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T930(E)(A1)TAPRIL EXAMINATIONNATIONAL CERTIFICATEMATHEMATICS N1(16030121)1 April 2016 (X-Paper)09:00–12:00Nonprogrammable scientific calculators and graph paper may be used.This question paper consists of 7 pages and 1 formula sheet of 2 pages.Copyright reservedPlease turn over

(16030121)-2-T930(E)(A1)TDEPARTMENT OF HIGHER EDUCATION AND TRAININGREPUBLIC OF SOUTH AFRICANATIONAL CERTIFICATEMATHEMATICS N1TIME: 3 HOURSMARKS: 100INSTRUCTIONS AND INFORMATION1.Answer ALL the questions.2.Read ALL the questions carefully.3.Number the answers according to the numbering system used in this question paper.4.Write neatly and legibly.Copyright reservedPlease turn over

(16030121)-3-T930(E)(A1)TQUESTION 1Choose the correct word(s) from those given in brackets. Write only the word(s) next to thequestion number (1.1–1.10) in the ANSWER BOOK.1.1Natural numbers start at (-2; -1; 0; 1; 2 ).1.2 xThe ratio of x to y is xy; ; yx; x y 1.3The coefficient of x 4 in the term of 10x 4 is (40 ; x ; 10 ; -10 ; 10 x).1.4240 km/h equals to (864; 66,667; 0,067; 667) m/s.1.5Calculate the new price if the price of chocolate is R1,20 c and it is increased by 8%.(R1,25; R1,30; R1,10; R1,50) y . 1.6 2 The y-intercept of y 2 x 5 2; ; 5; 5 . 5 1.7The side opposite the 90 is called (adjacent; hypotenuse; pythagoras; angle).1.8 x a y .The formula to calculate gradient is ; ;m y x x; x 1.9(Equilateral; Scalene; Isosceles; Right-angled) triangle has two equal sides and twoequal angles.1.10Solve for x if3x 3 ; Then x 3; 12; 4;4 3 .4 (10 x 1)Copyright reserved[10]Please turn over

(16030121)-4-T930(E)(A1)TQUESTION 22.1Simplify the following expressions by only using exponential and log laws:2.1.12.1.22.1.32.2 a 3 b c a 4 b c 1 2 2 (3) 3(3)27a 3b 42ab 729b03(4)Use logarithm base 10 to determine the value of x . Show ALL the calculations.x 0,48 1330,122.3Add the following terms: 16x 2 y 4 xy 2 7 xy and 6 xy 2 4 xy 10x 2 y.2.4Remove the brackets and simplify:8 x [ x 3( x 2)](6)(3)(4)[23]QUESTION 33.1Divide: 6 x 3 7 x 6 by x 2.3.2Use 32 x 3 y 4 z 2 ; 48x 5 y 3 z 3 and 70x 2 y 5 z 4 to answer the questions.3.3(7)3.2.1Show the prime factors of each of the terms.(3)3.2. 2Determine the LCM.(2)3.2.3Determine the HCF.(2)Fully factorise the following :3.3.1ab 8 xy 2bx 4ay(5)3.3.21 2 11x xy x 2 y 2244(4)Copyright reservedPlease turn over

(16030121)3.4-5-T930(E)(A1)TSimplify:24x 2 4 x 30x 5 5x3x(4)[27]QUESTION 44.1Solve for y :4( y 3) 6 y 2( y 4)4.2(5)Solve the number:Four less than four times a number is equal to 24.4.3(4)Make t the subject of the formula:p 1 2gt3(3)[12]QUESTION 54Given the function y :x5.1Use the table method to sketch the graph ofy 4xfor the domain{-4;-3; -2; -1; 0; 1; 2; 3; 4}.(8)5.2Give the name of the graph.(1)5.3What is the y-intercept?(1)5.4In which quadrants is the graph drawn?Copyright reserved(1)[11]Please turn over

(16030121)-6-T930(E)(A1)TQUESTION 6Calculate the magnitude of x in the following diagram:6.16x4x6.22xAdjust the sketch to show that the sides are equal.x800x6.3BA1520C(3 x 3)Copyright reservedPlease turn over[9]

