7 Linear Programming
5.
7 Linear Programming
Review Exercise 7 (p. 7.3)
1.
(a) Yes
(c) No
(e) No
2.
(a)
3x + 2y = 6
x 2 0
y
6
3
4
3
(b) Yes
(d) No
(f) Yes
x
y
1
3
0
1
1
1
Activity
Activity 7.1 (p. 7.6)
1. (a) For point P, x + y = 1 + 4 = 5
For point Q, x
NSS Mathematics in Action 5B Full Solutions
4.
10 More about Probability
(a)
1st toss
2nd toss
Review Exercise 10 (p. 10.4)
1.
H
Total number of possible outcomes = 7
(a) Number of favourable outcomes = 3
3rd toss
H
3
P(a yellow card with a happy face) =
Bio 1B Evolution (Mishler) Practice questions Fall 2008 *Answers are on the last page, but please don't peek till you've tried hard on the question * 1. Evolution is often described as "the theme that ties together all aspects of biology." This is because
Biology Lesson 6 Eukaryotic Cells
Mitochondrial Structure
-PDC and Krebs Cycle occur in the matrix
-ETC Complexes are located in the inner membrane
-Protons are pumped (actively) from the matrix to
the intermembrane space
-ATP synthase is located in the i
x
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Study Questions for BIO 319 / BEE 574 - Midterm Exam; Lectures 1-7
1. What are the 2 types of data storage in GIS? How is data stored in each of these
systems? How would information about elevation be indicated in each of these
systems?
2. What is Landsca
Goal:
Learn how quantitative
patterns of phenotype or
genotype change over time
provide evidence for the
action of natural selection.
1
Natural selection but
no evolution.
Why are there
intermediate
phenotypes in the
F2?
Directional Selection Homozygote A
Goal
Review some basic concepts of heredity that
are also important for evolu8on:
Linkage and Linkage Disequilibrium
Heritability
What is Linkage?
Linkage is defined genetically: the failure of two genes to assort
independently.
Goal
Understand how quantitative patterns of
phenotype or genotype change over
time provide evidence for the action of
natural selection.
1
Darwins Finches and
Natural Selection
Adapted from a set of power point slides by
Cheryl Heinz, Dept. of Biologica
Exercise 1
The figure shows a square ABCD inscribed in another
square PQRS. The length of sides of ABCD is 10. Let
AP BQ CR DS x.
(a) If the area of the shaded region is y, show that
y 2x 10 2 x 2 .
(b) Find the value of x if the area of the shaded region
Exercise 1
Choose the BEST answer for each question.
1. A good is not scarce if
A.
B.
C.
D.
its supply is increased.
it is distributed by the government free of charge.
only one person wants to have it.
no one wants to have the good.
2. Which of the follo
Unit 26 Solutions
Unit 26 Further Applications
B
4.
Jenny spent over $500 once.
Exercise (P. 26-4)
She can play the game once.
Probability of winning the second prize
1.
B
=
=
which is 5 times $0.3.
The decrease in the number of cans sold
= 5 15
2
6
=
The
Unit 25 Solutions
Unit 25 Statistics
5.
B
1
HKCEE reference 01Q5
Total number of employees
Exercise (P. 25-6)
= 3 + 9 + 14 + 12 + 5 + 4 + 3
= 50
1.
Number of employees whose salaries lie between
C
The relationship between a persons weight and the
$4 000 a
Unit 23 Solutions
1
Substituting (1, 4) into the expression x + y,
Unit 23 Linear Programming
x+y=1+4=5<6
Exercise (P. 23-4)
II is not true.
Substituting (1, 4) into the expression x,
1.
x=1>0
A
x 0 .(i)
III is true.
The equation of the y-axis is x = 0.
O
Unit 22 Solutions
Unit 22 Probability
5.
1
C
[Note: A number is divisible by 3 when the sum of its
Exercise (P. 22-6)
digits is divisible by 3.]
+ can be 0, 2, 4, 6, 8, 10, 12, 14, 16 or 18.
1.
C
Among these values, only 4, 10 and 16 can be added
P(blue
Unit 21 Solutions
Unit 21 Permutation and
6.
A
(n 2)(n 3) (n t)
Combination
(n 2)(n 3).( n t )(n t 1)(n t 2) . 3 2 1
(n t 1)( n t 2) . 3 2 1
( n 2)!
(n t 1)!
( n 2 )!
[( n 2) (t 1)]!
Exercise (P. 21-3)
1.
1
D
Number of different selections
2
P n1
t
= 16
Unit 20 Solutions
Unit 20 Coordinate Geometry II
6.
