BNU1501/2019 Basic Numeracy BNU1501 Semester 2, 2019 Department of Decision Sciences 01 02 03 04 Assignments 15 August 825342 26 August 775833 6 September 830498 17 September 816775 FOR SEMESTER 2 STUDENTS ONLY ASSIGNMENT 01 Study material: Chapters 1, 2 and 3 in the Study Guide Unique assignment number: 825342 FIXED DUE DATE: 15 August 2019 Important: • This is a multiple-choice assignment that must be answered and submitted ONLINE using myUnisa. Go to Assessment Info on the BNU1501 module site and follow the steps. Make sure that you complete the submission process. • Always keep your detailed workings in a file to be able to compare your solutions to the ones that will be published on the BNU1501 module site on myUnisa after the due date. Also, keep a copy of the options you have chosen, in case of a query. • The due date of this assignment is fixed. No extension can be granted because the solutions will be posted on the BNU1501 module site shortly after the closing date. Question 1 Round 20,54545... off to three decimal digits. [1] 21,045 [2] 20,545 [3] 20,550 [4] 21,545 Question 2 Round 20,54545... off to two decimal digits. [1] 20,60 [2] 21,04 [3] 20,55 [4] 21,05 Question 3 Round 20,54545... off to an integer. [1] 20,6 [2] 21 [3] 20 [4] 25 2 BNU1501 Question 4 A shuttle and a bus leave Unisa at 9:00, heading for the FNB stadium. The bus arrives at the stadium 15 minutes after the shuttle. Suppose the bus takes y minutes to travel from Unisa to the stadium. An expression for the time it takes the shuttle to travel to the stadium is ... [1] [2] (y − 15) minutes. (9 + y − 15) minutes. [3] (y + 15) minutes. [4] (y + 15 − 9) minutes. Question 5 A mother divides an amount of money among her three children, Kagiso, Dikeledi and Thabo. Kagiso gets twice as much as his sister, Dikeledi, and Dikeledi gets R100 less than Thabo. Suppose Thabo gets x rand. How much does Kagiso get in terms of x? x + 100 rand [1] 2 100 − x [2] rand 2 [3] [4] 2 (x + 100) rand 3 2(x − 100) rand Question 6 The petrol consumption of a certain boat is 15 litres per 100 kilometres. Suppose you want to travel d kilometres and the petrol price is p rand per litre. How much, in rand, will it cost you to travel the d kilometres? 15 [1] 100dp 100 [2] 15dp 15p [3] 100d 15dp [4] 100 Question 7 A plumber charges a call-out fee of R160 plus R240 per hour to do a job. At least how many hours must he work to earn more than R1 120 for a specific job? (Hint: Suppose he must work at least x hours). [1] 4,7 hours [2] 4 hours [3] 2,8 hours [4] 5,3 hours 3 Question 8 Alexander travels x kilometres in p hours. At what average speed does Alexander travel? [1] xp km/h [2] (x − p) km/h [3] [4] x p p x km/h km/h Question 9 Suppose I buy 10 shirts. Some cost R40 a shirt and others cost R45 a shirt. If the total cost is R435, how many of the R45 types of shirt did I buy? [1] 10 [2] 7 [3] 5 [4] 3 Question 10 Simplify the following expression as far as possible: x(x − 2) − 2(1 − x2 )x − 4x [1] [2] [3] [4] x2 − 8x − 2x3 −x3 + x2 − 6x − 2 −x3 + x2 − 4x − 4 2x3 + x2 − 8x Question 11 Simplify the following expression as far as possible: ab(a − b) − b(c2 − ba) − (a2 − c2 )b [1] [2] [3] [4] 4 −2ab2 − 2bc2 ab − a2 b 0 −a2 b4 − b2 c4 BNU1501 Question 12 Simplify the following expression as far as possible: √ √ b8 · b16 [1] b32 [2] b8 [3] b12 [4] b64 Question 13 Simplify the following expression as far