Download A2 Pure Mathematics (C3 and C4) by Roger Porkess PDF

By Roger Porkess

The highly-acclaimed MEI sequence of textual content books, assisting OCR's MEI dependent arithmetic specification, has been up to date to compare the necessities of the recent requisites, for first instructing in 2004.

Show description

Read Online or Download A2 Pure Mathematics (C3 and C4) PDF

Best schools & teaching books

Critical Issues in Early Childhood Education

"This booklet is a precious contribution to the production of a extra serious and theoretically varied method of early early life coverage and perform. via many shiny examples and a diversified cast-list of authors, either lecturers and practitioners, it exhibits the opportunity of this process for pedagogical paintings in early formative years associations and the schooling of the early formative years group.

A Friendly Introduction to Mathematical Logic

This easy creation to the foremost ideas of mathematical good judgment specializes in options which are utilized by mathematicians in each department of the topic. utilizing an assessible, conversational kind, it methods the topic mathematically (with distinct statements of theorems and proper proofs), exposing readers to the power and tool of arithmetic, in addition to its boundaries, as they paintings via not easy and technical effects.

Home-School Connections in a Multicultural Society: Learning From and With Culturally and Linguistically Diverse Families

Educators all over confront severe matters concerning households, education, and instructing in varied settings. without delay addressing this truth, Home-School Connections in a Multicultural Society indicates pre-service and training academics the right way to realize and construct at the wealthy assets for reinforcing tuition studying that exist inside of culturally and linguistically diversified households.

Additional info for A2 Pure Mathematics (C3 and C4)

Example text

Similarly g 3(x) means three applications of g. In order to apply a function repeatedly its domain and co-domain must be the same. Order of functions If f is the rule ‘square the input value’ and g is the rule ‘add 1’, then x So f ⎯→ square x2 g ⎯→ add 1 x 2 + 1. gf(x) = x 2 + 1. 37 Notice that gf(x) is not the same as fg(x), since for fg(x) you must apply g first. In the example above, this would give: C3 3 Functions x g ⎯→ add 1 (x + 1) f ⎯→ square (x + 1)2 and so fg(x) = (x + 1)2. Clearly this is not the same result.

5 has no solution π (i) for 0 р θ р – (ii) for any value of θ? 2 EXERCISE 3D 1 The functions f, g and h are defined by f(x) = x 3, g(x) = 2x and h(x) = x + 2. Find each of the following, in terms of x. 2 gf fgh (viii) (fh)2 (ii) (iii) (iv) (v) (vi) fh ghf h2 (ix) Exercise 3D fg hf (vii) g2 (i) C3 3 Find the inverses of the following functions. f(x) = 2x + 7 (ii) f(x) = 4 – x 4 (iii) f(x) = –––– (iv) f(x) = x 2 – 3 x у 0 2–x The function f is defined by f(x) = (x – 2)2 + 3 for x у 2. (i) 3 (i) (ii) 4 Sketch the graph of f(x).

2 gf fgh (viii) (fh)2 (ii) (iii) (iv) (v) (vi) fh ghf h2 (ix) Exercise 3D fg hf (vii) g2 (i) C3 3 Find the inverses of the following functions. f(x) = 2x + 7 (ii) f(x) = 4 – x 4 (iii) f(x) = –––– (iv) f(x) = x 2 – 3 x у 0 2–x The function f is defined by f(x) = (x – 2)2 + 3 for x у 2. (i) 3 (i) (ii) 4 Sketch the graph of f(x). On the same axes, sketch the graph of f –1(x) without finding its equation. Express the following in terms of the functions f: x → g: x → x + 4. (i) x→ x+4 (ii) x →x + 8 (iii) x→ x+8 (iv) x→ x and x+4 5 The functions f, g and h are defined by 3 h(x) = 2 – x.

Download PDF sample

Rated 4.78 of 5 – based on 7 votes