6 8
,
centre of circle
2
2
(3, 4)
For I,
Exercise (P. 20-5)
1.
HKCEE reference 04Q53, 02Q53
C
I is true.
C
For II,
radius of circle 32 4 2 11
14 11
II is not true.
For III, distance between centre
Unit 19 Solutions
Unit 19 More about Graphs of
5.
points of the graph of y = f(x) and x-axis are a, d and
f.
Exercise (P. 19-5)
The answer is C.
D
The slope of y = 2x is 2.
6.
points of the graphs of y = 2 sin 2x and y = 1 are 15
Since y = 2x and y = ax
Unit 18 Solutions
Unit 18 More about Equations
5.
D
y = x + 6
x=6y
Substituting x = 6 y into y = 2x2,
Exercise (P. 18-4)
y = 2(6 y)2
1.
y = 2(36 12y + y2)
B
From the graph, the points of intersection are (2 , 3)
2y2 25y + 72 = 0
and (6 , 3).
(2y 9)(y 8)
Unit 17 Solutions
Unit 17 Trigonometry II
Applications of
Trigonometry
3.
A
HKCEE reference 00Q30
Exercise (P. 17-6)
1.
B
HKCEE reference 03Q23
With the notation in the figure,
a = 40
CBA = 60
b = 60 40
= 20
c=b
= 20
With the notation in the figure,
d =
Unit 16 Solutions
Unit 16 Trigonometry I Basic
Trigonometry
4.
C
Exercise (P. 16-6)
In the figure, using Pythagoras theorem,
1.
B
x 132 12 2 5
5
cos
13
HKCEE reference 00Q51
5.
Since 0 x 90, 0 cos x 1.
In the figure, using Pythagoras theorem,
0 4 cos x
Unit 15 Solutions
Unit 15 Deductive Geometry II
Circles
3.
A
OC = radius
1
AB
2
1
AM = (25 + 9) cm
2
AM = 17 cm
AM =
Exercise (P. 15-6)
1.
C
AB = AC
For I,
OE = (25 17) cm
1
AD = DB = AB
2
1
AE = EC = AC
2
AM = 8 cm
EC = 17 2 82 cm
EC = 15 cm
AD =
Unit 14 Solutions
Unit 14 Coordinate Geometry I
5.
C
HKCEE reference 05Q32
Let D = (x, y).
The diagonals of a parallelogram bisect each other.
Exercise (P. 14-6)
The mid-point of AC = the mid-point of BD
1
1.
D
2
The distance between the points A(2, 4) a
Unit 13 Solutions
Unit 13 Inequalities in One
Unknown
For III: Let x = 2 and y = 1, then xy < 0.
Exercise (P. 13-4)
The answer is B.
1.
B
For I:
HKCEE reference 10Q11
x + y = 2 + (1) = 1 > 0
III may not be true.
4.
Let x = 1 and y = 2, then x > 0 > y.
2
Unit 12 Solutions
Unit 12 Rate, Ratio and Variation
4.
D
100
U.S. dollars
85.2
100
=
94.1 Japanese yen
85.2
= 110 Japanese yen, cor. to the nearest
Japanese yen
1 Euro =
Exercise (P. 12-5)
1.
D
Rate of pipe A =
1
tank/h
12
5.
1
Rate of pipe B =
tank/h
8
Unit 11 Solutions
Unit 11 Laws of Indices,
Exponential Functions
and Logarithmic
Functions
8.
C
4a = 8b
(22)a = (23)b
22a = 23b
2a = 3b
i.e.
a3
b2
a:b =3:2
Exercise (P. 11-4)
1.
D
(a3x)3x = a(3x)(3x) = a 9 x
2
9.
C
2x + 3 = 2x + 28
2.
C
2 x 23 2 x 28
(3n)
Unit 8 Solutions
4.
Unit 8 Equations
1 x 5 1 x 1
2
4 3 3 2
Exercise (P. 8-6)
1.
B
A
x 5 2x 1 24
x 7 24
HKCEE reference 06Q6, 01Q11
For I,
x 17
L.H.S. = (x + 3) (x 3)
L.H.S. = x2 9
5.
L.H.S. R.H.S.
L.H.S. = (x + 1)2
For II,
Substituting x = 2 into
2
L.
Unit 7 Solutions
Unit 7 Number Systems
5.
B
Let
Exercise (P. 7-4)
x = 0.24 . (i)
100x = 24.24 . (ii)
(ii) (i):
1.
D
x=
253
0.253
999
1
0.253 , 196 and 3 are rational, and 2 is
3
irrational.
6.
A
Let
C
For I,
For II,
999 999x = 234 567
x=
5 11
is ration