GENERAL EDUCATION AND TRAINING MATHEMATICS END OF THE YEAR EXAMINATION NOVEMBER 2014 GRADE 8
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1 GENERAL EDUCATION AND TRAINING MATHEMATICS END OF THE YEAR EXAMINATION NOVEMBER 014 GRADE 8 MARKS: 100 DURATION: HOURS Number of pages including cover page: 7 1
2 INSTRUCTIONS AND INFORMATION 1. This question paper consists of FIVE questions. Answer ALL the questions.. Question 1 consists of 5 multiple choice questions. Learners must write the letter of the correct answer in their answer book. (e.g. 1.1 B). Clearly show ALL the calculations, diagrams, graphs, etcetera you have used in determining the answers. 4. An approved calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 5. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 6. Number the answers EXACTLY as the questions are numbered. 7. Diagrams are NOT necessarily drawn to scale. 8. It is in your own interest to write legibly and to present the work neatly. Mathematics Gr.8 of 7 Nov. 014
3 QUESTION If Alex and Mpho have to share R0 in the ratio :. How much will Mpho get? A. R4 B. R8 C. R10 D. R1 1.. What is the rule in the flow diagram? A. t=-p B. p =-t C. t= p- D. p=t- 1.. The co-ordinates of A and B are: A. A (;-) & B (; 1) B. A (-, ) & B (1, 1) C. A (-, ) & B (1, ) D. A (, )& B (1, ) 1.4. The mean of the following set of numbers is 1, 14, 6, 8, 15, 1, 1, 8, 11, 1,, 15, 5, 7 A. 7 B. 8 C. 10 D. 1 Mathematics Gr.8 of 7 Nov. 014
4 1.5. The perimeter of the figure is: 5cm cm A 7 B 10 C. 14 D. QUESTION.1 Simplify the following:.1.1 (5X=10) 1 4 () xy x 4y 5xy 5x xy y ().1. a ( a 8) () 4 16a 8a.1.4 4a.1.5 4a 1 1 () () ( ) 5 () 4 x y z.1.7 x y z (). Solve the following equations:..1 x 1 9 ().. 7 a 1 50 () (1) Mathematics Gr.8 4 of 7 Nov. 014
5 QUESTION.1. Convert 4.76 x 10 5 to a whole number () 5.. Simon received R55 as pocket money. She spent 8 on make-up. Calculate the money she spent on make-up. ().. Calculate the price of milk per litre if a dairy charges R45.0 for 5 litres of milk. ().4. Calculate the simple interest on R1 000 at a rate of 1% interest per year for three years. (4).5. Calculate the rand value of a camera that costs yuan in China. The exchange rate on the day of the sale was R1= 0.7 yuan. ().6. Given the number pattern: 8; 15; ; 9;.6.1 Describe the pattern in your own words. ().6. Determine the general rule of the pattern in the form T n.. ().6. Determine T 50 ().7. Study the pattern below, and draw stage 4 () Stage 1 Stage Stage.8. Vuyo is training for a triathlon competition. In a triathlon, an athlete swims a certain distance, then cycles part of the way and runs part of the way. Vuyo only trains for the running and the cycling, this is his training programme He runs a distance of km in 0 minutes He cycles for 10 minutes and covers 4km He rests for 5 minutes He takes 5 minutes to cycle km He rests for 5 minutes He turns back and takes 5 minutes to cycle 4km Mathematics Gr.8 5 of 7 Nov. 014
6 .8.1. Draw the graph to show how Vuyo trained for the triathlon. (5).8.. How long did his training programme take in total? () (9) QUESTION Write TWO properties of a kite. () 4.. In the diagram, lines MS, NS and OS meet PQ at S, QSO 0, NSO x and PSM MSN x N M O P x x S x 0 o Calculate the value of x (4) 4... What is the size of PSN () 4.. In the diagram, transversal SQ cuts parallel lines XY and ZP at M and N, with XMN 144 and QNP x Q S X 144 o M Y Z N x Q P Express MNZ in terms of x and give a reason for your answer () 4... Calculate the value of x () 4.4. ABCD is a rectangle. Determine x and y. (4) 5 8 x y Mathematics Gr.8 6 of 7 Nov. 014
