GCSE Curved Graphs Dr J Frost jfrosttiffin kingston

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GCSE: Curved Graphs Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com GCSE

GCSE: Curved Graphs Dr J Frost (jfrost@tiffin. kingston. sch. uk) www. drfrostmaths. com GCSE Revision Pack Reference: 94, 95, 96, 97, 98 Last modified: 31 st August 2015

GCSE Specification 1 3 The diagram shows the graph of y = x 2

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

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

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

Skill #1: Recognising Graphs Quadratic ? ? The line for a quadratic equation is

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

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

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

Skill #1: Recognising Graphs Reciprocal ? ? The lines x = 0 and y

Skill #1: Recognising Graphs 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 Exponential y ? x ?

Skill #1: Recognising Graphs Exponential y ? x ?

Skill #1: Recognising Graphs Circle The equation of this circle is: x 2 +

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

Quickfire Circles 1 3 1 -1 -1 2 = 16 x 2 + y?

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

Card Sort Match the graphs with the equations. A B E F I C

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

0 8 90 ? 180 270 360 ? -1? 0 1 90 180 270

0 8 90 ? 180 270 360 ? -1? 0 1 90 180 270 360 -1 Skill #2: Plotting and recognising trig functions. Click to brosketch

Test Your Understanding 90 ? 1 180? 0

Test Your Understanding 90 ? 1 180? 0

0 8 90 1 0 ? ? 180 -1? 270 0? 360 1? 1

0 8 90 1 0 ? ? 180 -1? 270 0? 360 1? 1 90 180 270 360 -1 Click to brosketch

Quickfire Coordinates ? ? ? ? ?

Quickfire Coordinates ? ? ? ? ?

SKILL #3: Using graphs to estimate values Bro Tip for (b): Look at what

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

Test Your Understanding ? ?

Test Your Understanding ? ?

Using a Trig Graph Q 1 ? 90 180 270 360 -1 Q ?

Using a Trig Graph Q 1 ? 90 180 270 360 -1 Q ?

Test Your Understanding ? 1 ? 90 180 270 360 -1

Test Your Understanding ? 1 ? 90 180 270 360 -1

Exercise 1 (on provided sheet) 3 Match the graphs to their equations. 1 Identify

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

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

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

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

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

Exercise 1 8 ? ? ?

Exercise 1 8 ? ? ?

 (3, 175) (1, 7) Bro Hint: Substitute the values of the coordinates in

(3, 175) (1, 7) 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? ?

Test Your Understanding Q ? N ?

Test Your Understanding Q ? N ?

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

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