1. GCSE: Curved Graphs Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 31 st December 2014 GCSE Revision Pack Reference: 94, 95, 96, 97, 98

2. GCSE Specification The diagram shows the graph of y = x 2 – 5x – 3 (a) Use the graph to find estimates for the solutions of (i) x 2 – 5x – 3 = 0 (ii) x 2 – 5x – 3 = 6 1 2 3 4

3. Skill #1: Recognising Graphs Linear The line is known as a straight line. ?? ?

4. Quadratic The line for a quadratic equation is known as a parabola. ?? ? Skill #1: Recognising Graphs

5. Cubic x y x y ? ? ? ? Skill #1: Recognising Graphs

6. Reciprocal ? The lines x = 0 and y = 0 are called asymptotes.  An asymptote is a straight line which the curve approaches at infinity. ? ? You don’t need to know this until A Level. Skill #1: Recognising Graphs

7. Exponential x y ? Skill #1: Recognising Graphs ?

8. 5 -5 5 The equation of this circle is: x 2 + y 2 = 25 ? Circle Skill #1: Recognising Graphs

9. Quickfire Circles 1 1 x 2 + y 2 = 1 3 -3 3 x 2 + y 2 = 9 4 -4 4 x 2 + y 2 = 16 8 -8 8 x 2 + y 2 = 64 10 -10 10 -10 x 2 + y 2 = 100 6 -6 6 x 2 + y 2 = 36 ? ? ? ? ? ?

10. Card Sort Match the graphs with the equations. ABCD EFGH IJKL x) y = x 2 + x - 2 ix) y = 2x 3 i) y = 5 - 2x 2 vii) y=-2x 3 + x 2 + 6x iv) y = 3/x iii) y = -3x 3 viii) y = -2/xii) y = 4 x xii) y = 2x – 3 v) y = x 3 – 7x + 6 xi) y = sin (x) vi) A: quadratic B: cubic C: quadratic D: cubic E: cubic F: reciprocal G: cubic H: reciprocal I: exponential J: linear K: sinusoidal L: fictional Equation types: ? ? ? ? ? ? ? ? ? ? ? ?  Click to reveal answers.

12. 90 180 270 360 8 1 090180270360 0100 ????? Click to brosketch Skill #2: Plotting and recognising trig functions.

13. Test Your Understanding 90 1 180 0 ? ?

14. 90 180 270 360 8 1 090180270360 1001 ????? Click to brosketch

15. Quickfire Coordinates ???? ????

16. SKILL #3: Using graphs to estimate values Bro Tip for (b): Look at what value has been substituted into the equation in each case. ? ? ?

17. Test Your Understanding ? ?

18. 90 180 270 360 1 Using a Trig Graph Q ? Q ?

19. 90 180 270 360 1 Test Your Understanding ? ?

20. Exercise 1 (on provided sheet) Identify the coordinates of the indicated points. 1 1 ? ? ? ? ? 2 a b c ? Match the graphs to their equations. ? 3

21. -15 -7 -6 1 Reveal ???? Exercise 1 (on provided sheet) 4

22. Exercise 1 7 ? ? b c a 5 6 ? ? ? ? ? ? ?

23. 8 ? ? ?

24. (1,7) (3,175) ? Bro Hint: Substitute the values of the coordinates in to form two equations. You’re used to solving simultaneous equations by elimination – either adding or subtracting. Is there another arithmetic operation?

25. Test Your Understanding Q  ? ?

26. Exercise 1 (continued) 9 2 3 4 ? ? ? ?