Lesson 1.4 Miscellaneous exercise 1

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A note on the miscellaneous exercises

The miscellaneous exercises are essential because they develop and test your ability to draw on a number of concepts at the same time in order to solve a new problem. This is one of the skills that is required by the Cambridge International curriculum at AS level, and it is an important skill involved in everyday life, especially if you work as a professional. Here are some tips to help you with the miscellaneous exercises.

  • As with any complex skill, you will be unable to solve problems involving a number of skills together if you haven't mastered the skills on their own. It is therefore important that you complete the exercises labelled A, B, C, etc., before you tackle the miscellaneous exercises.
  • You may at first find the miscellaneous exercises quite challenging, since they often don't name the skill or concept that you are expected to use. For example, they will expect you to use your knowledge of gradients, distances between points, etc., without saying which of these is applicable to the particular problem. As a result, you might wonder, on first reading the questions, how they relate to the chapter. Be assured that they do! Read the question carefully, look over the notes you have made during the lessons of the chapter, and think about how those concepts may be used to solve the problem. For example, a question may concern a parallelogram. Since parallelograms have opposite sides parallel and diagonals whose midpoints occur at the same point, you can use what you know about gradients and midpoints to work with parallelograms.
  • Don't be discouraged if you can't see the solution immediately. Try one thing and then another, think about what you are doing and why it is or isn't working, and keep at it until you solve the problem.


This video works through one of the exercises (no. 5) — or at least part of it!

Weight lifting

Complete the following exercises from your text book:

Miscellaneous exercise 1

  • Questions 1,2,3,4,6,9
  • Questions 10,11,12,14,15,17,18
  • Questions 20,21

You can download the answer key from here, or from your download area on the My Account menu. Do so, and mark your work as explained in the Preliminaries.