Algebra Answers

Let z, w ∈ C. Show |z + w| =

p

|z|

2 + 2Re(zw) + |w|

2 =

p

|z|

2 + 2|z||w| cos(θz − θw) + |w|

2 and

|z + w| = (|z| + |w|)

s

1 −



√

2 sin([θz−θw]/2)

|z|/|w|+

√

|w|/|z|

2

, if z 6= 0 and w 6= 0.

f(x)=4x+2 and g(x)=3x-1, find (f-g)(4)

Two water tanks at PPV Aman and PPV Damai consists of x and 3000 litres of water, respectively, on the first day.

a) Subsequently, y litres of water is used from the tank in PPV Aman everyday. Volume of water left at the end of 18th day is 2520 litres and the tank will be expected empty by the day 81. Find the value of x and y. [8 marks]

b) The usage of water in PPV Damai constantly 30 litres per day. Find the day for both, tank at PPV Aman and PPV Damai, has the same amount of water. [4 marks]

Suppose C and D represent two different school populations where C > D and C and D must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary.

A: (C + D)²

B: 2(C + D)

C: C² + D²

D: C² − D²

(10 points)

All outbound packages from a distribution center are routed to a person for packing. 60% of packages are easy and can be packed at a rate of 45 packages per hour. The remaining packages are more difficult and can only be packed at a rate of 12 packages per hour. There is no specialization, packages are randomly assigned to any available packer. What is the average packing rate for each packer?

Simplify the sum Σ from r=0 to 2n+1 of [3/(r+1)(r+2)]

A town has a population of 2000 and grows at 4.5% every year. What will be the population after 13 years, to the nearest whole number?

A Kitten Is Given An Injection Of A 0.5% Solution. The Dose Rate Is 1mg/Kg/Day And The Kitten Weighs 0.5lg. What\'S The Volume Injected?

Explain how to help learners develop algebraic reasoning in the Intermediate Phase. Give

examples to justify your thinking.

2.2 Simphiwe bought meal tickets to use at the school’s cafeteria. Each meal requires 2

tickets, and she bought 14 tickets in total. She has already used some of the tickets, and

she still has some left.

2.2.1 Write four equivalent expressions that gives the number of tickets Simphiwe has

left in terms of x, where x is the number of meals she has already bought. (4)

2.2.2 14 − 2x represents the number of tickets Simphiwe has left after she bought x

meals. How can 14, −2, and 2x be interpreted in terms of tickets and meals? (6)

2.2.3 2(7 − x) also represents the number of tickets Simphiwe has left after she

bought x meals. How can 7, (7 − x), and 2 be interpreted in terms of tickets and

meals? (6)

2.2.4 Discuss the purpose and the importance of the instructional activity in relation to

fostering algebraic reasoning in mathematics education. (4)