@PROFDOCDIGITALLIBRARIES
Table of Contents
Chapter 1: Linear Equations and Straight Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Programming, A Geometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Counting 5–1
Chapter 6: Probability 6–1
PR
Chapter 7: Probability and Statistics 7–1
Chapter 8: Markov Processes 8–1
O
Chapter 9: The Theory of Games 9–1
FD
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Logic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
O
C
, C
O
FD
O
PR
,@PROFDOCDIGITALLIBRARIES
Chapter 1
Exercises 1.1
6. 5
Left 1, down
1. 2
Right 2, up 3 y
y
(2, 3)
x
x
2
7. Left 20, up 40
2. Left 1, up 4 y
y
PR
(–20, 40)
(–1, 4)
x
x
O
8. Right 25, up 30
3. Down 2 y
y
FD
(25, 30)
x
x
(0, –2)
O
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
y (—2, 2).
C
10. Point P is 3 units to the right and 2 units down or
(3,—2).
x
(2, 0) 1
11. —2(1) + (3) = —2 +1 = —1so yes the point is
3
on the line.
5. Left 2, up 1 1
y 12. —2(2) + (6) = —1 is false, so no the point is not
3
on the line
(–2, 1)
x
, 1 24. 0 = 5
13. —2x + y = —1 Substitute the x and y
no solution
3
coordinates of the point into the equation: x-intercept: none
l'1 ıh 'l1ıh 1 When x = 0, y = 5
'y' , 3ı → —2' ı+ (3) = —1 → —1+1 = —1 is y- intercept: (0, 5)
2 J y 2J 3
a false statement. So no the point is not on the 25. When y = 0, x = 7
line. x-intercept: (7, 0)
l 1 h l1 h 0=7
14. —2 ' ı +' ı (—1) = —1 is true so yes the point is no solution
y-intercept: none
'y3ıJ 'y3ıJ
on the line. 26. 0 = –8x
x=0
15. m = 5, b = 8 x-intercept: (0, 0)
y = –8(0)
16. m = –2 and b = –6
PR
y=0
17. y = 0x + 3; m = 0, b = 3 y-intercept: (0, 0)
1
27. 0 = x – 1
2 2
18. y = x + 0; m = , b=0
3
3 3
x=3
19. 14x + 7 y = 21 x-intercept: (3, 0)
O
1
7 y = —14x + 21 y = (0) – 1
3
y = —2x + 3
y = –1
y-intercept: (0, –1)
FD
20. x — y = 3 y
—y = —x + 3
y = x —3
(3, 0)
x
21. 3x = 5
(0, –1)
5
O
x=
3
1 2 28. When x = 0, y = 0.
22. – x+ y = 10
C
2 3 When x = 1, y = 2.
2 1 y
y= x +10
3 2
3
y= x +15 (1, 2)
4 x
(0, 0)
23. 0 = —4x +8
4x = 8
x=2
x-intercept: (2, 0)
y = –4(0) + 8
y=8
y-intercept: (0, 8)
Table of Contents
Chapter 1: Linear Equations and Straight Lines 1–1
Chapter 2: Matrices 2–1
Chapter 3: Linear Programming, A Geometric Approach 3–1
Chapter 4: The Simplex Method 4–1
Chapter 5: Sets and Counting 5–1
Chapter 6: Probability 6–1
PR
Chapter 7: Probability and Statistics 7–1
Chapter 8: Markov Processes 8–1
O
Chapter 9: The Theory of Games 9–1
FD
Chapter 10: The Mathematics of Finance 10–1
Chapter 11: Logic 11–1
Chapter 12: Difference Equations and Mathematical Models 12–1
O
C
, C
O
FD
O
PR
,@PROFDOCDIGITALLIBRARIES
Chapter 1
Exercises 1.1
6. 5
Left 1, down
1. 2
Right 2, up 3 y
y
(2, 3)
x
x
2
7. Left 20, up 40
2. Left 1, up 4 y
y
PR
(–20, 40)
(–1, 4)
x
x
O
8. Right 25, up 30
3. Down 2 y
y
FD
(25, 30)
x
x
(0, –2)
O
9. Point Q is 2 units to the left and 2 units up or
4. Right 2
y (—2, 2).
C
10. Point P is 3 units to the right and 2 units down or
(3,—2).
x
(2, 0) 1
11. —2(1) + (3) = —2 +1 = —1so yes the point is
3
on the line.
5. Left 2, up 1 1
y 12. —2(2) + (6) = —1 is false, so no the point is not
3
on the line
(–2, 1)
x
, 1 24. 0 = 5
13. —2x + y = —1 Substitute the x and y
no solution
3
coordinates of the point into the equation: x-intercept: none
l'1 ıh 'l1ıh 1 When x = 0, y = 5
'y' , 3ı → —2' ı+ (3) = —1 → —1+1 = —1 is y- intercept: (0, 5)
2 J y 2J 3
a false statement. So no the point is not on the 25. When y = 0, x = 7
line. x-intercept: (7, 0)
l 1 h l1 h 0=7
14. —2 ' ı +' ı (—1) = —1 is true so yes the point is no solution
y-intercept: none
'y3ıJ 'y3ıJ
on the line. 26. 0 = –8x
x=0
15. m = 5, b = 8 x-intercept: (0, 0)
y = –8(0)
16. m = –2 and b = –6
PR
y=0
17. y = 0x + 3; m = 0, b = 3 y-intercept: (0, 0)
1
27. 0 = x – 1
2 2
18. y = x + 0; m = , b=0
3
3 3
x=3
19. 14x + 7 y = 21 x-intercept: (3, 0)
O
1
7 y = —14x + 21 y = (0) – 1
3
y = —2x + 3
y = –1
y-intercept: (0, –1)
FD
20. x — y = 3 y
—y = —x + 3
y = x —3
(3, 0)
x
21. 3x = 5
(0, –1)
5
O
x=
3
1 2 28. When x = 0, y = 0.
22. – x+ y = 10
C
2 3 When x = 1, y = 2.
2 1 y
y= x +10
3 2
3
y= x +15 (1, 2)
4 x
(0, 0)
23. 0 = —4x +8
4x = 8
x=2
x-intercept: (2, 0)
y = –4(0) + 8
y=8
y-intercept: (0, 8)
