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Using Algebra to Solve Problems

Using Algebra to Solve Problems. Form 1 Mathematics Chapter 2 and Chapter 4. Revision. “ >”: 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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Using Algebra to Solve Problems

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  1. Using Algebra to Solve Problems Form 1 Mathematics Chapter 2 and Chapter 4

  2. Revision • “>”: 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 “=” Ronald HUI

  3. Inequality (不等式) • 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” Ronald HUI

  4. Inequality (不等式) • 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! Ronald HUI

  5. Inequality (不等式) • 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 Ronald HUI

  6. Inequality (不等式) • 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.” Ronald HUI

  7. Revision • 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, … Ronald HUI

  8. Time for Practice • Page 165 of Textbook 1A • Questions 1 - 8 • Page 77 of WB 1A Homework • Questions 1 - 4

  9. Revision • 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? Ronald HUI

  10. Formula (方程式) • 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 Ronald HUI

  11. Formula (方程式) • 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 Ronald HUI

  12. Formula (方程式) • P.169 Question 22a: It is given that V=Ah3. 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 Ronald HUI

  13. Formula (方程式) • P.169 Question 22b: It is given that V=Ah3. 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 Ronald HUI

  14. Time for Practice • Page 169 of Textbook 1A • Questions 5 - 14 • Pages 80-81 of WB 1A Homework • Questions 1 - 5

  15. Sequence (數列) • 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) Ronald HUI

  16. Sequence (數列) • 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 Ronald HUI

  17. Sequence (數列) • 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, … Ronald HUI

  18. Sequence (數列) • 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

  19. Sequence (數列) • 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 Ronald HUI

  20. Time for Practice • Pages 83 - 84 of WB 1A • Questions 1 - 4 • Page 175 of Textbook 1A • Questions 1 - 12

  21. Reminder • 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!

  22. Good Luck! Enjoy the world of Mathematics! Ronald HUI

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