as possible: 2−2 · 23 [1] 2 [2] 2−6 [3] −2 [4] −24 Question 14 Simplify the following expression as far as possible: ax+3 · a−x−2 [1] a [2] a2 [3] a−x [4] 2a 2 −6 Question 15 Solve the following expression as far as possible: 2 3xy 2 z 3 × 2x3 y 4 ÷ xy 2 z 3 [1] 3x4 y 8 z 3 [2] 18x4 y 6 z 3 [3] 18x4 y 4 z 2 [4] 12x4 y 6 z 3 END OF ASSIGNMENT 01 OF SEMESTER 2 5 FOR SEMESTER 2 STUDENTS ONLY ASSIGNMENT 02 Study material: Chapters 4, 5, 6 and 7 in the Study Guide Unique assignment number: 775833 FIXED DUE DATE: 26 August 2019 Important: • This is a multiple-choice assignment that must be answered and submitted ONLINE using myUnisa. Go to Assessment Info on the BNU1501 module site and follow the steps. Make sure that you complete the submission process. • Always keep your detailed workings in a file to be able to compare your solutions to the ones that will be published on the BNU1501 module site on myUnisa after the due date. Also, keep a copy of the options you have chosen, in case of a query. • The due date of this assignment is fixed. No extension can be granted because the solutions will be posted on the BNU1501 module site shortly after the closing date. Question 1 Write 3 [1] [2] [3] [4] 4 as an improper fraction. 7 7 7 25 7 12 21 12 7 Question 2 Write [1] [2] [3] [4] 6 100 as a mixed fraction. 7 2 100 7 3 11 7 2 98 7 2 14 7 BNU1501 Question 3 Determine the LCM (Lowest Common Multiple) of the following three numbers: 9, 8 and 6 [1] 72 [2] 432 [3] 54 [4] 144 Question 4 Determine the LCM of the following three terms: a2 bc, abc and ab3 [1] a4 b4 c2 [2] abc [3] a2 b3 c [4] a2 b3 Question 5 Determine the LCM of the following three terms: 6x3 , 8x2 y 2 and 12xy 5 [1] 2xy 5 [2] 24x3 y 5 [3] 576xy [4] 24x6 y 7 Question 6 Simplify the following expression as far as possible without using a calculator: 4 5 1 − + 5 6 4 [1] 0 [2] − 15 [3] [4] 13 60 1 1 20 7 Question 7 Simplify the following expression as far as possible without using a calculator: 3 2 4 ÷ × 8 3 5 [3] 9 20 1 5 45 64 [4] 5 [1] [2] Question 8 Simplify the following expression as far as possible without using a calculator: 3 7 1 + ÷ 7 9 3 [1] 3 13 21 [2] 2 16 21 [3] 13 17 9 49 [4] Question 9 Simplify the following expression as far as possible: 1 2 + 4x2 5x [1] [2] [3] [4] 4x2 3 + 5x 5x 8x2 5 + 8x 20x2 3 9x2 Question 10 [1] 2 as a decimal number, rounded to four decimal digits, without using a calculator. 9 0,223 [2] 2,9000 [3] 4,5000 [4] 0,2222 Write 8 BNU1501 Question 11 [1] 5 as a decimal number, rounded to three decimal digits. 8 0,625 [2] 10,580 [3] 10,625 [4] 10,160 Write 10 Question 12 Write 2,525 as an ordinary fraction in its simplest form. 1 [1] 2 2 21 [2] 2 40 11 [3] 2 40 1 [4] 2 8 Question 13 A blended fruit juice contains three main ingredients, namely mango juice, orange juice and distilled water, mixed in the ratio 4 : 5 : 1, respectively. How many litres of orange juice are needed to make 25 litres of this fruit juice? [1] 2,5 litres [2] 5 litres [3] 10 litres [4] 12,5 litres Question 14 Bargains-4-U sells a washing machine for R1 320, excluding VAT. We assume that VAT is 14%. If you pay cash, the company offers a 5% discount. How much will you save if you buy this washing machine in cash? [1] R75,24 [2] R66,00 [3] R135,43 [4] R118,80 9 Question 15 A school has 880 pupils. If the ratio of the number of boys to girls is 7 : 4, respectively, how many more girls should