Cambridge Math AS level

Pure Mathematics 1

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, byHugh 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 getthis,type\left(\frac{1}{2x}+x^3\right)^8.

Install MiKTeXfirst,and then,install theLaTexEditor,Texmaker. See here LaTex tutorial by Michelle Krummel.

A quick guide toLaTexhere, by Dickinson College.LaTex setup and tutorial, by Prof Elizabeth Arnold at James Madison Univ. And, finally, learn LaTeX in 30 minutes byShareLaTeX.

Notes, Practices & Assignments:

- Introduction to the course.
**Pretest.**This diagnosis test is based on the Algebra II text book in use in Florida, USA. - Geometry and coordinate geometry. Students should check online resources:
**Properties of quadrilaterals**, pdf, 2 pages; also**Proofs in Coordinate Geometry.** **Chapter 1**:**Coordinates, points and lines**.**Practice 01**page 15 exercises 1 to 12**.****Answers to****practice 01**.- Aug 30th: review chapter 01. Next week, Tues 9/4,
**quiz chapter 1**.

**Chapter 2**.**Surds and indices**.,**Practice 02 here**.**Practice 03**, ex 10 to 20 page 30 of the textbook.**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. **Assignment 03, questions**.**Functions, domain, graphs**.**Assignment 03, answers**.- Online review: graphing polynomials, Paul's online math notes.
- Week 09/24-9/28:
**Chapter 4**:**Quadratics****Practice 05**, Miscellaneous ex 4, page 62. - Week 10/08-10/12. Quiz 3. Quadratics.
**Chapter 5, Inequalities**.**Practice 06**, page 72 (ex 1 tru 11)- Assignment 04. Question 4 page 72, from a) to l). Due 10/12.
**Chapter 6, Differentiation**.**Practice 07**, 6D page 86-87, #1 tru 13.**Solutions****here.****Rules for differentiation, proofs. Practice 08**page 93, exercises 6E and miscellaneous ex 6, page 94, 1 tru 6.- Assignment 05, page 86, chapter 6, exercise 6D # 5, 6, 7, 8, 9 and 14.
**Practice 09**,**differentiation**, miscellaneous exercise 6 page 94, questions 7 tru 15. Questions 1 tru 6 included as part of**Pratice08**.**Applications of differentiation**.**Practice 10a**, Exercise 7C, from #6 to 16 page 110.**Practice 10a, answers**.- Assignment 06, due Fri 11/2nd. Item c) for each question on exercise 7B.
**Derivatives as rates of change**.**Practice 10b**, miscellaneous exercise 7, from question 1 to 17, pages 110 to 113.

Practical Tips for Modeling Optimization Problems.**Sequences**,**chapter 8**.**Practice 11,**section 8C (from 8 to 11, p125) and miscellaneous exc 8, p125-126, form 1 to 15**. Sequences answers**here.- Assignment 07, Sequences, problems 10 & 11 page 125.
- 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, Trigonometry****practice 13**: excercises 10D, page 152 & miscellaneous 10, page 153 from 1 to 4.**Trigonometry Practice 14**, miscellaneous 10, page 153 to 155, # 5 tru 20.**Solution here**.- Assignment 10, transformation of graphs of trig functions.

**Chapter 11, combining and inverting functions, Practice 15,**miscellaneous exercise 11 page 172-173 #1 thru #20. Assignment 11, p172: 1 - 4.**Solutions****here**.**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 18****Miscellaneous exercise 13**p207-209. see also Michael Corral, vector Calculus, first 18 pages. Basic theory on vectors, recommended ! click**here.****Assignment 13,**Vectors:**exercise 13D: 12-16 page 20**7**questions & answers 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.** - The modulus function: chp 2, pure 2.
**Practice 28**, problems on page 28.**Assignment 18**: from 2a p23 1 b) & j. from 2b p28 1 f) 2 g) and 3 c).

Paul's Online Math Notes: Absolute Value Equations, Absolute Value Inequalities and Rational Inequalities.

- 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**

**Video:**Fx-115 ES Plus (This Webinar features the fx-115ESPlus calculator)

- 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.

- Solving equations numerically:
**Practice 35**, 8A p112 and 8B, p114.

**Assignment 24**: 8B p114 # 2 c, & 3.

Related topics: solving cubics by factoring, rational zeros theorem & Descartes rule of sign and Abel's impossibility theorem. Recommended video: chaos, fractals, and dynamics by Robert L. Devaney ( He explains the process of iteration in the context of dynamical systems.)

- The trapezium rule.
**Practice 36**, excercise 9 p 125.

**Assignment 25:**Exercise 9 p125 #4 a, b, c. - Parametric equations. Derivatives of parametric eq.

**Practice 37**, exc 10A p 133 & 10B p 136.

Assignment 26**:**10B, #9 a) b) - Curves defined implicitily. Derivative of implicit functions.
, 11 A p 147 #1 to 6, and 11B p150.

Practice 38

Assignment 27: 11B #5 & #6. *Discussion of final exams*.**Quiz**based on past examinations: week April 29- May 3rd**Final test****:**May 7, Pure 1, 1h 45 mins - 11 questions, max 60 pointsPure Math 2, May 13, 1h 15 mins - 8 questions, max 40 points.

- Integration by substitution. A glimpse to AP Calc.
- Intro. History of math. The Golden ratio, etc
- School year 2012-2013 ends !

**Numberphile, Cambridge University: amazing youtube channel:**

Infinity is bigger than you think - **Numberphile:
**