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 ? Write down the 2 side Square them Is it add or take? = 36 Square root 6

Trig. – finding the angle Must be right angled triangle Question will be about finding an angle given 2 sides ?? 10 H 6O6O Write down SOHCAHTOA Label the 2 sides Write O ÷ H = shift SIN 6 ÷ 10 = shift Sin 36.9 ?? 6 3 Ans = 60 TRY

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

Triangles without a right angle Question involves 2 sides and 2 angles Find PAIRS 40/8 & ?/10 = Sine rule Start with ? ? Sin ? = Sin Rearrange sin? = Sin40 x 8 = then shift Sin = ans = ? Ans = 10.9

Triangles without a right angle Question involves 3 sides and 1 angle Cosine rule Write the formula out Replace letters Know how to use your calculator 5 ? 3 40 a² = b² + c² - (2bcCosA) use brackets a² = 5x5 + 3x3 – (2x3x5xCos40) = then square root = 3.32 TRY 5 2 ? 50 Ans = 4

Typical question Find the area of DCB A B C D No right angle so need ½ abSinC Can I find CD or BD? OR would it be easier to find BD and angle DBC? What can I do with triangle ABD? Sine rule won’t work but Cosine will. 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 = kT 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 144j when the velocity is 4m/s. Find i) the K.E. when the velocity is 10m/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/v E α 1/v² E = k/v² 144 = k/4x4 K = 144 x 16 = 2304 E = 2304/v² E = 2304/10x10 = 23.04j 360 = 2304/v² v² = 2304/360 = 6.4 v = √6.4 = 2.53m/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 18N is needed to stretch it 9cm find i) the force needed to stretch it 49cm ii) the amount a 24N force will stretch it. Use the key words Check if its just L K should be 6 i) Force will be 42N ii) Length will be 16cm

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 5x² - 3x – 10 = 0. Write the answer correct to 2 significant figures Key words mean use the formula Write out the formula - b +or- √b² - 4ac 2a Write out a (+5), b (-3) and c (-10), remember +/- Replace the letters by the numbers or- √ -3x-3 – (4 x 5 x -10) ÷ 2x5 Use your calculator to do the underlined part (=209) Then( √209) ÷ 2x5 and also ( √209) ÷ 2x and-1.15 answer is 1.8 and -1.2

Try using the formula Solve 2x² - x – 15 = 0 The √ bit should work out as 121 = 11 The answers are +3 and -2.5