Find the first three terms in the expansion of:

\((5a - 2b)^6\)

\(=15625a^6 - 37500a^5b \\+37500a^4b^2 ...\)

If £180 is invested with an interest rate of 4% compounded monthly, find the value of the investment after 5 years. £219.78

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

\((2,4),(7,7),(-1,9)\)

(4,12)

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

Find

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

\(0.474\)

Factorise:

\(x^2-9\)

\((x+3)(x-3)\)

Factorise:

\(x^2+x-12\)

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

Draw a rough sketch of the graph of:

\(y=x+2\)

Gradient 1

y intercept 2

What is the value of:

\(125^{\frac{1}{3}}\)

\(= 5\)

Find angle ABC if AB = 5.5m and BC = 6.5m. 32.2^{o}

Find AC if angle ABC = 53^{o} and BC = 3.7m. 2.95m

Describe the red region.

\(y = 4x^3 - 5x^2 + 3x\)

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

\(12x^2 - 10x + 3\)

\(y = \dfrac{8}{x^7} - 4\sqrt[5]{x}\)

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

\(-\frac{56}{x^8} - \frac{4}{5}x^{-\frac{4}{5}}\)

\(y=\sqrt{8x^8-2x}\)

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

\((32x^7-1)(8x^8-2x)^{-\frac{1}{2}}\)

\(y=x(4x^2+5)^7\)

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

\((4x^2+5)^7+56x^2(4x^2+5)^6\)

\(y=\frac{ \ln x}{x^2}\)

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

\(\frac{(1-2lnx)}{x^3}\)

Find the equation of the tangent to the curve:

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

where \(x = -1\)

\(y = 1 - 5x\)

Find the equation of the normal to the curve:

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

where \(x = -2\)

\(y = \frac{x}{14} + 11\frac{1}{7}\)

\(y =15x^2 - 14x + 6\)

Find \( \int y \quad dx\)

\(5x^3 - 7x^2 + 6x+c\)

A game is played 13 times and the probability of winning is 0.4. Calculate the probability of winning exactly 4 times. 0.184

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:

\(u_{7} = 40\)

\(u_{20} = 131\)

Find the sum of the first 32 terms.3408

Find the equations of the asymptotes of:

\(y=\dfrac{2x+5}{2x+3}\)

\(x=-\frac{3}{2},y=1\)

In the triangle ABC,

BC = 8.7cm.

CA = 11.5cm.

BĈA = 44.7°

Find AB to 1 dp.

8.1cm

Evaluate:

$$\sum_{n=0}^{5} 2^n$$

63

\(f(x)=3x^2+2x+6\)

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

-68, No real roots

\(f(x)=x^2-8x+4\)

By completing the square find the coordinates of the vertex.

(4, -12)

Write the following in terms of logs to base 10:

\(\log_a(z)\)

\( \dfrac{\log_{10}(z)}{\log_{10}(a)}\)

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:

(-9, -11) and (8, 23)

\(y=2x+7\)

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

\(f(x)=\frac{\sqrt{x}-16}{15}\)

\((15x+16)²\)

\(f(x)=7x-3 \\ g(x)=3x^2 \\[1cm] \text{Find }g \circ f(x)\)

\(147x^2-126x+27\)

Write in standard form:

\(a \times 10^2 \times b\times 10^3\)

where \(a \times b \) is a two digit number \((10 \le ab \lt 100)\)

\(\frac{ab}{10}\times10^6\)

Draw a rough sketch of

\(y=\dfrac{5}{x}\)

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

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

Solve:

\( 5a+2b+c=19 \\ 3a+4b+2c= 24 \\ a+5b+c=20\)

x=2, y=3, z=3

Find the perimeter of a sector with radius 9.4cm and angle \( \frac{2\pi}{3}\)

🍕

38.5cm

How many ways can fourteen people be divided into two equal groups?

1716

Find the equations of the asymptotes of:

$$y=\dfrac{-x^2+3x-2}{x}$$x=0,y=3-x

Evaluate:

$$ \sum_{k=1}^{8} \left( \dfrac12 \right)^{k-3} $$

7.97

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.