1. SCHOLAR National 5 Mathematics Revision Session Thursday 14 th 7:30pm You will need a pencil, paper and a calculator for some of the activities

2. SCHOLAR online tutor for Maths and Author of the SCHOLAR National 5 & Higher courses Margaret Ferguson

3.  Hints & Tips for the Exam  Vectors Journeys  Completing the Square  Algebraic Factions  The Straight Line  Trig Identities  Surds & Indices  Percentages  Simultaneous equations  Functions  Problem solving involving Triangles and Circles  Statistics  Similarity Tonight’s Session will cover You will need paper, a pencil and a calculator for some of the activities and I will invite you to vote for the correct answer during the presentation.

4. Paper I  Paper I is the non-calculator paper and lasts for 1 hour  There are usually 13 questions and the paper is worth 40 marks  Try to complete questions 1 - 4 in the first 10 minutes  Allow no more that 5 minutes for each of the remaining questions  This will leave you 5 minutes at the end to go over the paper. Paper II  Paper II is the calculator paper and lasts for 1 hour 30 minutes  There are usually 13 questions and the paper is worth 50 marks  If you can’t do a question highlight it and come back to any highlighted questions when you have finished the paper. The National 5 Maths Exam

5. Formula List The roots of ax 2 + bx + c = 0 are Sine rule: Cosine rule:a 2 = b 2 + c 2 – 2bc cos A or Area of a triangle:A = ½ ab sin C Volume of a sphere:V = Volume of a cone:V = ⅓πr 2 h Volume of a pyramid:V = ⅓Ah Standard deviation:

6.  In the diagram below, ABC is an isosceles triangle and M is the mid-point of BC. Express in terms of u and w. What is in terms of u and w? A B C u w M w + u What is in terms of u and w? ½(w + u) = ½w + ½u What is in terms of u and w? = -w + ½w + ½u = ½u - ½w

7. Express x 2 + 5x + 7 in the form (x + a) 2 + b Vote for the correct answer now ✓ x 2 + 5x + 7 = (x 2 + 5x) + 7

8. Simplify Factorise x 2 – 2x – 3, what do you get?(x – 3)(x + 1) Factorise x 2 – 9, what do you get?(x – 3)(x + 3)

9. What is the gradient of the line with equation 7x – 2y = 5 a)-7 b)7 c)- d) ✓ Vote for the correct answer now 7x – 2y = 5 -2y = -7x + 5

10. Prove that tan 2 θ - tan 2 θsin 2 θ = sin 2 θ LHS = tan 2 θ - tan 2 θsin 2 θ = tan 2 θ(1 – sin 2 θ) = tan 2 θ x cos 2 θ = sin 2 θ = RHS What do you do first? What is 1 – sin 2 θ the same as? What is tan 2 θ the same as? What can we do now? Remember

11. Rationalise the denominator and simplify fully a) b) c) d) ✓ Vote for the correct answer now

12. Expand (2a -½ - 3)(a -½ + 2) giving your answer in its simplest form. (2a -½ - 3)(a -½ + 2) = 2a -1 + 4a -½ - 3a -½ - 6 = 2a -1 + a -½ - 6

13. In a sale all items are reduced by 20%. If Graham bought a guitar in the sale for £319.20, how much was the full price? a)£399.00 b)£383.04 c)£255.36 d)£351.12 ✓ Vote for the correct answer now £319.20 = 80% What percentage is £319.20? What is 1%? 1% = 319.20 ÷ 80 = 3.99 What is 100%? 3.99 x 100 = £399.00

14. A theatre sells seats in the stalls and the circle. For opening night of a new play all 640 seats were sold. Seats in the stalls costs £42 and seats in the circle cost £48. The total income from tickets was £28632. How many seats are there in the stalls and the circle respectively? s + c = 640 42s + 48c = 28632 x (-42) -42s - 42c = -26880 42s + 48c = 28632 6c = 1752 c = 292 1 2 Let c = 292 in equation 1. s + 292 = 640 s = 348 Let s be the number of seats in the stalls and c in the circle? There are 348 seats in the stalls and 292 in the circle. What can we do now? +

15. The function f(x) = x 2 – 12x + 16 What is the value of x when the function is equal to -20? a)176 b)-144 c)18 d)6 ✓ Vote for the correct answer now f(x) = -20  x 2 – 12x + 16 = -20 x 2 – 12x + 36 = 0 How do we find x? Factorise (x – 6)(x – 6) = 0 x – 6 = 0 x = 6

16. The shape of the Tyne swing bridge is an arc of a circle. The length of the span is 86m and the radius of the circle it was formed from is 84m. What is the height of the span of the bridge? 43 x What is the length of x? x = 72.16 How do we find h, the height of the span? h = radius - x h = 84 – 72.16 = 11.84m h 86m 84m What can we add to the diagram?

17. The mean daytime temperature on the island of Aruba is 31°C with a standard deviation of 0.7. The mean daytime temperature in Hawaii is 29°C with a standard deviation of 1.9. Make two valid comparisons between the temperature recordings on the two islands. What what can you say about the average temperatures? The average temperature on Aruba is slightly higher than Hawaii because the mean is 2 °C higher. What what can you say about the standard deviations? The temperature on Aruba is more consistent than Hawaii because the standard deviation is lower. Why might that be important?

18. The two bottles of perfume are said to be similar. Calculate the cost of the large bottle. 4.8cm 10.8cm £19.80 £??.?? Do we need a scale factor for enlargement of reduction? Enlargement What is the length scale factor? What does the price depend on?Volume What is the volume scale factor? What is the cost of the large bottle? = £225.53

19. Question Time Make sure you arrive in good time for the exam Check the batteries in your calculator, if in doubt get new ones Get plenty of practice over the next few days If you are stuck on anything go and see your teacher Don’t waste time in the exam if you are stuck Carry on and go back to these questions at the end Good luck I hope to see you next year for Higher If you have any questions about the National 5 course or the exam ask now Please give us feedback by following the link provided