Find the first three terms in the expansion of:

\((5a - 3b)^7\)

\(=78125a^7 - 328125a^6b \\+590625a^5b^2 ...\)

If £120 is invested with an interest rate of 3% compounded monthly, find the value of the investment after 4 years. £135.28

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4^{th}?

\((1,1),(4,4),(-2,4)\)

(1,7)

\( X \sim N(9.03, 0.89^2)\)

Find

\( P(7.15\lt X \lt9.01) \)

\(0.474\)

Factorise:

\(x^2-16\)

\((x+4)(x-4)\)

Factorise:

\(12x^2-5x-3\)

\((3x+1)(4x-3)\)

Draw a rough sketch of the graph of:

\(y=-x+2\)

Gradient -1

y intercept 2

What is the value of:

\(3^{1}\)

\(= 3\)

Find angle ABC if AC = 4.4m and BC = 6.3m. 44.3^{o}

Find BC if angle BCA = 56^{o} and AB = 4.7m. 5.67m

Describe the red region.

\(y = 2x^3 - 9x^2 + 2x\)

Find \( \dfrac{dy}{dx}\)

\(6x^2 - 18x + 2\)

\(y = \dfrac{5}{x^9} - 3\sqrt[4]{x}\)

Find \( \frac{dy}{dx}\)

\(-\frac{45}{x^10} - \frac{3}{4}x^{-\frac{3}{4}}\)

\(y=(2x^6+4)^8\)

Find \( \dfrac{dy}{dx}\)

\(96x^5(2x^6+4)^7\)

\(y=x(3x+5)^3\)

Find \( \dfrac{dy}{dx}\)

\((3x+5)^3+9x(3x+5)^2\)

\(y=\frac{e^{3x}}{ \cos 4x}\)

Find \( \dfrac{dy}{dx}\)

\(\frac{(3e^{3x}cos4x+4e^{3x}sin4x)}{cos^24x}\)

Find the equation of the tangent to the curve:

\(y = 4x^2 + 2x - 1\)

where \(x = -2\)

\(y = -14x - 17\)

Find the equation of the normal to the curve:

\(y = 2x^2 - x + 3\)

where \(x = -1\)

\(y = \frac{x}{5} + 6\frac{1}{5}\)

\(y =24x^2 - 14x + 4\)

Find \( \int y \quad dx\)

\(8x^3 - 7x^2 + 4x+c\)

A game is played 17 times and the probability of winning is 0.1. Calculate the probability of winning exactly 10 times. 0.000000930

What's this?

\( \tan \theta \equiv \dfrac{ \sin \theta}{ \cos \theta}\)

Trigonometric identity

What letter is this?

Two terms of an arithmetic sequence:

\(u_{9} = 59\)

\(u_{19} = 129\)

Find the sum of the first 23 terms.1840

Find the equations of the asymptotes of:

\(y=\dfrac{2x-7}{6-2x}-5\)

\(x=3,y=-6\)

In the triangle ABC,

BC = 9.3cm.

CA = 12.9cm.

BĈA = 26.6°

Find AB to 1 dp.

6.2cm

Evaluate:

$$\sum_{n=1}^{8} 2n+6$$

120

\(f(x)=7x^2-5x+4\)

What is the value of the discriminent and what does it indicate?

-87, No real roots

\(f(x)=x^2+9x-1\)

By completing the square find the coordinates of the vertex.

(-4.5, -21.25)

Simplify \(\log_{10}10^5\)

5

Find the integral:

\(\int \cos(x)e^{\sin(x)} \;dx\)

\(e^{\sin(x)}+c\)

Find the equation of the straight line that passes through:

(-7, -12) and (0, 2)

\(y=2x+2\)

Find the inverse of the function \(f\):

\(f(x)= \sqrt{x+13}\)

\(x²-13\)

\(f(x)=2x+3 \\ g(x)=2x^2 \\[1cm] \text{Find }fgf(x)\)

\(16x^2+48x+39\)

Write in standard form:

\(a \times 10^{-1} \times b\times 10^{-1}\)

where \(a \times b \) is a three digit number \((100 \le ab \lt 1000)\)

\(\frac{ab}{100}\times10^0\)

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

$$\cos{\frac{\pi}{6}} \times \cos{60°}$$\(\dfrac{\sqrt{3}}{4}\)

Without a calculator find the exact value of

$$\tan{\dfrac{19\pi}{3}}$$\(\sqrt{3}\)

Solve:

\( 5a+2b+c=25 \\ 3a+4b+2c= 29 \\ a+5b+c=19\)

x=3, y=2, z=6

Find the perimeter of a sector with radius 4.6cm and angle \( \frac{\pi}{6}\)

🍕

11.6cm

How many ways can eleven children sit in a row without the youngest being in the middle?

36288000

Find the equations of the asymptotes of:

$$y=\dfrac{x^2+x-6}{x-1}$$x=1,y=x+2

The sum of the first 7 terms of a geometric sequence is 58593 and the sum of the first 8 terms is 292968. What is the first term?

3

Find the first 4 terms in the expansion of:

\((1+4x)^{\frac{3}{2}}\)

\(1+6x+6x^2-4x^3\)

Evaluate:

\(\int^{4}_{0} e^x dx\)

\(e^{4}- 1 \approx 53.6\)

What is the probability that it was machine B that broke down if at least one of the machines broke down today, given machine A has a 8% chance and machine B has a 13% chance of breaking down on any given day?

\(0.651\)

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.

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.