MATHEMATICS QUARTERLY TEST MARCH 2015 GRADE 9

Transcription

1 GENERAL EDUCATION AND TRAINING MATHEMATICS QUARTERLY TEST MARCH 01 GRADE 9 MARKS: 100 DURATION: HOURS Number of pages including cover page: 6

2 Mathematics Grade 9 March Test 01 INSTRUCTIONS AND INFORMATION 1. This question paper consists of FIVE questions. Answer ALL the questions.. Question 1 consists of multiple choice questions. Learners must write the letter of the correct answer in their answer book. (e.g.: 1. B). Clearly show ALL the calculations.. An approved calculator (non-programmable and non-graphical) may be used.. Number the answers EXACTLY as the questions are numbered. 6. Diagrams are NOT necessarily drawn to scale. 7. It is in your own interest to write legibly and to present the work neatly.

3 Mathematics Grade 9 March Test 01 QUESTION 1 [Mixed] 1.1 Which of the following numbers is a rational number? A: B: 8 C: 91 D: Which number is missing in the number sequence? ; ;1 ; ; 8 A: 6 1 B: 8 1 C: 9 1 D: 1 1. If the ratio of boys in a class of 0 is 8 6, how many girls are in the class? A: B: 10 C: 1 D: 0 1. A boy bought a bicycle for R excluding VAT. If VAT is charged at 1%, how much did he pay including VAT? A: R 1 76 B: R1 700 C: R 1 8 D: R ( ) A: a + b B: C: 1 D: 0 (10) QUESTION [Real Numbers].1 Between which two consecutive integers does lie? Show all your workings (). Convert the recurring decimal 0, 1 to a common fraction in simplest form. (6). Express 700 as a product of its prime factors. (). Calculate the following: a) of 7 () b) (Express your answer as a mixed fraction.) (). Musa spends hours a week on his Mathematics homework, hours a week on Natural Science homework and 8 hours a week on Technology homework. How many hours does he spend each week on Social Science homework if he spends hours a week on homework for the four subjects? ()

4 Mathematics Grade 9 March Test 01.6 The mass of a truck when loaded with sand is 87, kg. After unloading the sand it has a mass of 010, kg. What is the mass of the sand? () () QUESTION [Ratio, Rate, Proportion and Financial Mathematics].1 Write the ratio 1 : in simplest form (). Decrease 0kg by 1% (). Doctor and Jabulane are sharing the profits from their business in the ratio of :. The business has made a profit of R 1 6 this year. Calculate how much each receives. (). The international call tariffs of Telkom are given in the following table: Number of minutes 9 y Cost R,9 R8, x R8,0..1 Is the proportion direct or indirect? Why? ().. Determine the cost of a 9-minute call ( x ) ().. Determine the duration of a call if the cost is R8, 0 ( y ) (). A bus driver covers a certain distance in hours at an average speed of 80km/h. a) How long will the journey take at an average speed of 0km/h? () b) How long will it take to travel km at an average speed of 96km/h? ().6 Calculate the final amount that I will have in my savings account if I invest R600 for years at a rate of 6% per annum compound interest. ().7 Calculate how long will it take for an investment of R 000 at % per annum simple interest to earn an interest of R80? ().8 Given wants to order mathematics dictionary from the internet. The price of the book is $, 86. What is the price of the book in rands? Take the exchange rate as $1 for R9, 9. () ()

5 Mathematics Grade 9 March Test 01 QUESTION [Exponents].1 Write 1 in exponential form. (). Simplify the following: a) ( 1 1 ) () b) () c) () d) (). Simplify and express your answer in scientific notation:. In one teaspoonful of water there are about water molecules. Calculate the number of water molecules in teaspoons full of water and write your answer in scientific notation. () QUESTION [Numeric and Geometric patterns; Functions and Relationships].1 A sequence is given..1.1 Write the next two terms of the sequence ().1. Describe the sequence in your own words. ().1. Write down the general term of the sequence in the form Tn ().1. Which term in the sequence is equal to 10? Show all your workings. () () (18). Use the rule provided to calculate values of a and b. () Rule: y = 10 (x + ) X Y a b

