Algebra Answers

1- Find the domain of function f(X)=ln (-2/X2-x-6) +√x2 -1

2- Find the inverse function of the function f(X)=X2 -4x +5; X €(3,4)

3- construct the tangent line to the graph of the function f(X)= 4x.√x-2 .√x which is parallel to the line y=x.

Multiply 62 by 35, firstly by breaking down 35 in its terms (30 + 5) and secondly by breaking down 35 in its factors (5 x 7). Show all your steps.

(a) 62 x (30 + 5)

(b) 62 x (5 x 7)

Which base-10 (Dienes) blocks represent the sum of 1034 and 675?

Show your calculation and explain how the base 60 number system is used to subtract 48 minutes from 2 hour 13 minutes.

My calculation (3)

Explanation of my steps (3)

Many learners struggle to make the leap from understanding whole number to understanding rational number (which includes whole numbers and fractions). Describe what you will do to help a learner who cannot position  correctly on a number line.

In modern mathematics teaching we want relational understanding, in addition to instrumental understanding. Describe how a teacher would teach for both instrumental and relational understanding of long division 357÷19.

Teaching long division of 357÷19 for instrumental understanding

Teaching long division of 357÷19 for relational understanding

Base 10 place value system                                                                                   

(a) Where is early evidence of the base 10 place value system? (1)

(b) Approximately to what year does this evidence date back? (1)

(c) Give some detail of the base 10 place value system. (2)

(d) When in CAPS do learners start learning the base 10 place value system? (1)

Multiplication and division                                                                         

(a) Where do we find early evidence of multiplication and division? (1)

(b) Approximately to what year does this evidence date back? (1)

(c) Give detail of how people multiplied and divided in your example. (2)

(d) Where in CAPS do learners start multiplying and dividing? (1)

1.2.Explain how and who came up with these algebraic concepts or used these algebraic concepts deloped over time.

1.2.1 decimal number system

1.2.3 abstract symbol s

1.2.3 negative numbers

1.3 Describe the stages in the development of symbolic algebra. Give at least one example of equation for each of these stages.

a) If 28 counters are a whole set, how many are there in five sevenths of the set?  

b) If 32 counters are four fifths of a set, how many counters are in a full set? Illustrate the your answer.