Algebra Answers

1.5 You want to put up a poster in your mathematics classroom, where learners can see the

seven (7) properties of operations on real numbers. List those properties, with one very

clear example next to each one of the properties, so that learners can immediately see

what these properties mean in the mathematics they do. Do NOT use the examples of

the Study Guide, but your own

2.1 The number 100 can be written as the sum of five consecutive whole numbers like this:

100 = 18 + 19 + 20 + 21 + 22. Showing all your working, find

2.1.1 four consecutive odd numbers whose sum is 120. (5)

2.1.2 five consecutive whole numbers which add up to 1000. (5)

2.1.3 a rule for the sum of any four consecutive even numbers. (5)

2.2 A moringa tree, when planted, was 90cm tall. It then grew an equal number of centimetres

each month. At the end of the seventh month, it was 132cm tall. How tall was the tree at

the end of the twelfth month? Show all your calculations.

1.1 Explain the expression algebraic thinking to an Intermediate Phase teacher. (2)

1.2 Give two reasons why you would say that algebraic thinking is very important for

Intermediate Phase mathematics? (2)

1.3 The entities in algebra can be distinguished, but they are deeply related to one another.

Discuss the three main entities that are used in algebra, and clearly indicate how these

three entities relate to each other. Relate the first entity you listed, to the second and the

third, and the first entity to the third entity as well. (6)

1.4 Explain what is meant by the following terms, and give an example of both so that the

difference and similarity between both terms become clear:

1.4.1 Algebraic expression (3)

1.4.2 Algebraic equation

The fitness contest includes a walking challenge. On the first day, each walker starts by walking 2,000 steps. The goal is to add 500 steps per day until 10,000 steps, or about 5 miles. Angel begins the challenge.

Part A

Write and solve a statement to find the number of days Angel will need to walk to meet the challenge.

X(2x^3)n-1

For the given problems in context,

(i) set up and solve the algebraic statement

(ii) evaluate the problem.

(a) There were 579 patients infected with COVID-19 at a hospital. Of these patients, 123 were children and there were twice as many men as women. How many women who have become infected with the coronavirus were in the hospital? (5)

(b) Phumza bought 12 metres of curtaining. Some of the material came from a roll with a slight flaw in it and cost R7,00 per metre instead of the normal R8,00 per metre. If Phumza paid R93,50 altogether, how many metres of the damaged material did she buy? (5)

(c) Nancy buys 15 meters of ribbon. Her sister buys 6 meters less ribbon but pays twice as much per metre. Between them they pay R6,60. What is the price per meter of the two different types of ribbon? (5) (d) You have twice as many 20 cent coins as 10 cents coins and half the number of 5 cent coins as 10 cent coins. If you have R4,20 altogether, find out how many of each coin denomination do you have?

a) Set up an algebraic equation that could represent the following life situation: (5)

Nkateko sells bananas at the low but fixed price of R3/kg. In order to ensure that she makes a reasonable profit, she adds a certain fixed amount of money to any quantity of bananas purchased. A customer who bought 4 kg of bananas was observed paying R14

b) Draw the situation for which the equation was set up in (b) above. You should be able to use this drawing to explain the situation clearly to a learner as part of remedial work. (5)

Questions 1 and 2 are based on the following information:

The demand and total cost functions for a commodity are

Q = 6 000 − 30P      and     TC = 5 000 + 2Q,

where P and Q are the price and quantity, respectively.

 1

The total revenue function (TR), in terms of P and the company's quantity, if a commodity sells for R199.00                     are?

a. TR = 6 000 − 30P ; Q = 30.

b. TR = 6 000P − 30P ²; Q = 30.

c. TR = P (6 000 − 30P ); Q = 24.

d.  TR = 6 000 − 30P ; Q = 24.

2

What is the company's profit function in terms P?

a.   Profit = −30P ² + 6 060P − 17 000

b.    Profit = −30P ² + 5 940P − 17 000

c.   Profit = −30P ² + 5 940P + 7 000

d.    Profit = −30P ² + 6 060P − 7 000

Items bought by for R158 are sold for R120. The loss expressed as a percentage of cost price is?

a friend hands you the slip of paper shown below and challenges you to circle exactly four digits that have a sum of 19. 1 3 3 5 5 7 7 9 9 9