need to enroll if the school authorities want the ratio of number of boys to the number of girls to be 1 : 1? [1] 320 [2] 560 [3] 240 [4] 880 END OF ASSIGNMENT 02 OF SEMESTER 2 10 BNU1501 FOR SEMESTER 2 STUDENTS ONLY ASSIGNMENT 03 Study material: Chapters 4, 5, 6 and 7 in the Study Guide Unique assignment number: 830498 FIXED DUE DATE: 6 September 2019 Important: • This is a multiple-choice assignment that must be answered and submitted ONLINE using myUnisa. Go to Assessment Info on the BNU1501 module site and follow the steps. Make sure that you complete the submission process. • Always keep your detailed workings in a file to be able to compare your solutions to the ones that will be published on the BNU1501 module site on myUnisa after the due date. Also, keep a copy of the options you have chosen, in case of a query. • The due date of this assignment is fixed. No extension can be granted because the solutions will be posted on the BNU1501 module site shortly after the closing date. Question 1 Consider the diagram below. Measurements are indicated on the diagram. The semi-circle fits perfectly into the shorter side of the rectangle. 6 c m cm 4 ,8 4 c m 2 c m 6 c m Calculate the perimeter of the area that is shaded in the diagram. [1] 31,37 cm [2] 21,72 cm [3] 15,43 cm [4] 25,08 cm 11 Question 2 Consider the diagram that has one right angle below. Measurements are indicated on the diagram. 1 0 m m 4 0 m m m 2 m 4 1 , m 4 4 ,7 m 1 0 m m 1 0 m m 5 0 m m Calculate the area of the shaded part in the diagram. [1] 200 mm2 [2] 206 mm2 [3] 223,5 mm2 [4] 194 mm2 Question 3 In the diagram below, a rectangle fits perfectly into the circle. The measurements are indicated on the diagram. 5 cm 4 c m 3 c m Calculate the area of the shaded part of the diagram. [1] 66,54 cm2 [2] 7,64 cm2 [3] 6,30 cm2 [4] 27,27 cm2 12 BNU1501 Question 4 Refer to the sketch below. A cylindrical piece of steel, which is 30 mm long and has a radius of 6 mm, has a square hole right through it in its length. The hole is in the centre of the rod. The sides of the square are each 5 mm. m 3 0 m 6 m m 5 m m Calculate the volume of metal that this small object contains. [1] 98,2 mm3 [2] 264,29 mm3 [3] 2,64 cm3 [4] 2,49 cm3 Question 5 A circular water reservoir has a maximum capacity of 10 000 kilolitres and its diameter is 30 metres. How deep is the reservoir? [1] 14,1 m [2] 3,5 m [3] 106,1 m [4] 11,1 m Question 6 Solve the following equation: 7 − 4a = 2 (3 − 5a) [1] [2] [3] [4] a = −1 1 a= 6 13 a=− 14 1 a=− 6 13 Question 7 A rectangular glass tank is half filled with water. The tank is 25 centimetres long, 20 centimetres wide and 30 centimetres high. How many litres of water have to be added to raise the water level with 5 centimetres? 3 0 c m cm 2 5 2 0 c m [1] 7,9 [2] 2 500 [3] 2,5 [4] 10 Question 8 Solve the following equation: [1] [2] 1 2 a+ =a 7 3 a = −7 a= [3] a= [4] a= 7 9 7 18 3 12 Question 9 1 If s = ut + at2 , make a the subject of the formula. 