Selected Questions.
Suggested solutions by C. Sotuyo: Pure Mathematics 1 by Hugh Neill and Douglas Quadling, Cambridge University Press, 2002.
Miscellaneous exercises 1, page 15: 1. Show that the triangle formed by the points (-2,5), (1, 3) and (5, 9) is right-angled.
Miscellaneous exercises 4, page 62: 4. For what values of k does the equation have a repeated root?
Exercises 6D, page 87:
12. A curve has equation , where a is a constant. Find the equations of the tangents to the graph at the points where it crosses the x-axis.
Exercise 6E, page 93.
2. Find the derivative of the function at x=p. (Use the difference of two squares formula as often as you can.)
11. Show that the curves
have exactly one point in common, and use differentiation to find the gradient of each curve at this point.
Excercises 7C, page 110 16. A circular cylinder is to fit inside a sphere of radius 10 cm. Calculate the maximum possible volume of the cylinder. (It is probably best to take as your independent variable the height, or half the height, of the cylinder.)
Miscellaneous exercises 8, page 126 No. 8 & 9 8. An arithmetic progression has first term a and common difference -1. The sum of the first n terms is equal to the sum of the first 3n terms. Express a in terms of n.
9. Find the sum of the arithmetic progression 1, 4, 7, 10, 13, 16,...1000.
Every third term of the above progression is removed, i.e. 7, 16, etc.
Find the sum of the remaining terms.
Miscellaneous exercises 10, No 19 page 155:
The road to an island close to the shore is sometimes covered by the tide. When the water rises to the level of the road, the road is closed. (...) See pdf doc for a solution to this problem.
Excercise 13D, # 16 page 207:
The roof of a house has a rectangular base of side 4 metres by 8 metres. The ridge line of the roof is 6 metres long, and centred 1 metre above the base of the roof. Calculate the acute angle between two opposite slanting edges of the roof.
Let's begin with a pair of rabbits. Assume that that rabbits begin to reproduce two months after their own birth. This is, after reaching the age of two months each pair produces one male and one female, and another pair each month thereafter. Also assume that no rabbit dies. This is the sequence of numbers of rabbits generated by the original pair of rabbits:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, and so on...
The Fibonacci Sequence!
Exponential Growth:
In 1859, an Australian farmer, Thomas Austin, imported two dozen wild English rabbits and set them free on his land. Within six years Austin's 24 rabbits had multiplied to 22 million. At a rate of 2.29, the following equation explains the rabbits population growth during that period of time:
Notice: Oct 20, 2014. I taught Pure 1 & 2 two years ago, 2012-2013. I kept the webpage, however. Reviewing the webpage stats I've learned that tens of people visit this page every day looking for resources. I am using La Tex (textmaker editor) to create the pdf file. It takes time the typesetting of math. Solutions of some problems are downloable for free.
I'm working on the rest of the practices. Practices with answers appear in red, see below.
The content of the practices --exercises, page number etc of Pure Mathematics 1, by Hugh Neill and Douglas Quadling, Cambridge University Press, 2002, are indicated below. The answers consists of step by step solutions. In some instances, like practice 4, the answers take 6 pages; in practices 5 & 6, five pages each.
Selected Questions: Suggested solutions by C. Sotuyo, here.
Typesetting math with LaTex: in order to get this, type \left(\frac{1}{2x}+x^3\right)^8. Install MiKTeXfirst, and then, install the LaTex Editor, Texmaker. See here LaTex tutorial by Michelle Krummel. A quick guide to LaTexhere, by Dickinson College. LaTex setup and tutorial, by Prof Elizabeth Arnold at James Madison Univ. And, finally, learn LaTeX in 30 minutes by ShareLaTeX.
Introduction to the course. Pretest. This diagnosis test is based on the Algebra II text book in use in Florida, USA.
Quiz 02, surds and indices, based on practice 2 week 9/10-9/14.
Week 09/17-9/21: Chapter 3. Functions and graphs & ex 3 to 19 page 49: Practice 04.
Assignment chapter 01 & Assignment chapter 02 due 09/28.
Assignment 01 is page 15 --textbook, except question 4.
Assignment 02 is page 29 excercises 4 to 8, and miscellaneous from 1 tru 5, same page.
Chapter 9, The binomial Theorem. Practice 12 Ex 9B and Miscellaneous 9 from number 1 to 33, pages 135 to 137. Solutions here. Exercises 9B #6 to 13 (page 135) & Miscellaneous excercise 9, #1 to 11.
Chapter 10, Trigonometrypractice 13: excercises 10D, page 152 & miscellaneous 10, page 153 from 1 to 4.
Chapter 12, extending differentiation. Related rates problems ! Practice 16: p182-183. All of them, 1 tru 9. Practice 17, differentiation, related rates: miscellaneous exercise 12, pages 184-186.
Vectors,Practice 18Miscellaneous exercise 13 p207-209. see also Michael Corral, vector Calculus, first 18 pages. Basic theory on vectors, recommended ! click here.
Geometric Sequences: Jan 7 & 9. Practice 19, exercises 14A p213-214; Practice 20, 14B p.217 & Practice 21 exercises 14C p 221. Quiz 7 Fri 1/11
Assignment 14, Geometric seq: page 213, 14A. # 3, b) c) #4 c) #5 b) #6 c) and from 14B page 217 #2 a). Practice 22, geometric sequences miscellaneous exercise 14 pages 222-224.
Second derivatives: Practice 23, 15A p228 & 229, also 15B p232.
Second derivatives: Practice 24, miscellaneous exercise 15 pages 234-235.
Integration: Practice 25, 16B p245 & p251, 16C. Assignment 15: p240 exer 10e, 14, 15e, & p244, 4e and #9. Integration, Practice 26, miscellaneous exercise 16 pages 255-257.
Volumen of revolutions (Integration). Practice 27, ex 17 from 4 to 9 and miscellaneous exercise 17 pages 262-263. Assignment 16 p262 #2 d), #3 f), #6 & 7.
Radians. Practice 28, miscellaneous exercise 18 p275-276. Assignment 17: Page 275 exercise 18D, question 2 a) b) c)
Pure Mathematics 2
Polynomials. Practice 27: Pure 2, page 16, misc 1 on 02/13 & 15; Wed 2/20, quiz. Recommended: College ALGEBRA, Univ of Texas. Tutorials 36, 37, 38.
Exponential and logarithmic functions. Practice 29, 3B 1 & 2; 3C 1 tru 8; 3D, 1 (a,b,c,d,e); miscellaneous 3 p48 from 1 tru 11. Assignment 19: 3A p34 #8 a, b, c; from 3C p40 #1 g, h, i.
Differentiating exponentials and logarithmic functions. Practice 30, 4A p54. Practice 31: 4b ( 1 thru 6), 4C ( 1 tru 6), 4D ( 1, 2 & 3). Misc p62 1 tru 4. Assignment 20: 4A, 6 a), 7 f) 8 e) 4B 1 c) 4 a) 4C 1 f)
Trigonometry (identities, equations): Practice 32: p68 ex 5A 7 to 12. Ex 5C p75 from 1 tru 10. Assignment 21: 5C p75, 10b only
Differentiating trigonometric functions: chapter 6. Practice 33, 6A p88 #1 to 6, 6B p92#s 1 tru 3. Assignment 22: 6A, p88 #2 d, g. #3, g. #5, b. #6, c.
Differentiating products: chapter 7. Practice 34, 7A pg 102 # 2 thru 6, 7B p105 #s 1 thru 5. Assignment 23: 7A, p102 #2 e, f; #5, b. 7B, p105, #3 a, #4 a.