\frac{10a}{b}\times10^5\)
Draw a rough sketch of
\(y=\sin(x)\)
Sketch a height-time graph as this jar is filled.
Without a calculator find the exact value of
$$\cos{0°} + \sin{\frac{\pi}{6}} + \cos{60°}$$\(2\)
Without a calculator find the exact value of
$$\sin{780°}$$\(\dfrac{\sqrt{3}}{2}\)
Solve:
\(2x+y-3z= 19 \\ 3x+y+z= 35 \\ x-y+2z = 3\)
x=8, y=9, z=2
Find the area of a sector with radius 3.5cm and angle \( \frac{\pi}{4}\)
🍕
4.81cm2
How many ways can ten people be divided into two equal groups?
126
Find the equations of the asymptotes of:
$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x
Evaluate:
$$ \sum_{k=1}^{15} 5 \times (-2)^k $$
10
Find the first 4 terms in the expansion of:
\(\dfrac{1}{\sqrt[3]{1+x}}\)
\(1 - \frac{x}{3} + \frac{2x^2}{9} - \frac{14x^3}{81}\)
Evaluate:
\(\int^{140}_{70} \dfrac{1}{x} dx\)
\(\ln{2} \approx 0.693\)
The probability that I drop and brake my phone when I visit a coffee shop is 0.05. Today I visited two coffee shops and broke my phone in one of them. What is the probability that it was the first shop where the accident occurred?
\(0.513\)
Find the parametric equation of the line:
\( \dfrac{x-5}{8} = \dfrac{8-y}{7} = \dfrac{z}{5} \)
\( x=5+8\lambda \quad y = 8 -7\lambda \quad z=5 \lambda \)
Simplify
$$ (3+i)^{-2} $$
\(\frac{2}{25}-\frac{3}{50}i\)
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. 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.
Here's a projectable set of randomly-selected revision questions for the end of the lesson.
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.