2 2s − ut [1] a= t2 s − ut [2] a= 2t2 2(s − ut) [3] a= t2 q [4] a = s−ut t 14 BNU1501 Question 10 If S = P (1 + i)n , make i the subject of the formula. S [1] i= −1 Pn q [2] i = n PS − 1 q [3] i = n PS + 1 q [4] i = n PS − 1 END OF ASSIGNMENT 03 OF SEMESTER 2 15 FOR SEMESTER 2 STUDENTS ONLY ASSIGNMENT 04 Study material: Chapters 4, 5, 6 and 7 in the Study Guide Unique assignment number: 816775 FIXED DUE DATE: 17 September 2019 Important: • This is a multiple-choice assignment that must be answered and submitted ONLINE using myUnisa. Go to Assessment Info on the BNU1501 module site and follow the steps. Make sure that you complete the submission process. • Always keep your detailed workings in a file to be able to compare your solutions to the ones that will be published on the BNU1501 module site on myUnisa after the due date. Also, keep a copy of the options you have chosen, in case of a query. • The due date of this assignment is fixed. No extension can be granted because the solutions will be posted on the BNU1501 module site shortly after the closing date. Question 1 The straight line passing through points (−3; 1) and (1; −1) is... [1] a descending line. [2] an ascending line. [3] a vertical line. [4] a horizontal line. Question 2 Joseph invests R36 000 at a simple interest rate of 6% per year. How long will it take for Joseph’s investment to grow to R55 440? [1] 5,8 years. [2] 7,4 years. [3] 9,0 years. [4] 1,1 month. 16 BNU1501 Question 3 How much, to the nearest rand, can Lerato borrow from a bank if she can repay the loan by means of quarterly payments of R2 000, starting at the end of the first quarter? The interest rate is 18% per annum, compounded quarterly, and the duration of the loan is 10 years. Assume that the interest rate will stay fixed for the term of the loan. [1] R214 061 [2] R50 206 [3] R240 000 [4] R36 803 Question 4 What would the difference in interest earned be if R3 750 is invested for 3 years at 8% simple interest per year versus if it is invested for the same period at 8% per year, compounded yearly? [1] R973,92 [2] R73,92 [3] R3 676,08 [4] R3 823,92 Question 5 Sarah wants to save R100 000 for a deposit on a townhouse. She wants to deposit R500 per week into a savings account that offers 9% interest per year, compounded weekly. How long will it take her to save enough for the deposit? [1] 10,2 years [2] 14,3 years [3] 3,3 years [4] 4,7 years Question 6 Jacky bought a second-hand car for R80 000 from a dealer in Pretoria. She managed to secure a loan at an interest rate of 10,5% per year, compounded monthly. The term of the loan was five years and the interest rate stayed fixed for the term of the loan. Determine Jacky’s minimum monthly payment. [1] R1 019,51 [2] R1 719,51 [3] R16 200,55 [4] R1 333,33 17 Question 7 Consider Jacky’s loan in question 6 above. What would the outstanding amount on the loan to the nearest rand be after two years’ payments had been made on time? [1] R77 952 [2] R52 904 [3] R0,00 [4] R2 709 Question 8 Refer to Jacky’s loan in question 6 above. How much did the car cost Jacky in total over the five years? [1] R134 928,24 [2] R8 597,55 [3] R103 170,60 [4] R171 951,00 Question 9 Consider the amortisation of Jacky’s loan in question 6 above. Suppose Jacky made all minimum monthly payments on time into this loan account. In which month was the principal, which was paid off, for the first time more than the interest paid off? [1] in the 2nd year, 7th month [2] in the 5th year, 12th month [3] in the 2nd year, 6th month [4] in the 1st year, 1st month Question 10 Refer to Jacky’s loan in question 6 above. How much would Jacky save if she decided to pay R2 000 per month into this loan account from the start? [1] R4 275,78 [2] R34 275,71 [3] R23 172,72 [4] R0,00 END OF ASSIGNMENT 04 OF SEMESTER 2 END OF TUTORIAL LETTER 18