Session 1 Quadratics and Beyond - MathedUp · Aim High Session 1 Algebra and Beyond v2.notebook April 09, 2017 0 x 2x3 4x2 5x1 x 2 x 4 2x 5 x 3 Time in seconds Frequency Density Mr

Aim High Session 1 Algebra and Beyond v2.notebook April 09, 2017

Session 1Quadratics and Beyond


x2 - 6x - 16 = 0

Factorising

Completing the Square Quadratic Formula

Solving Quadratics 1

(x 8)(x + 2) = 0

x = 8 and x = 2

(x 3)2 25 = 0(x 3)2 = 25x 3 = ±5

x = ±5 + 3x = 8 and x = 2

?

?a=1,b=6,c=16 and b24ac=100

2x = 6±√100

x = 8 and x = 2?


x2 - 6x - 16 = 0

Factorising

Completing the Square Quadratic Formula

Solving Quadratics 1

(x 8)(x + 2) = 0

x = 8 and x = 2

(x 3)2 25 = 0(x 3)2 = 25x 3 = ±5

x = ±5 + 3x = 8 and x = 2

a=1,b=6,c=16 and b24ac=100

2x = 6±√100

x = 8 and x = 2


3x2 + 11x - 4 = 0

Completing the Square

Quadratic Formula

2x2 + 12x - 9 = 0

Quadratic Formula

FactorisingSolving Quadratics 2

(3x 1)(x + 4) = 0

x = 1/3 and x = 4?

a=3,b=11,c=4 and b24ac=169

x = 11±√169

x = 1/3 and x = 46?

2(x2 + 6x) 9 = 02(x + 3)2 27 = 0

x + 3 = ±√13.5x = ±√13.5 3

x = 0.67 and x = 6.67

(x + 3)2 = 13.5

a=2,b=12,c=9and b24ac=216

x = 12±√2164

x = 0.67 and x = 6.67?

?


3x2 + 11x - 4 = 0

Completing the Square

Quadratic Formula

2x2 + 12x - 9 = 0

Quadratic Formula

FactorisingSolving Quadratics 2

(3x 1)(x + 4) = 0

x = 1/3 and x = 4

a=3,b=11,c=4 and b24ac=169

x = 11±√169

x = 1/3 and x = 46

2(x2 + 6x) 9 = 02(x + 3)2 27 = 0

x + 3 = ±√13.5x = ±√13.5 3

x = 0.67 and x = 6.67

(x + 3)2 = 13.5

a=2,b=12,c=9and b24ac=216

x = 12±√2164

x = 0.67 and x = 6.67


If in doubt, use the quadratic formula


Quadratic FormulaA quadratic equation is usually written in the form It needs to be in

this form for us to be able to solve it


a =

Example

b = c = b2 4ac = 3 -6 2 12


Factorising with a coefficient of x2

Example 1 Solve this:


Solve together

The area of the shaded region is 6 cm2.Work out the value of x.


Shape & Quadratics

The area of the shaded region is 6 cm2.Work out the value of x.

3x(4x + 1) - 2(6x - 3) = 612x2 + 3x - 12x + 6 = 6

12x2 - 9x = 03x(4x - 3) = 0x = 0 and x = 3/4

Have we solved the problem?


Form a quadratic equation for each of these problems.Once you have found them all, solve them using a suitable method


2

ABCH is a square.HCFG is a rectangle.CDEF is a square.They are joined to make an Lshape.The area of the Lshape is 163 cm2.


Shape & Quadratics


2

ABCH is a square.HCFG is a rectangle.CDEF is a square.They are joined to make an Lshape.The area of the Lshape is 163 cm2.

4x2 + 24x + 36

6x + 18 9

4x2 + 30x + 63 = 1634x2 + 30x - 100 = 0

2x2 + 15x - 50 = 0(2x - 5)(x + 10) = 0

x = 2.5 and x = -10


(3x 2) cmE F

GHCD

x cm

4x cm

(2x + 2) cm

ABCD is a trapezium.EFGH is a square.The area of the trapezium is equal to the area of the square.Work out the value of x.


Shape & Quadratics


9x2 - 12x + 4 = 5x2 + 5x4x2 - 17x + 4 = 0

(4x - 1)(x - 4) = 0x = 0.25 and x = 4

(3x 2) cmE F

GHCD

x cm

4x cm

(2x + 2) cm

ABCD is a trapezium.EFGH is a square.The area of the trapezium is equal to the area of the square.Work out the value of x.

9x2 - 12x + 4

5x2 + 5x


(x + 3)

9

Work out the value of x.


Shape & Quadratics


4x2 + 4x + 1 = x2 + 6x + 903x2 - 2x - 89 = 0

x = -5.12 and x = 5.79

(x + 3)

9

Work out the value of x.

x = 2 ±√10726


Solve together


There are n sweets in a bag.Four of the sweets are green.The rest of the sweets are blue.

