Maths GCSE revision Read the question Identify key

Maths GCSE revision • • Read the question Identify key words Think what type of maths COULD be used Go through the stages • ANYTHING is better than nothing

Triangles • Area = base x vertical height 2 • BUT if there is no right angle use the formula (b x c x Sin A) ÷ 2

Right angled triangles For pythag. the triangle must have a right angle and there will be the lengths of 2 sides and it will ask about the other length. 10 8 Write down the 2 side - 10 8 Square them 100 64 Is it add or take? 100 - 64 = 36 Square root ? 6

Trig. – finding the angle • Must be right angled triangle • Question will be about finding an angle given 2 sides Write down SOHCAHTOA Label the 2 sides Write O ÷ H = shift SIN 10 H 6 ÷ 10 = shift Sin 36. 9 6 O ? ? 6 TRY 3 ? ? Ans = 60

Trig – finding a side • Must show a right angle • Question will give one side and another angle and ask about a side Write down SOHCAHTOA Label the known side and the wanted one 10 H ? O Write Sin 30 = O/H = ? /10 Rearrange 10 x Sin 30 = 5 30 Ans is 20 10 60 ? Must be larger than 10

Triangles without a right angle • • • Question involves 2 sides and 2 angles Find PAIRS 8 10 40/8 & ? /10 40 = Sine rule ? Start with ? Sin ? = Sin 40 8 10 Rearrange sin? = Sin 40 x 8 = 0. 51423 10 then shift Sin = ans = 30. 9 10 70 50 ? Ans = 10. 9

Triangles without a right angle • Question involves 3 sides and 1 angle • Cosine rule 5 • Write the formula out • Replace letters • Know how to use your calculator ? 40 3 a² = b² + c² - (2 bc. Cos. A) use brackets a² = 5 x 5 + 3 x 3 – (2 x 3 x 5 x. Cos 40) TRY = 11. 02 5 ? 50 2 Ans = 4 then square root = 3. 32

Typical question No right angle so need ½ ab. Sin. C • Find the area of DCB B 3 OR would it be easier to find BD and angle DBC? C What can I do with triangle ABD? Sine rule won’t work but Cosine will. 5 A Can I find CD or BD? 70 4 30 D Use Cosine rule to find BD (5. 22) Then I have enough information in triangle BCD to use Sine rule to find angle DCB (60. 5) This allows me to find angle DBC (89. 5) I can then use area rule. (7. 83)

Bearings • Key words are from and to. • From tells you where to start • The angle between N and to is the bearing N N Look to see if F angles can help If joining all the points produces a triangle then Sine/Cosine rules are possible

Proportionality • • Directly proportional W α T Is it just T – read Include k W = k. T Use the data to find k Write out the equation Use the equation • Inversely proportional • W α 1 T Is it just T Include k W = k/T Use the data to find k Write out the equation Use the equation

The kinetic energy (E) of an object varies inversely with the square of its velocity (v). If the kinetic energy is 144 j when the velocity is 4 m/s. Find i) the K. E. when the velocity is 10 m/s and ii) the velocity when it has a K. E. of 360 joules. • • Key word inversely Is it just v? Include k Use the data to find k • Write out the equation • Use it to find E • Use it to find v • • E α 1/v² E = k/v² 144 = k/4 x 4 K = 144 x 16 = 2304 E = 2304/v² E = 2304/10 x 10 = 23. 04 j 360 = 2304/v² v² = 2304/360 = 6. 4 v = √ 6. 4 = 2. 53 m/s

The force (f) needed to stretch a rubber band is directly proportional to the square root of its length (L) If a force of 18 N is needed to stretch it 9 cm find i) the force needed to stretch it 49 cm ii) the amount a 24 N force will stretch it. • • • Use the key words Check if its just L K should be 6 i) Force will be 42 N ii) Length will be 16 cm

Circle theorems • How many rules are there? • Can you draw them? The example contains 4 rules. Which are they? What is a and b How many other angles can you find?

Solving quadratic equations using the formula • • Solve 5 x² - 3 x – 10 = 0. Write the answer correct to 2 significant figures Key words mean use the formula Write out the formula - b +or- √b² - 4 ac 2 a Write out a (+5), b (-3) and c (-10), remember +/Replace the letters by the numbers - -3 +or- √ -3 x-3 – (4 x 5 x -10) ÷ 2 x 5 Use your calculator to do the underlined part (=209) Then(- - 3 + √ 209) ÷ 2 x 5 and also (- -3 - √ 209) ÷ 2 x 5 1. 75 and -1. 15 answer is 1. 8 and -1. 2

Try using the formula • Solve 2 x² - x – 15 = 0 • The √ bit should work out as 121 = 11 • The answers are +3 and -2. 5