This exercise on integration is aimed mainly at students in their 13th year of schooling. They are slightly difficult, but some help is given in a few of the more obscure examples. It is my belief they provide very good practice prior to the final pre-university examinations. Answers have been provided, and the script checked for errors, especially as the typing provide to be quite difficult.

This chapter is exclusively directed at giving practice in the use of “Integration by parts” formula. Quite often it can be a problem finding a sufficient number of examples with this purpose in mind. Here we hope this exercise will be useful top-up for those students who are looking for examples to help up their game.

A fairly detailed expo of basic sequences and series, leading on to arithmetic and geometric series, but not beyond that in this unit. Suitable mainly for ages 14 to 18. Proof of formula and answers to exercises are included. Intended as a resource for teachers, but also for self instruction to students.

THIS PASSAGE MAKES NO ATTEMPT TO DELVE INTO PHILOSOPHY. IT CONCERNS ITSELF ENTIRELY WITH UTILITY AND MANIPULATION, AND HOPES THAT GRAPPLING WITH THE EXERCISES WILL EQUIP THE READER WITH AN INTUITIVE GRASP OF THE BASIC IDEAS AND THE ABILITY TO SOLVE PROBLEMS FROM THE VERY SIMPLEST TO THOSE OF A MORE SUBTLE CHARACTER WHILE OF COURSE HELPING WITH EXAMINATION REVISION. IT IS ALSO HOPED THAT TEACHERS WILL FIND THE EXERCISES A USEFUL SUPPLEMENT TO THEIR OWN RESOURCES. FOR THE HIGHER LEVEL QUESTIONS SOME KNOWLEDGE OF BASIC ALGEBRA WILL BE OF ADVANTAGE.

THIS SECTION ON TRIGONOMETRY IS AIMED AT STUDENT AGED 15 AND OVER, TO GIVE EXTRA PRACTICE IN TRIGONOMETRY. THE BASIC FORMULAE ARE NOT SUPPLIED AS THEY ARE EASILY AVAILABLE IN TEXTBOOKS OR ONLINE. THE SECTION CONTAINS EXERCISES ONLY, WITH ANSWERS, WITH A HANDFUL MEANT TO STRETCH THE STUDENT. SOME WILL EXPERIENCE FRUSTRATION AS THE TECHNIQUES WILL NOT ME OBVIOUS , WHICH THE WRITER HOPES WILL FORCE THEM T O DEVELOP THEIR INGENUITY.

THESE TABLES ARE A READY RECKONER FOR CALCULATING THE PROBABILITIES OF OBTAINING A CHOSEN SCORE WHEN A GIVEN NUMBER OF DICE ARE ROLLED TOGETHER AND THEIR SCORES ADDED. FOR TEACHERS THEY ARE HANDY FOR COPYING AND PLACING ON A CLASSROOM WALL TO CATCH ATTENTION. YOUNGSTERS WITH ARTISTIC LEANINGS MIGHT LIKE MAKING AN ATTRACTIVE CHART FROM THE INFORMATION GIVEN. NO EXERCISES ARE INVOLVED, BUT A FORMULA FOR CALCULATION IS GIVEN AT THE END.

THIS IS NOT AN INSTRUCTION MANUAL. IT CONTAINS EXERCISES IN INTEGRATION FOR PRACTICE PURPOSES ONLY TO SUPPLEMENT WORK THAT THE STUDENTS HAVE ALREADY COVERED IN CLASS OR ELSEWHERE. THE EXERCISES ARE CATEGORIZED BY TYPE OF INTEGRAL TO MAKE IT EASIER FOR THE STUDENT TO GO DIRECTLY TO THE TYPE THEY NEED REVISION PRACTICE ON. IN EACH SECTION WE BEGIN WITH THE MOST STRAIGHTFORWARD EXAMPLES AND GRADUALLY PROCEED TO MORE CHALLENGING QUESTIONS. THE EARLIER EXERCISES WILL CONCENTRATE ON HOW TO SOLVE THE INTEGRAL. APPLICATIONS OF INTEGRATION WILL BE LEFT TO LATER EXERCISES. APPLICATIONS WILL INCLUDE AREAS, VOLUMES, MOMENTS OF INERTIA, PROBLEMS IN DYNAMICS AND BASIC PROBABILITY. FOR THE TRICKIER EXAMPLES, HINTS ARE OFFERED TO FACILITATE PROGRESS AND ANSWERS TO ALL QUESTIONS ARE PROVIDED.

It’s a selection of exercises in basic integration to supplement the work of first year A-level Maths Students.

These are practice revision examples in definite Integration.Answers and Hints supplied. This is not meant to be an introduction to the subject, just follow up practice.