| General note |
Chapter 1 number-related problems – <br/>Overview –<br/>Problem solving proper –<br/> A. Linear in one-unknown in 'x' –<br/> B. Linear in two-unknowns in 'x' or 'x and y' –<br/> C. Linear in three-unknowns in 'x' or 'x,y, and z' –<br/> D. Quadratic in one-unknown in 'x' –<br/> E. One linear one quadratic in 'x' or 'x and y' –<br/> F. Quadratic in two-unknowns in 'x' or 'x and y' –<br/>Chapter 2 digit-related problems – <br/>Overview –<br/>Problem solving proper –<br/> A. Linear in one-unknown in 'x' –<br/> B. Linear in two-unknowns in 'x' or 'x and y' –<br/> C. One linear one quadratic in two-unknowns in 'x' or 'x and y' <br/> D. Linear in three-unknowns in 'x, y, and z' –<br/>Chapter 3 age-related problems – <br/>Overview –<br/>Problem solving proper –<br/> A. Linear in one-unknown in 'x' –<br/> B. Linear in two-unknowns in 'x' or 'x and y' –<br/> C. One linear one quadratic in two-unknowns in 'x' or 'x and y' –<br/>Chapter 4 geometry-related problems – <br/>Preliminary remarks –<br/>Metric system of measurement –<br/>I. The line segment –<br/>Overview –<br/>Problem solving proper –<br/> A. Linear in two unknowns in 'x' or 'x and y' –<br/> B. Linear in three unknowns in 'x' or 'x, y, and z' –<br/> C. One linear one quadratic in three-unknowns in 'x, y, and z' –<br/>II. Angles –<br/>Overview –<br/>Problem solving proper –<br/> A. Angles of a triangle –<br/> B. Sides or altitude of triangles in general –<br/> C. Sides of right triangles –<br/> D. Practical applications –<br/> E. Isosceles triangle –<br/>IV. The rectangle –<br/>Overview –<br/>Problem solving proper –<br/> A. Rectangles in general –<br/> B. Sides or altitude of triangles in general –<br/> C. Sides of right triangles –<br/> D. Practical applications –<br/> E. Isosceles triangle –<br/>IV. The rectangle –<br/>Overview –<br/>Problem solving proper –<br/> A. Rectangles in general –<br/> B. Diagonal of a rectangle –<br/> C. Practical applications –<br/>V. The square –<br/>Overview –<br/>Problem solving proper –<br/>VI. The circle –<br/>Overview –<br/>Problem solving proper –<br/>VII. Non-specific proper –<br/>VIII. Comparison of same sizes of different geometric figures –<br/>Chapter 5 money-related problems – <br/>Preliminary remarks –<br/>A. Collection of coins/bills –<br/>Overview –<br/>Problem solving proper –<br/>B. Interest-related problems –<br/>Overview –<br/>Problem solving proper –<br/>A. Two-unknowns –<br/>B. Three-unknowns –<br/>C. Price-related problems –<br/>Overview –<br/>Problem solving proper –<br/> A. Single item –<br/> B. Cost contribution –<br/> C. Double-triple items –<br/>D. Distribution of a certain fund –<br/>Overview –<br/>Problem solving proper –<br/>Chapter 6 balance-related problems – <br/>Overview –<br/>Nature of unknowns and probe solving illustrations –<br/>A. Rod/Teeterboard/Seesaw –<br/> 1. Determining the amount of force to be applied –<br/> 2. Determining weight of one of two load –<br/> 3. Determining weight of one of three loads –<br/> 4. Determining weight of two loads –<br/> 5. Determining lever arm of one of two loads –<br/> 6. Determining lever arm of one of three loads –<br/> 7. Determining lever arm of two loads –<br/> 8. Determining total length of the lever –<br/> 9 Determining balancing point of two loads –<br/> 10. Determining balancing point with single load –<br/>B. Cowbar applications –<br/> 11. Determining amount of force to be applied –<br/> 12. Determining weight of a load –<br/> 13 Determining balancing point –<br/>Chapter 7 mixture-related problems – <br/>Overview –<br/>A. Blends/Assortments –<br/> Overview –<br/> Problem solving proper –<br/> 1. Single unknown –<br/> 2. Two unknowns –<br/>B. Solutions alloys –<br/> Overview –<br/> Formulation & problem solving –<br/> 1. Single unknowns (Case #01 to #07) –<br/> 2. Two unknowns (Case #08 to #11) –<br/>Chapter 8 clock related problems – <br/>Overview –<br/>Problem solving proper –<br/>Chapter 9 work related problems – <br/>Introduction –<br/>Work rate in terms of the reciprocal of units of time spent to finish a job –<br/> A. Determining total time to finish a job –<br/> B. Determining additional time to finish a job left by another –<br/> C. Determining individual rates of work –<br/> D. Determining work rate of an individual in a team of workers –<br/>Work rate in terms of quantity of job done per unit of time –<br/>Chapter 10 motion-related problems –<br/>Overview –<br/>Formulation & problem solving proper –<br/>A. Single formula applications –<br/> 1. Equal distance implied and overtaking situation –<br/> 2. Total distance implied and departing or meeting situations –<br/> 3. Difference in distances covered –<br/> 4. Total time implied over same distance –<br/> 5. Total time implied with rest time, over same distance –<br/> 6. Total time implied over different distances –<br/> 7. Time differences implied –<br/> 8. Equal distances implied with or against force –<br/> 9. Total time implied, with or against force –<br/> 10. Time differences implied with or against force –<br/> 11. Motion about right angle path –<br/> 12. Equal times implied –<br/> 13. Vertical motions –<br/>B. Systems of formula applications –<br/> 1. Original vs changed condition in single described motion –<br/> 2. Changing conditions in single described motions –<br/> 3. Original vs changed condition in two described motions –<br/> 4. Alterations resulting in time differences –<br/> 5. Sum and difference of speeds –<br/> 6. Original vs changed condition with or against force –<br/> 7. Original vs, changed conditioned with or against force resulting in time differences –<br/> 8. Usual vs. changed route and mode of travel –<br/> 9. Usual vs. changed route and mode of travel with stalling. |
| Summary, etc |
It is the belief of the author that a complete instruction of a course in algebra should, by and large acquaint the student on the fundamentals of verbal problem solving, a measure, also, by which to test his mastery of the skills needed in resolving the same.<br/>A student's familiarity with the skills in the analysis and solution of verbal problems in algebra would serve later as an important and critical step towards answering problems requiring even higher levels of mathematical abstractions as in the related fields of science as chemistry and physics.<br/>The student must, therefore, be assisted in every way useful as to inculcate in him a certain measure of self-confidence in solving diverse problems he is likely to encounter incidental to the course.<br/>This book is intended for use as a reference and reviewer both for high school and college." - The Author |