7 4.5. Calculate the area of a triangle, with the height of.5cm and the base of 6cm h () 6cm 4.6. Calculate the unknown length. Leave your answer in surd form. (4) 1m a m (4) QUESTION The following table shows the sales of cars per month at a second hand car dealership. Month JAN FEB MAR APR MAY JUN JUL AUG SEPT OCT NOV DEC No. of sales Draw a bar graph for the data. (5) Calculate the Mean. () Determine the median. () Calculate the data range. () 5.. A box contains blue, 4 white and 5 green marbles of the same size If you take out 1 marble, what is the probability that you will take out a green marble? (1) 5... What is the probability of then taking out a white marble if you replace the marble that you took out of the box previously? () 5... If you take out a white marble and do not replace it, what is the probability of taking out another white marble? (1) (16) GRAND TOTAL 100 Mathematics Gr.8 7 of 7 Nov. 014
8 GENERAL EDUCATION AND TRAINING MATHEMATICS MEMORANDUM NOVEMBER 014 GRADE 8 MARKS: 100 DURATION: HOURS Number of pages including cover page: 7
9 Mathematics Grade 8 November 014 QUESTION 1 QUESTION ANSWER D A C C D QUESTION (10) NO. ANSWER ALLOCATION OF MARKS MARKS mark for simplification mark for correct LCM xy x 4y 5xy 5x xy y xy 5xy xy x 5x 4y y xy 7x 5y 1 mark for addition and subtraction of like terms.1. a(a 8) a 8a 1 mark for each correct term.1.4 4a ( 4a a 1) 4a marks for common factor and simplification 1 marks for answer = 4a a mark for simplification ( ) mark for simplification 81 of 7
10 Mathematics Grade 8 November x y z 1 mark for simplification x y z yz..1 x x 10 x a a 49 a 7 7 a a 1 QUESTION 1 mark for additive inverse 1 mark for additive inverse 1 mark for simplification NO. ANSWER ALLOCATION OF MARKS marks for answer.. x x R4.8 R45.0 R Interest for 1 year: yz y Interest for years: R1440 R40 z 1 mark for correct statement 1 mark for correct calculation 1 mark for correct statement 1 mark for correct statement 1 mark for correct statement (1) M AR KS 4 of 7
11 Mathematics Grade 8 November R1 0. 7yuan x x xrands R mark for proportionality 1 mark for simplification.6.1 Add seven from the previous number to get the next number marks for correct rule.6. T n 7n 1 marks for correct rule.6. T n 7n 1 7(50) 1 Tn T n mark for substitution 51.7 marks for correct pattern mark for correct scale 1 mark for labeling x and y axis 1 mark for heading 1 mark for correct points 1 mark for joining points 5.8. Totaltime mark for correct = 50 minutes statement (9) 4 of 7
12 Mathematics Grade 8 November 014 QUESTION 4 NO. ANSWER ALLOCATION OF MARKS 4.1 Two pairs of adjacent sides are equal 1 mark for each correct in length property One pair of opposite angles equal Or any other correct property MARKS 4..1 x x x (sum of s on straight line) 5x x 150 x PSN x x 4x 4(0) MNZ x (vert opps with PNQ) o + MNZ =180 o (co-inter s ) But MNZ x x x 6 Or any other correct method 4.4 x 8 x 11 y 5 y 7 1 mark for statement 1 mark for reason 1 mark for multiplicative inverse 1 mark for substitution 1 mark for statement 1 mark for reason 1 mark for statement 1 mark for reason 1 mark for equation of x 1 mark for x value 1 mark for equation of y 1 mark for y value Area b h 1 mark for formula 1 mark for substitution of 7
13 Mathematics Grade 8 November 014 =10.5cm 4.6 a = +1 =9+1 a =10 a = a= QUESTION 5 1 mark for statement 1 mark for simplification 1 mark for determining square root 4 (4) NO. ANSWER ALLOCATION OF MARKS Sales of cars at second hand dealership 1 mark for heading 1 mark for correct scale 1 mark for labeling x axis 1 mark for labeling y axis 1 mark for correct bars MARKS Mean= mark for statement 1 mark for sum 1 1 = ;7;7;8;9;11;11;1;1;14;14;15 Median=11 1 mark for arranging Range = 15- = P(G) = of 7
14 Mathematics Grade 8 November p( w) 1 p( w) 11 1 marks for probability in simplest form 1 mark for probability not simplified 1 (16) GRAND TOTAL of 7
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