Using Algebra to Solve Problems

Form 1 MathematicsChapter 2 and Chapter 4

Ronald HUI

“>”: Greater than

“<”: Less than

“”: Greater than or equal to (or Not less than)◦ A combination of “>” and “=”

“”: Less than or equal to (or Not greater than)◦ A combination of “<“ and “=”

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P.166 Question 9: Add 5 to 4 times of a number p and the sum is greater than 33.

Add 5 “+5” 4 times of a number p “4p” The sum “4p+5” Then, the inequality is “4p+5 > 33”

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P.166 Question 11: When the sum of a number s and 3 is multiplied by 2, the product is smaller than -10.

The sum of s and 3 “s+3” Multiplied by 2 “2” The product “(s+3) 2” or 2(s+3) The inequality is “2(s+3) < -10”

Write 3 numbers by guessing!

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P.166 Question 13a: Mike has 2 packs of $1.9 stamps, 1 pack of $2.4 stamps and y packs of $1.4 stamps. Each pack contains 10 pieces of stamps. Write an inequality…

2 packs of $1.9 2 $1.9 10 = $38 1 pack of $2.4 1 $2.4 10 = $24 y packs of $1.4 y $1.4 10 = $14y Total value $38+$24+$14y The inequality is $38+$24+$14y <$100

or 14y+62 < 100

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P.166 Question 13b: Find the value of y if the total value of the stamps that Mike has is $76.

Total value $38+$24+$14y The equation is $38+$24+$14y = $76

or 14y+62 = 76 14y = 14

y = 1 Therefore, y = 1. or “Mike has one pack of $1.4 stamps.”

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Some special terms: One half = 二分之一 One third = 三分之一 One quarter / One fourth = 四分之一 One fifth = 五分之一

First, Second, Third, Fourth, Fifth,Sixth, Seventh, Eighth, Ninth, Tenth,Eleventh, Twelfth, Thirteenth, Fourteenth, …

Page 165 of Textbook 1A◦ Questions 1 - 8

Page 77 of WB 1A Homework◦ Questions 1 - 4

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A formula is an equation with◦ At least 1 variables on the right of equal sign.◦ Only 1 variable (Subject) on the left of equal sign.

e.g. A = (U + L) H 2◦ A is the subject of the formula◦ U, L and H are the variables of the formula

Do you know what this formula means?

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P.169 Question 18: v = u + gt(u = -8, g = 10, t = 3, v = ?)

v = u + gt = (-8) + (10) (3) Method of

substitution = -8 + 30 = 22

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P.169 Question 20: In the formula S=88+0.5t , if S=120, find the value of t.

S = 88 + 0.5t (120) = 88 + 0.5t

120 - 88 = 0.5t 32 = 0.5t

32 2 = t 64 = t

t = 64

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P.169 Question 22a: It is given that V=Ah3. If V = 40 and h = 6, find the value of A.

V = Ah 3 (40) = A (6) 3

40 3 = 6A 120 = 6A

120 6 = A 20 = A A = 20

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P.169 Question 22b: It is given that V=Ah3. Find the value of h such that A = 5 and the value of V is half of that given in (a)

In (a), V = 40. So, in (b), V = 20.V = Ah 3

(20) = (5) h 3 20 3 = 5h

60 = 5h 60 5 = h

h = 12

Page 169 of Textbook 1A◦ Questions 5 - 14

Pages 80-81 of WB 1A Homework◦ Questions 1 - 5

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Consider a sequence: 2, 4, 6, 8, 10, …

Can you guess what are the next numbers? What is the 10th term? What is the 100th term? What is the nth term?

1, 2, 3, 4, 5, …, 10, …, 100, …, n (第幾個 ) 2, 4, 6, 8, 10, …, 20, …, 200, …, 2n (答案 )

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A Sequence is a group of numbers with number pattern.

Each number in the sequence is called a Term.

The first one in the sequence is called the First Term.

In the sequence, 2, 4, 6, 8, 10, … 2 is the first term, 4 is the 2nd term, 6 is … The general term (通項 ) is 2n or an=2n

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What is the NEXT TWO terms of the following sequences?

4, 8, 12, 16, 20, … 12, 24, 36, 48, 60, … -1, -2, -3, -4, -5, … 5, 6, 7, 8, 9, … 6, 8, 10, 12, 14, … -20, -10, 0, 10, 20, …

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What is the GENERAL terms of the following sequences?

4, 8, 12, 16, 20, … 12, 24, 36, 48, 60, … -1, -2, -3, -4, -5, … 5, 6, 7, 8, 9, … 6, 8, 10, 12, 14, … -20, -10, 0, 10, 20, …

Ronald HUI

Given a general term: an=2n-1 What is the first 5 terms? The first 5 terms are:

◦ a1 = 2(1)-1 = 1

◦ a2 = 2(2)-1 = 3

◦ a3 = 2(3)-1 = 5

◦ a4 = 2(4)-1 = 7

◦ a5 = 2(5)-1 = 9 What is the 17th term? The 17th term is a17 = 2(17)-1 = 33

Pages 83 - 84 of WB 1A◦ Questions 1 - 4

Page 175 of Textbook 1A◦ Questions 1 - 12

Folder◦ 13 Nov (Tuesday)

WB (P.77, 80, 81)◦ 13 Nov (Tuesday)

SHW (III) (Chapter 4)◦ 14 Nov (Wednesday)

Open Book Quiz (Chapter 4)◦ 14 Nov (Wednesday)

Close Book Quiz (Chapter 4)◦ 21 Nov (Wednesday)

You must hand in on time!

Good Luck!

Enjoy the world of Mathematics!

Ronald HUI