Nicky takes at random a sweet from the bag.He eats the sweet.

Nicky then takes at random another sweet from the bag.He eats the sweet.

The probability that Nicky eats two blue sweets is .

Find the total number of sweets in the bag.

n


Solve together


You need to change 60 to 68.



x(x5) x x+3

35

P S

The Venn diagram shows information about

ξ = 66 football shirts in the collecon

P = football shirts from teams in the ‘Premier League’

S = football shirts that are signed

A football shirt is chosen at random. It is signed.

Work out the probability that it was a football shirt from a team in the ‘Premier League’.

x2 - 3x + 38 = 66x2 - 3x - 28 = 0

(x - 7)(x + 4) = 0x = 7 and x = -4


The probability that both beads will be different is .

How many beads are in the box?

10x - 50 x2 =

4 9

90x - 450 = 4x2 4x2 - 90x + 450 = 02x2 - 45x + 225 = 0(2x - 15)(x - 15) = 0

x = 7.5 and x = 15


x 2x3 4x2 5x10

x2

x4

2x5

x3

Time in seconds

Frequency Density

Mr Ladak gives his students an equation to solve. He records the time it takes for each student to solve the equation. The data gathered is used to create a histogram.

68 students take between '2x3' and '4x2' seconds to solve the equation. How many students did Mr Ladak ask?

x2 + 0.5x = 68

2x2 + x - 136 = 0

x = -8.5 and x = 8

x2 + 0.5x - 68 = 0

x = -1 ±√10894


There are n sweets in a bag.Four of the sweets are green.The rest of the sweets are blue.

Nicky takes at random a sweet from the bag.He eats the sweet.

Nicky then takes at random another sweet from the bag.He eats the sweet.

The probability that Nicky eats two blue sweets is .

Find the total number of sweets in the bag.

n2 - 9n + 20n2 - n =

1 3

3n2 - 27n + 60 = n2 - n2n2 - 26n + 60 = 0

n2 - 13n + 30 = 0(n - 3)(n - 10) = 0

n = 3 and n = 10


f(x) = 10 − x2 for all values of x

g(x) = (x + 8)(x + 3) for all values of x.

Solve f(x) = g(x)

10 - x2 = x2 + 11x + 242x2 + 11x + 14 = 0

(2x + 7)(x + 2) = 0 x = -3.5 and x = -2


9x2 + 6x + 1 = 3x2 + 16x2 + 6x = 0

6x(x + 1) = 0 x = 0 and x = -1


(x - 5)2 - 11 = 5x2 - 10x + 14 = 5

(x - 9)(x - 1) = 0 x = 9 and x = 1

x2 - 10x + 9 = 5


x2 - 6 = x4 - 12x2 + 30

(a - 9)(a - 4) = 0 a = 9 and a = 4

a2 - 13a + 36 = 0x4 - 13x2 + 36 = 0, let a = x2

x2 = 9 and x2 = 4 x = ±3 and x = ±2


Challenge!


Uses for the 'Formula'


Other uses for the 'Formula'

101 uses

http://plus.maths.org/content/101-uses-quadratic-equation

Attachments

tatiana.ppt

Quadratic equations * *

Tatiana

Christmas Day 2006 Tatiana escaped


*


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SMART Notebook

Page 1: Quadratics & BeyondPage 2: Solving Quadratics 1Page 3: Solving Quadratics 1Page 4: Solving Quadratics 2Page 5: Solving Quadratics 2Page 6: Apr 9-16:07Page 7: Quadratic FormulaPage 8: ExamplePage 9: Apr 9-16:00Page 10: Shape & Quadratics 1Page 11: Shape & Quadratics 1Page 12: Apr 9-15:38Page 13: Shape & Quadratics 2Page 14: Shape & Quadratics 2Page 15: Shape & Quadratics 3Page 16: Shape & Quadratics 3Page 17: Shape & Quadratics 4Page 18: Shape & Quadratics 4Page 19: Shape Beyond GCSEPage 20: Apr 9-15:48Page 21: Data & Quadratics 4Page 22: Apr 9-15:46Page 23: Data & QuadraticsPage 24: Data Beyond GCSEPage 25: Data & Quadratics 1Page 26: Data & Quadratics 2Page 27: Data & Quadratics 3Page 28: Data & Quadratics 4Page 29: Functions & QuadraticsPage 30: Apr 9-15:55Page 31: Functions Beyond GCSEPage 32: Functions & Quadratics 1Page 33: Functions & Quadratics 2Page 34: Functions & Quadratics 3Page 35: Functions & Quadratics 4Page 36: Challenge!Page 37: Uses for the 'Formula'Page 38: Other uses for the 'Formula'Attachments Page 1

Documents

Session 1 Quadratics and Beyond - MathedUp · Aim High Session 1 Algebra and Beyond v2.notebook April 09, 2017 0 x 2x3 4x2 5x1 x 2 x 4 2x 5 x 3 Time in seconds Frequency Density Mr