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Using Algebra to Solve Problems

daria-murphy avatar
daria-murphy
22 diapositives · 383 Views · Nov 13, 2014

This resource covers key concepts from Form 1 Mathematics, including inequalities and sequences. It offers step-by-step examples, such as constructing inequalities from real-life scenarios and calculating general terms of sequences. Questions and exercises are provided to enhance understanding and practice skills, promoting proficiency in solving mathematical problems. Additionally, the resource integrates Chinese terms to aid bilingual learners. Suitable for revision or homework purposes, it bolsters the foundational algebraic skills necessary for advanced studies.

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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