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relationships.notebook
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January 20, 2017
Completing the square , write in the form (x + a)2 + b.
x2 - 6x + 7
= x2 - 6x + 9 - 9 + 7
= x2 - 6x + 9 - 2
= (x - 3)2 - 2
x2 + 10x - 12
= x2 + 10x + 25 - 25 - 12
= x2 + 10x + 25 - 37
= (x + 5)2 - 37
Quadratic Formula
ax2 +bx + c = 0
Solve for x to 2 decimal places
3x2 - 7x + 2 = 0
a = 3 b = -7 c = 2
x = -(-7) ± √( (-7)2 - 4 x 3 x 2)
2 x 3
= 7± √256
= 7 + 5 = 7 - 56 6
x = 2 and 0.333333
x = 2 , 0.33
relationships.notebook
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January 20, 2017
Quadratic formula
1 Solve for x to 2 decimal places
(a) 2x2 + 10x + 6 =0 (b) 3x2 + 6x - 1 =0
(c) 5x2 - 8x - 2 = 0 (d) x2 - 9x - 5 = 0 ax2 +bx + c = 0
Complete the Square, write in the form (x + a)2 + b.
2 (a) x2 + 10x - 5 (b) x2 + 6x + 10
(c) x2 - 8x - 1 (d) x2 - 8x + 2
Write x2 - 10x + 1 in the form (x + a)2 + b. 3
4 Solve the quadratic equation
3x2 - 9x + 2 = 0 using the approptiate formula
Give the answer to 1 decimal place
Textbook page 211 Q 60 & Q 61
Discriminant
if b
-4ac = 0 then the roots are real and equal
-4ac < 0 then the roots are not real
Find the nature of the roots of y = 3x2 -6x + 4
b2 -4ac
relationships.notebook
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January 20, 2017
Converse of Pythagoras
Is this triangle right angled at A?
A
B
C
12cm6cm
8cm
Similarity
relationships.notebook
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January 20, 2017
Cost depends on
volume
Getting smaller so = 0.8 1620
0.83
0.83 x 260 = £133.12
Discriminant Q 1 & 2 parts (c) (f) (h) (o)
Converse of Pythagoras (a) (d) (f)
Similar figures any three
relationships.notebook
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January 20, 2017
gradient = m = y2-y1
x2 -x1
y - b =m(x - a)
1 Find the equation of the line passing through the
points (9, 5) and (-3, -1)
Straight line
gradient = m = y2-y1
x2 -x1
= 5 - -19 - -3
= 612
= ½
y - b =m(x - a)
a = 9 b = 5 m = ½
y - 5 = ½(x - 9)
y - 5 = ½x - 4.5
y = ½x + 0.5
Straight line
Find the equation of the line:
(a) Gradient 3 passing through (3,1)
(b) Gradient -2 passing through (-7,5)
(c) Gradient ½ passing through (4,-2)
(d) Passing through
1
2
A(3 , 6) B (-3,10)
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January 20, 2017
Inequations
2p + 8 < 5 + 5p
8 < 5 + 3p-2p -2p
-5 -53 < 3p
1 < p÷3 ÷3
3(x - 5) ≥ x + 10
2x - 15 ≥ 10-x -x
+ 15 +15
2x ≥ 25
x ≥ 12.5
÷2 ÷2
3x - 15 ≥ x + 10
Solving inequations
5x - 12 < x - 7-x -x4x -12 < -7
+12+124x < 5÷4 ÷4x < 1.25
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January 20, 2017
Solving inequations
5x - 12 < x - 7-x -x4x -12 < -7
+12+124x < 5÷4 ÷4x < 1.25
Solve for x
1
make up the two equations
solve
Communicate your answer
3b + 2c = 2704b + 3c = 365
12
1 x 3
2 x 2
9b + 6c = 810
8b + 6c = 730
Subtract b + 0 = 80b = 80mm
Substitute b = 80 into 1
3b + 2c = 270
3 x 80 + 2c = 270
240 + 2c = 2702c = 30c = 15 mm
The bricks are 80 mm deep and the cement is 15 mm deep
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January 20, 2017
9 10
13
Page 42 Q 16 17 & 18
Changing the subject of the formulae
Treat the formula as an equation.
Use opposite functions.