6 Mathematics Grade 9 March Test 01. Consider the following table and answer the questions that follow: X n y m Determine the following: a) value of m () b) value of y if x = n () (1) GRAND TOTAL 100 6

7 GENERAL EDUCATION AND TRAINING MATHEMATICS GRADE 9 MARCH 01 MEMORANDUM MARKS: 100 Number of pages including cover page: 6

8 QUESTION 1 QUESTION ANSWER QUESTION D A B C C NO. ANSWER ALLOCATION OF MARKS MARKS Let x = 0, ❶ x 1,1 ❶ ❷ ❷-❶ 100 x x 1,1 0,1 99x 1 x x a) 0 b) 6 11 (10) 1 mark for expressing each square root of 11 and 1 respectively. 1 mark for simplifying the square roots. 1 mark for equation 1. 1 mark for multiplying equation ❶ by mark for subtracting equation ❶ from ❷. 1 mark for simplification. 1 mark for the fraction. 1 mark for simplification of the fraction. 1 mark for table with correct factors. marks for correct Full marks for answer only. 1 mark for multiplying. 1 mark for changing mixed number to improper fractions. 1 mark for simplification. 1 mark further simplifying. 6 Mathematics Grade 9 Memorandum March 01

9 mark for adding hours. SS 8 1 mark for each correct step SS 0 1 SS SS or hours mark for subtracting. 1 mark for correct answer and units. QUESTION NO. ANSWER ALLOCATION OF.1. 8 : : kg. Doctor R16 R89,71 7 Jabulane R16 R897, Direct proportion, it increases at the same rate of R1,6 per minute. MARKS 1 mark for changing mixed numbers to improper. 1 mark for simplified ratio. 1 mark for correct manipulation. 1 mark for expressing each ratio as a fraction. 1 mark for each correct Or finding 1 ratio then finds the answer and subtracts the answer from the total. 1 mark for direct proportion. 1mark for the reason... 9min utes R1,6 R1, 8 1 mark for multiplying... R8,0 R1,6 17 min utes 1 mark for dividing. Mathematics Grade 9 Memorandum March 01 MARKS

10 . a) b) Dis tan ce speed time 80km / hh 0km Distance is constant dis tan ce Time speed 0km 0km / h,8hours hours8 min utes Dis tan ce Time Speed km 96km / h,hours hours0 min utes n A p(1 i) 600(1 0,06) R67,16 Prt SI t t t 7 $1 R9,9 $,86 x x 9,9,86 R7,1 1 mark for calculating distance. 1 mark for concluding that distance is constant 1 mark for the formula 1 mark for correct 1 mark for formula and substitution. 1 mark for the 1 mark for the formula. 1 mark for two correct substitutions. answer 1 mark for the formula. 1 mark for each correct substitution answer 1 mark for making relationship. 1 mark for multiplying. Mathematics Grade 9 Memorandum March 01

11 QUESTION NO. ANSWER ALLOCATION OF MARKS MARKS.1 1 marks for the correct mark for changing into a) exponential form. (b) (c) a b c 0ab c a c (d) , 10 1,010 8.,0 10 1,0610 1, mark for changing 1 mark for simplification. mark for multiplying numerator and denominator correctly. 1 mark for the 1 mark for each correct square or cube root. 1 mark for the 1 mark for multiplying correctly. step. 1 mark for the 18 Mathematics Grade 9 Memorandum March 01

12 QUESTION NO. ANSWER ALLOCATION OF MARKS and 1 1 mark for each.1. Add four to the previous term to get the next term. correct marks for any reasonable explanation..1. T n = n mark for n n 6 n 108 n 7 1 mark for correct constant. 1 mark for equating T n to 101. (CA) to be considered. 1 mark for simplification. MARKS. a 10 1 mark for each a) b 90 correct. x 1 mark for a) (1) substitution. 1 1 mark for the answer b) T n n 1 mark for n. 1 mark for - TOTAL 1 GRAND TOTAL 100 Mathematics Grade 9 Memorandum March 01 6