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1.1 counting

(a)where in the world do we find some early evidence that people counted?

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

(c) give details of how counting was done in the example in which you chooww.

(d) where in caps in this type of counting covered as a topic

1.3 geometry

(a) where in the world do we find some early evidence of geometry?

(b) approximately to whatyeardoes this evidence date back?

(c) give detail of how geometry was practiced in your example

(d)where in the caps is this type of geometry covered as a topic

1.4multiplication and division

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

(b) approximately to what year does thus evudence date back?

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

(d)where in caps do learners start multiplying and dividing

Convert 1-i / 2 into trigonometric form

C. How many centimeters are in a meter?

D. What is the mode of the data set below:


E. Calculate the area of the darker shaded outer part below.The larger rectangle is 15cm long and 9 cm wide, the sides of the smallest square are 5cm each.

An aeroplane flies at a ground velocity (i.e. velocity relative to the ground) of 300 km/h N 30o W, in a wind blowing at a velocityof 50 km/h N 20o E. What is the velocity (speed and direction)of the plane relative to the ground? (Use a calculator and round the speed)

to the nearest km/h, and the corresponding angle to the nearest degree.)

The simplest error detection scheme used in data communication is parity checking.

Usually messages sent consist of characters, each character consisting of a number of

bits (a bit is the smallest unit of information and is either 1 or 0). In parity checking,

a 1 or 0 is appended to the end of each character at the transmitter to make the total

number of 1's even. The receiver checks the number of 1s in every character received,

and if the result is odd it signals an error. Suppose that each bit is received correctly

with probability 0.999, independently of other bits. What is the probability that a

7-bit character is received in error, but the error is not detected by the parity check?

(Hint: use the Binomial distribution)

1.Find the domain of the function 𝑓(π‘₯)=log4(π‘₯2+4π‘₯βˆ’5𝑒π‘₯βˆ’1).


2. Construct the tangent line to the graph of the function 𝑓(π‘₯)=√π‘₯+2π‘₯ which is perpendicular to the line π‘₯+3π‘¦βˆ’2=0.


3. Find the maximal intervals of monotonicity of the function 𝑓(π‘₯)=arctg(π‘₯2βˆ’4π‘₯).


4. Calculate the integral ∫π‘₯2(π‘₯3+4)2 𝑑π‘₯2βˆ’1.


5. Find the particular solution of the differential equation 𝑦′=βˆ’(2𝑦+1)β‹…tg(π‘₯) which fulfills the initial condition 𝑦(πœ‹4)=12.


6. Solve the matrix equation 2𝒳+π’œ=3β„¬βˆ’π’œπ’³ if π’œ=(βˆ’4βˆ’332), ℬ=(1βˆ’121).


What's is mathematics

Learners have to demonstrate knowledge and skills in calculating quantities such as mass, length, perimeter, temperature and the volume of objects. When teaching conversions, emphasis must be placed on multiplication by a thousand (since "kilo" means thousand) and one thousandth (since "milli" means one thousandth). Design an instructional activity to explain how you would teach grade 4 learners the conversion of units when measuring length. Refer to page 25 of the CAPS document, the second bullet under β€˜Calculations and problem-solving involving length’. Your focus should be on whole numbers (

Solve the problem with 3 different Voting Method.

The Plurality Method\

The Plurality Method with Elimination

The Borda Count Method

The owner of a restaurant decides to poll regular customers to choose which dish she’ll submit to an annual citywide competition. The choices are lemon-crusted salmon (L), crab-stuffed chicken (C), garlic prime rib (G), and wasabi rolls (W). The results are shown in the preference table.

# of votes 8 8 5 5 4

C 1 4 3 2 2

G 3 3 2 1 4

L 4 1 4 4 3

W 2 2 1 3 1

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