Search & Filtering
An office building contains 27 floors and has 37 offices
on each floor. How many offices are in the building
Let a, b, c, d be a set of real numbers, show that a²+b²+c²+d²=1
If
a²-1 ab ac ad
ba b²-1 bc bc
ca cb c²-1 cd
da db dc d²-1
equal to zero.
3.1 (1) Distinguish between number concept and number sense. Give an example of each. 4
3.2 (4) Why do you think the Hindu-Arabic numerical system is currently the most used number system in the world? Where and how are base 60 numbers still used? 3
3.3 (6) Explain why the phrase natural numbers is used when referring to counting numbers and also say why fractions are not part of this number set. 3
3.4 (9) Explain with examples the difference between rational and irrational numbers. 4 3.5 (10) Draw a number line and plot (or graph) the following numbers: -0.6; √10; 2 5 3 3.6 (11) What number is represented by the Dienes blocks, called a block, longs and units in the diagram? With which Dienes blocks will you build the number 7 604? 4
3.7 Multiply 53 by 24, firstly by breaking down 24 in its terms (20 + 4) and secondly by breaking down 24 in its factors (6 x 4). Show all your steps. (a) 53 x (20 + 4) (b) 53 x (6 x 4) 4
when cost of petrol rises 25%, consumption is reduced by 16%. find % change in expenditure
Cities A, Band C are equidistant from each other. A motorist travels from A to
B at 30 km/h; from B to C at 40 km/h and from C to A at 50 km/h. Determine
his average speed for the entire trip.
a) how many hours needed to complete filling process of 150 000 mL in 1 mL bottles
*speed: 2 bottles per second
b) how many staff are needed at one time to complete packing the bottles in carton within 24 hours
* 1 carton = 10 bottles
* speed: 1 carton per 15 seconds
a) how many hours needed to complete the filling process of 150 000 bottles of 1 mL
* speed: 2 bottles per second
b) how many staff needed at one time to complete the packing bottles inside carton within 24 hours
*speed: 1 carton = 10 bottles = 15 seconds
four children had three boxes of coloured pencils. They decided to open all the three boxes, to shair the pencils fairly. There were 52 pencils in each box. How many pencils did each child get ? Now look at the attempt from grade 4 learner to solve this problem .
a ) briefly describe how the learners solved this problem.
b )use any strategy to judge the reasonableness of thr learner's solution.
Jane packed 6 hams in a shipping crate. Each ham weighs 5 pounds . The crate weighs 2 pounds How much does the total package weigh ?
(3.1)
(a) Find a and b such that −3ai − (−1 − i)b = 3a − 2bi.
(b) Let z1 = 12 + 5i and z2 = (3 − 2i)(2 + λi). Find λ without resorting to division such that z2 = z1.
(3.2) Let z = −2 + 3i and z' = 5 − 4i. Determine the complex numbers
(a) z2 − zz'
(b) 1/2(z + z)2
(c) 1/2[z − z] + [(−1 − z')]2.