G = 6t - r (t)
6t - r = G
6t = G + r
t = G + r6
t is being:
multiplied by 6 then subtract r
add r then divide by 6
3
s = (5t)2 (t)t is being:
Multiplied by five then squared
Square root then divide by five
(5t)2 = s
5t = √s
t = √s5
relationships.notebook
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January 20, 2017
Changing the subject of the formulae
Treat the formula as an equation.
Use opposite functions.
1 P = rt - q (t) 2 W = 6y + st (t)
3 A = πr2 (r) 4 R = 5y (y)πd
Page 102 Q 4 (a) (b) 5 & 6
Parabolas in the form y = kx2
Find the equ\tion of the graph in the form y = kx2
y
x
10203040
1 2 3-1-2-3
y
x
24610
1 2 3-1-2-3
(1 , 10)
(2 , 40)
(-1 , 10)
(-2, 40)
12 = 1
22 = 4
y = 10x2
k = 10
(1,4)
(-1,4)
12 = 1
y = 4x2
k = 4
relationships.notebook
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January 20, 2017
Quadratic Graph - The Parabola
y
x
y=kx2
(3,36)
y=kx2
(1,4)
y
x
Find the equations of these lines.
y=kx2
(1,-4)
y
xx
y=kx2
(1,8)
y
x
y=kx2
(6,-72)
y
x
y=kx2
(-4,160)
y
x
Draw and label the following graphs on the same x and y axis.
Show at least one point which lies on each graph. y=5x2 y=-x2
y
x
y
x
y=-2x2y=3x2
y
x
y
x
Solve quadratics by factorising
relationships.notebook
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January 20, 2017
Turning point from completing the square
y =(x - 5)2 + 7 Find the axis of symmetry and the turning point
Axis of symmetry x = 5
Turning point (5, 7)
y = (x + a)2 + b
1
2
Find a and b from the diagram
turning point (2,1)
y = (x - 2)2 + 1
Write down (a)the equation of the axis of symmetry
(b) coordinates of the turning point
1 y = (x + 6)2 + 7 2 y = (x - 5)2 + 10 3 y = (x + 9)2 -1
4 y = (x - 1)2 - 3 5 y = (x - 2)2 - 8
Turning point from completing the square
write down the value of a and b where a and b are integers
relationships.notebook
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January 20, 2017
y = kx2 (b) (e) (h)
y = (x - a)2 + b (a) (d) (g)
Change the subject 1 (a) (g) (l) 2(a) (g) (l)
Scientific Notation and significant figures
5 solar years = 3.156 x 107 x 5
= 3.156 EXP 7 x 5
or = 3.156 x10x 7 x 5
= 157 800 000
= 1.578 x 108
= 1.58 x 108
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January 20, 2017
1000 carbons = 2.03 x 10-23 x 1000
= 2.03 EXP (-) 23 x 1000
or = 2.03 x10x ± 23 x 1000
= 2.03 x 10-20
Scientific Notation and significant figures
Scientific Notation and significant figures
1
2
3
4
Page
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January 20, 2017
Angles in a circle
Angles in a circle
When a radius or diameter
meet a tangent they meet at right angles
relationships.notebook
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January 20, 2017
Angles in a circle
When a radius or diameter
meet a tangent they meet at right angles
A triangle drawn inside a semi
circle with the diameter has a
right angle on the
circumference.
Angles in a circle
When a radius or diameter
meet a tangent they meet at right angles
A triangle drawn inside a semi
circle with the diameter has a
right angle on the
circumference.
A triangle made from 2 radii is an
isosceles triangle.
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January 20, 2017
AOBC
Dif <ODA = 19o Calculate the size of angle < DBO
Trig Graphs
Draw the graph of y = 5sin2x 0 ≤ x≤ 360
y
x
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January 20, 2017
Trig Graphs
Draw the graph of y = -2cos4x 0 ≤ x≤ 360
y
x
y
x
5
-5
180 36090 270
Trig Graphs
What is the equation of this graph?
y
x
2
-2
180 36090 270
relationships.notebook
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January 20, 2017
Trig equations
2tan x˚ = 1.8 0 ≤ x < 360
Angles All
Trig graphs 1. (d) (g) (h) (i)
2. all
Trig equations 1. (a) (b) (c)
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January 20, 2017
