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How would you use a teacher-centred media resource to explain the meaning of (7×8) to grade 5 learner? Use two different illustrations to show your understanding



Show that in a finite dimensional vector space V(F) whose basic set is B={x₁,x₂,...xₙ} every vector x∈V is uniquely expressible as linear combination of the vector in B.

In the vector space Vs(Rₙ) let α=(1,2,1), β=(3,1,5), -γ=(3,-4,7) prove that the sub space planned by S={α,β} and T={α,β,γ} are same.

If p(x) denotes the set of all polynomials one indeterminates x over field F, then show that p(x) is a vector space over F with addition defined as addition of polynomials and scalar multiplication defined as the product of polynomials by an element of F. i.e if p(x)={p(x)/p(x)=a₀+a₁x+...+aₙxₙ...}={∑∞,ₙ₌∞ aₙxⁿ for as ∈ f}.


Define addition and scalar multiplication to prove.

Let V be set of real valued continuous function defined as [0,1] such that f(0/3)=2. Show that V is not a vector space over R (reals) under addition and scalar multiplication defined as : (f+g)(x)=f(x)+g(x) for all f,g € V.


(alpha f)(x)= alpha f(x) for all alpha € R, f€V.

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 ‘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



Find the initial speed which a projectile must be subjected to give it a maximum horizontal range of 490m. Assume the acceleration due to gravity as g=10m/s



if the demand fuction a commodity is Q=40-0,2P fixed cost are R1 000 and variable cost are R15 per unit procedure then profit function in terms of P is


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