3a of the mathematics in action

Topics: Negative and non-negative numbers, Inequality, Binary relation Pages: 28 (1442 words) Published: November 16, 2013
F.3 Mathematics Teaching Notes
Chapter 04
Linear Inequalities in One Unknown (一元一不等式)
Section
4.1

Topic
Basic Knowledge of Inequalities

New Century Mathematics (Oxford Canotta Maths)
Teaching Notes

- Students should be able to recall the Law of Trichotomy.
- Students should be able to use graphical presentation for inequality. - Students should be able to use the Transitive Property,
Additive Property, and
Multiplicative Property.
Reciprocal Property

4.2

Linear Inequalities in One Unknown - Students should be able to solve inequality.

Homework
Ex.4A Q.3

Ex.4A Q.7
Ex.4B Q.1-16, 21-25

Note:
1. Triangle Law﹙三角定律﹚will be introduced during the course. For any triangle, the longest side must be shorter than the sum of the other two sides, and the shortest side must be longer than the difference of the other two sides. 2.

非歐幾里得幾何﹙non-Euclidean Geometry﹚證明一個凸多邊形的頂角周圍所有角的總和小於 360o,但頂角周圍亦最少要有三個面。利用這些 資料,試測想有多少種可能出現的正多面形。

3.

No compound inequality (AND or OR) will be taught in F.3.

F.3

Mathematics Quiz

Chapter 04 Linear Inequalities in One Unknown
5
B. x ≤ 3

5
C. x ≤ -3

D. x ≥ -5

E. x ≤ -5

B. x > 0

C. x < 0

1
D. x < -2

E. No solution

B. x < 1000

C. 1 < x < 1000

D. x < 1000

E. 1 < x < 1000

8. Solve

1. Which of the following is a correct representation of the sentence: “a is greater than b and (c-b) is positive.”
A. a > b > c

5-x ≥ -2x
5
A. x ≤ 3
1
9. Solve -2 x < 0
A. x = 0

Section A: Multiple Choice

B. a < b < c

C. a < b > c

D. a > b < c

C. -1 > x > 0

D. 5 < x < 10

E
E. None of them

2. Which of the following is unreasonable?
A. 5 > x > -3

B. -3 > x > -8

E. None of them

C

3y < 2y

A. III only

B. I and II

4. x, y and k are real numbers.

C. I and III

D. II and III

E. I, II and III

13. Solve

II.

kx > ky

III.

-x < -y
C. I and II

D

D. II and III

I.

E. All of them

III.

ab > 0 implies that a > 0 and b > 0

B. II only

C. III only

16. Solve

D. I and II

B

E. All of them

7. Solve

18. Solve
C. x < 3

D. x < 9

E. x < -9

B

B. x > 1

C. x > 3

D. x < -1

E. x > -1

A

4 -x < -2x+5

A. x < 1

3x > -81

and

E. y-x

E

C

8
8
D. x < -2 or x > 3 E. -2 < x < 3

E

D. 1 < x < 3

E. -1 < x < 3

E

C. -27 < x > 3

D. -27 < x > -3

E. No solution

A

6 x > -6

D. x < -6

E. None of the above

A

C. 2 < x < 3

D. -3 < x < -2

E. No solution

A

-2x > 6
B. -3 < x < 27

x+3 < 2x+10
B. x > -7

2(x+1) > 3(x+2)

A. x < -4

B. x > 9

E. 0 < xy < 1

C. x > -1

B. x < 1

A. x > 2
17. Solve

6. Solve x-3 > 6
A. x > 3

8
8
B. x < 3 or x > 2 C. -3 < x < 2

A. -27 < x < -3

a+b < a+c implies that b < c

D. 0 < x < 1

14. Solve x-6 < 3-2x < 4 -x

15. Solve

ab < ac implies that b < c

II.

C. x < 0 or y < 0

-3 < 5-3x < 11

A. x < 3

5. If a, b and c are any real numbers, which of the following statement(s) is/are true?

A. I only

B. xy < 0

A. x > -2

x2 > y2

B. II only

A. x+y < 0

12. If x and y are negative and x > y, which of the following is always positive? 1 1
x y
y x
A. x - y
B. y - x
C. x - y
D. x+y

If x > y and k > 0, which of the following must be true?

I.

A. I only

E

y2 > y

III.

C

11. If log(x) + log(y) < 0

y-3 > y-6

II.

B

0 < log(x) ≤ 3

A. 1 < x

3. If y is a negative number, which of the following statement(s) is/are true? I.

10. Solve

D

2x < 4

A. x < 2

or

3(x+2) > 4(x+3)

B. -4 > x < -6
and

3x+1 < 10
B. x < 3
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