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NUMERICAL METHODS
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3.
f ( x) = ln ( x + 2) x + 1, x > 2, x \ .
(a) Show that there is a root of f(x) = 0 in the interval 2 < x < 3 .
(2)
(b) Use the iterative formula
to calculate the values of x1 , x2 and x3 giving you
Edexcel Core 3
Algebra and functions
Topic Assessment
1. Simplify
4x 2 1
.
2 x 2 + 5x 3
[3]
2. Write the following as single fractions in their simplest form.
3x
x
(i)
2
x3 x 9
x 2 3x 4 x + 1
(ii)
.
x 2 25
x 5
2 x 4 x3 + 3x 4
Dx + E
= Ax 2 + Bx + C + 2
2
FUNCTIONS
physicsandmathstutor.com
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8.
The functions f and g are defined by
f : x 6 1 2x 3 , x \
3
g : x 6 4, x > 0, x \
x
(a) Find the inverse function f -1 .
(2)
(b) Show that the composite function gf is
gf : x 6
8 x3 1
.
1 2 x3
(4)
(c) Solv
exp & ln
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5.
The radioactive decay of a substance is given by
R = 1000e ct ,
t
0.
where R is the number of atoms at time t years and c is a positive constant.
(a) Find the number of atoms when the substance started to decay.
(1)
It takes 5730 y
physicsandmathstutor.com
TRIGONOMETRY
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6.
(a) Use the double angle formulae and the identity
cos( A + B) cos A cos B sin A sin B
to obtain an expression for cos 3x in terms of powers of cos x only.
(4)
(b) (i) Prove that
cos x 1 + sin x
+
2 se
EdExcel Core 3
Numerical methods
Topic Assessment
1. (i) By considering turning points, show that x3 3x2 + 5 = 0 has only one real
root and that this root lies between 2 and 1.
[4]
(ii) Show that this root is -1.104, correct to 3 d.p.
[2]
2. (i) Show that
EdExcel Core 3
Differentiation
Topic assessment
1. Using the chain rule, differentiate (x2 1)6.
[3]
2. Show that the derivative of cosec x is cosec x cot x.
[3]
3. Show that the gradient of y = (x2 1)(x 2)3 is given by
dy
= ( x 2) 2 (5 x 2 4 x 3)
dx
4. Fi
physicsandmathstutor.com
TRANSFORMATIONS
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4.
y
A (5, 4)
O
x
B ( 5, 4)
Figure 1
Figure 1 shows a sketch of the curve with equation y = f ( x) .
The curve passes through the origin O and the points A(5, 4) and B( 5, 4).
In separate diagrams, sket
Edexcel Core 3
Trigonometry
Topic Assessment
1. Find all of the angles between 0 and 360 such that
(i) sec x = 2.5
(ii) cosec x = -1.5
[3]
[3]
2. Solve the equation sec 2 x + tan x =
1 for 0 x 2
[5]
3. Solve the equation sin( x +=
30) 2 cos( x + 45) for 0
physicsandmathstutor.com
ALGEBRA
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1.
Given that
2 x 4 3x 2 + x + 1
dx + e
,
(ax 2 + bx + c) + 2
2
( x 1)
( x 1)
find the values of the constants a, b, c, d and e.
(4)
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Name:
Unit 6 Study Guide
1. _ _- Energy from sources that are constantly being formed.
2. _ _- Energy from the sun.
3. _ _- Energy from plant material, manure, and any other organic
matter.
4. _ _- Energy produced from moving water.
5. _ _- Energy produce
Waste Lab 1: Compost Challenge
Objective: Today you and your classmates will work together to make a simple compost system in
under an hour. Throughout the rest of the semester, we will regularly check on our compost systems
and collect data from them. Th
THE GARBAGE STORY
Dealing With Solid Waste Disposal
THE GARBAGE STORY: Dealing With Solid Waste Disposal 1996 AGC/United Learning
Composting
Objective:
You will see how the composting process works by actually creating a compost pile and monitoring it.
Ma
Name_ Period_ Date_
What Are We Throwing Away?
Directions: As we explore whats in our garbage, list items where they fit in the table
below. Hint- They could belong to more than 1 category.
Reduce?
Reuse?
Recycle?
Dispose?
What can be recycled? There are
Conscientious Consumerism:
REDUCING by Choosing Products that are Made Responsibly
*THINK about the products you purchase or use every day. Do you know where they are made? How
they are made? Do the companies that make them try to preserve our environment
Compost Material
*Compost Controllers: This group is responsible for putting the compost material into the compost, but FIRST you will sort and
weigh it. Your most important job is to remove any items that cannot go into the compost, such as products that
Kitchen Cabinet Shocker: Learning About Hazardous Chemicals In Our Homes
TRUE or FALSE
_ 1. Manufacturers of household cleaning agents are required to list all
the ingredients of their products.
_ 2. Labels of all home and garden products must be precise,
Article Analysis
Name:
Directions: Find an article that involves/ deals with todays topic and read it. Complete section 1 while you are reading
the article and section 2 after you finish reading.
Section 1:
Article Title:
Date Published:
Bibliographic Inf
Analyze and Conclude:
1. Did you find it easier to identify & name abiotic biotic factors? _ Why?
_
2. Select 3 abiotic factors you observed and describe how each might affect some of the biotic factors you
observed: _
_
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_
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3. Can biotic factors affect
Name:_Period:_Creature Category:_
Biome Lab: Adapting to the Desert
Purpose: To explore how organisms are adapted to survive in the biomes where they live.
Task: Work with your group to complete the lab activity, but complete and turn in your own lab shee