WELCOME TO THIS PAGE INTENDED FOR A GROUP OF STELLENBOSCH MUNICIPALITY EMPLOYEES DOING THE UWC-LINKED RPL COURSE DURING JUNE 2009 :
RPL TEST JUNE 2009
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Note: Solutions follow below.
QUESTION 1 (5 marks)
An accountant saved 75% of an amount she needs for a new car which she intends to buy cash. She saved on the average R600 per month. If her savings thus far represent 60% of the total saving period (i.e. the total time in which she saves for the required amount), how much must she save in each of the remaining months?
QUESTION 2 (4 marks)
On 25 May 2009, 1 British pound cost 1.59116 US dollar while 1 British pound cost 13.1946 ZAR (South African Rands). Express the exchange rate as ZAR / US $
QUESTION 3 (3 marks)
A computer costs R4 999.99, inclusive of Value Added Tax or VAT (of 14%). Determine the amoun t of VAT.
QUESTION 4 (4 marks)
After receiving a discount of 15% you pay R100 for an article. At what price was the article marked originally?
QUESTION 5 (4 marks)
A pair of shoes costs R 225 and is sold for R 202. Calculate the percentage loss.
QUESTION 6 (8 marks)
(a) Calculate and write the answer in scientific notation correct to two decimal places:
(b) Use your scientific calculator to determine the following to 3 decimal places:
(c) What is zero raised to the power zero equal to? Motivate your answer.
QUESTION 7 (6 marks)
(a) A bookstore manager notes that the ratio of customers who browse in the store to those who actually buy something is 7 : 5. In a total of 180 customers, find the number in each category.
(b) If the ratio for male customers only is 5 : 3 and 60% of the customers are female, what is he ratio for the females
QUESTION 8 (8 marks)
A store has the following sales figures for beach umbrellas during the first 4 months of the year:
January |
February |
March |
April |
240 |
203 |
124 |
51 |
(a) Express each of the sales figures as a ratio compared to February (the base month) where the second number (for Feb) in the ratio is 100. (to the integer)
(b) Use your answer to (a) to calculate the percentage changes in sales in each of the other months compared to February.
(c ) Answer (a) and (b) again, using April as the base month.
QUESTION 9 (15 marks)
(a) Subtract 3x – 3y + 5 from 6x –4y +3.
(b) Remove the brackets ( that is, multiply): (3x – 2)(2x² - 3x + 4)
(c) Simplify: (1)
(2) - 3 (2x – 5)(2x + 5)
(d) Factorise completely: -12x² + 75
QUESTION 10 ( 7 marks)
(a) Solve for x -2(x- 7) = 14 + 0.5x
(b) The sum of two consecutive even numbers is 66. Determine these numbers.
QUESTION 11 ( 4 marks)
The sum of two numbers is -11 and their difference is -47. Find the numbers.
QUESTION 12 (7 marks
The profit function P(x) = R((x) – C(x) ,where R(x) = 5x and C(x) = 12.7 + 2x. Calculate the profit function and hence draw the graph of this profit function on the following grid:
SOLUTIONS TO ABOVE RPL TEST
1.
Note: Because only 25% is still needed, we multiply by a fraction which is SMALLER THAN 1, i.e 25/75. Similarly we multiply by 60/40 which is LARGER THAN 1, because we have less than half the time left.
2.
3. VAT =
4. ORIGINAL PRICE =
5. Percentage Loss =
6 (a) 0.169… = 1.70
(b) 995.961
(c) Undefined, does not have meaning in terms of the definition of a power. = 1 for any number, except 0.
7. (a) Browsers = 7/12 times 180 = 105
Buyers = 5/12 times 180 = 75
(b) Male Browsers = 0.4 or 40% of 180 times 5/8 = 5/8 times 72 = 45
Male Buyers = 0.4 or 40% of 180 times 3/8 = 3/8 times 72 = 27
Therefore Female Browsers = 105 – 45 = 60
And Female Buyers = 75 – 27 = 48
Hence the ratio of female browsers : buyers = 5 : 4
8. (a ) JAN = 240/203 times 100 = 118
FEB = 100 (the base month)
MARCH = 124/203 times 100 = 61
APRIL = 51/203 times 100 = 25
(b) Jan compared to Feb: 18% UP
March compared to Feb: 39% DOWN
April 75 % DOWN
(c) 240/41= 471 therefore 371 UP , etc.
9. (a)
(b)
(c)
(d)
(e)
10 (a)
(b) 32 and 34
11.
12. Profit Function =
© DESMOND DESAI, DMD EDU-HOME, 2009
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