Maths P2 predictions

What is mean equal to?

sum of values ÷ number of values

How do you find the total from a mean?

total = mean × number of values

If 5 numbers have mean 8, what is their total?

40

After a new value is added, new mean = ?

(new total) ÷ (new count)

A team plays 11 games with mean 17. After one more game the mean is 18.5. Score in last game?

(12 × 18.5) − (11 × 17) = 222 − 187 = 35

Angle at the centre is _____ the angle at the circumference (same arc)

twice

Angle in a semicircle is

90° (angle subtended by diameter)

Angles in the same segment are

equal

Opposite angles in a cyclic quadrilateral add up to

180°

A tangent meets a radius at

90° (perpendicular)

Two tangents from the same external point are

equal in length

Alternate segment theorem

angle between tangent and chord = angle in the alternate segment

Perpendicular from centre to a chord

bisects the chord

In a "two tangents from external point" diagram, the four angles in the kite (OAPB) sum to

360°

If angle ADC = 48° (between two tangents), then angle AOC (at centre) =

360 − 90 − 90 − 48 = 132°; reflex AOC = 360 − 132 = 228°

Co-interior (allied) angles between parallel lines add up to

180° (C-shape)

Alternate angles between parallel lines are

equal (Z-shape)

Corresponding angles between parallel lines are

equal (F-shape)

Angles on a straight line add up to

180°

Vertically opposite angles are

equal

In a trapezium, angles on the same arm between parallel sides add to

180°

Sum of interior angles of n-sided polygon

(n − 2) × 180°

Sum of exterior angles of any polygon

360° (always)

One exterior angle of regular n-gon

360° ÷ n

Number of sides if one exterior angle is 24°

360 ÷ 24 = 15

sin θ =

opposite ÷ hypotenuse

cos θ =

adjacent ÷ hypotenuse

tan θ =

opposite ÷ adjacent

To find angle when you know two sides, use

sin⁻¹, cos⁻¹, or tan⁻¹ (SHIFT button)

When to use SOHCAHTOA vs sine/cosine rule

SOHCAHTOA needs a right angle; sine/cosine rule for any