Trig & Pythag - 1

What is Pythagoras’ theorem?

a² + b² = h²

(where h is the hypotenuse)

Trig & Pythag - 2

How long is the hypotenuse?

10cm

15cm

h = 18cm

Trig & Pythag - 3

What are the trigonometric formulae?

sin A=opp cos A=adj tan A=opp hyp hyp adj

Trig & Pythag - 4

Find angle A

A B

C

6cm

8cmA = 53°

Trig & Pythag - 5

A ladder leans against a vertical wall so that is makes an angle of 35° with the wall.

The top of the ladder is 2m up the wall. How far out is the foot of the ladder?

2.9 m

Algebra - 1

Factorise the following expression:

12z² – 6z

= 6z(2z – 1)

Algebra - 2

Expand the following expression:

(x + 3)(x + 6)

= x² + 9x + 18

Algebra - 3

Factorise the following expression:

x² + 5x + 6

= (x + 3)(x + 2)

Algebra - 4

Solve the following pair of simultaneous equations:

x + y = 5

3x + y = 11

x = 3 y = 2

Algebra - 5

Expand the following expression:

(5x – 2)(5x + 2)

= 25x² – 4

Number work - 1

Write the following fraction as a mixed number:

25 = 8⅓ 3

Number work - 2

Without a calculator work out:

1.23 – 0.67 = 0.56

Number work - 3

Fill in the blank:

3.7 x 4.2 = 15.54

Number work - 4

Express 12mm as a percentage of 6cm.

20%

Number work - 5

Write the following number as an ordinary Number:

3.45 x 10³ - 9 x 10-¹ 3450 – 0.9 = 3499.1

Formulas - 1

What are the next 3 terms of this sequence?

2, 5, 10, 17, 26, 37, 40…

Formulas - 2

If R = pq – w R = 2

Find R when p = 2, q = 3 and w = – 4

Formulas - 3

A taxi firm charges 50p per mile plus a fixed charge of £2.00. Write down a formula for the cost (C) of hiring this taxi to travel ‘n’ miles.

C = 2 + 0.5n

Formulas - 4

If y = zx – 4w w = 3

Find w when y = 3, z = 3 and x = 5

Formulas - 5

Use an appropriate formula to find the radius of the following circle.Give your answer 3 sf

r = 3.18cm

Circumference = 20cm

Pot Luck - 1

Give the inequality which describes the shaded region.

x ≤ 2

Pot Luck - 2

Sally writes the letters of the word ‘MATHEMATICS' on separate cards and places them in a bag. She then draws a card at random.

What is the probability that Sally chooses the

letter 'A'?

P(A) = 2 11

Pot Luck - 3

You are about to leave for holiday, but you forgot socks! You race back to your room, but all the lights are off, so you can't see the colour of the socks.

Never mind, because you remember that in your drawer there are ten pairs of white socks, ten pairs of black socks, and eleven pairs of blue socks, but they are all mixed up.

How many of your socks do you need to take before you can be sure to have at last one matching pair?

4 socks

Pot Luck - 4

What is the volume of this prism?

Volume = 40cm³

Pot Luck - 5Give the set of inequalities which describe the

unshaded region.

x ≤ 3

y ≥ x

y ≥ 1