(16030121)T (E)(A1)T-7-QUESTION 77.121260 130 45 31Simplify the following expressions by making use of the special angle. Do not use acalculator.7.27.1.12 sin 30 3 cos 60 7.1.24 cos 30 (sin 45 ) cos 45 (2) (2)Find the perimeter of the following square:L 60 cm(2)7.2Determine the volume in cubic centimetre if the dimensions of the rectangular prismare: length 200 mm; breadth 125 mm and height 90 mm.TOTAL:Copyright reserved(2)[8]100

(16030121)-1-T930(E)(A1)TMATHEMATICS N1FORMULA SHEETRectangle: Perimeter 2(l b)Area l bSquare:Perimeter 4aArea a2Triangle: Perimeter a b cArea ½b hRectangular prism:Volume l b hRight triangular prism:Volume ½b h lCube:Volume a3Right pyramid:Volume 13 (base area h)Ellipse:Area π(major axis minor axis)4Circle: Circumference D or 2 rπD 2Area or r24Cylinder: Volume Cone: Volume πD 2 h or r2h4πr 2 hπD 2 h or343Annulus: A R 2 r 2Copyright reserved Please turn over

(16030121)-2-T930(E)(A1)TThe right-angled triangle:BcAaθCbThe theorem of Pythagoras:c2 a2 b2Ratios of angle θ :sinθ acCopyright reservedcosθ bctan θ ab

MARKING GUIDELINENATIONAL CERTIFICATEAPRIL EXAMINATIONMATHEMATICS N11 APRIL 2016This marking guideline consists of 8 pages.Copyright reservedPlease turn over

MARKING GUIDELINE-2MATHEMATICS N1T930(E)(A1)TQUESTION 11.11 1.2x y1.310 1.466,667 1.5R1,30 1.6-5 1.7Hypotenuse 1.8 y x1.9Isosceles 1.104 (10 x 1)[10]QUESTION 22.12.1.1 a 3 b c a 4 b c a 3b 3 c a 4 b 4 c a 3b 4 b 3 c 4 c a 7b c 2.1.2 1 2 2 (3) 3 3 1 4 3 4 1 43 64 Copyright reserved(3)Please turn over

MARKING GUIDELINE2.1.3-3MATHEMATICS N1T930(E)(A1)T27a 3b 4729b2ab0 31 33 a 3 b 4 3 2a(1) 6 3 b ab 2a 3 a b 2a 313 4 1 33 6313 3 3 2a 3ab6a 2 b 2.22.3x (4)0,48 1330,12 0,48 133 log x log 0,12 log 0,48 log133 log 0,12 0,319 2,124 0,921 0,319 2,124 0,921 log x 3,364 x 2312,065 (6)16x 2 y 4 xy 2 7 xy 10x 2 y 6 xy 2 4 xy6 x 2 y 10xy 2 11xy 2.48 x [ x 3( x 2)] 8 x [ x 3 x 6] 8x x 3x 6 10x 6 2(5 x 3) Copyright reserved(3)(4)[23]Please turn over

MARKING GUIDELINE-4MATHEMATICS N1T930(E)(A1)TQUESTION 36 x 2 12x 17 3.1x 26x3 0x 2 7x 66 x 3 12x 2 2 12 x 7 x 6 12x 2 24x 17x 617x 34 28 ( x 2 )( 6 x 2 12x 17) remainder -283.23.2.1(7)32 x 3 y 4 z 2 2 5 x 3 y 4 z 2 48x 5 y 3 z 3 2 4 3x 5 y 3 z 3 70x 2 y 5 z 4 2 5 7 x 2 y 5 z 4 3.2.23.3 25 3 5 7 x 5 y 5 z 4 3360x 5 y 5 z 4 (2)3.2.32 x 2 y 3 z 2 (2)3.3.1ab 8 xy 2bx 4ay ab 2bx 4ay 8 xy b a 2 x 4 y a 2 x b 4 y a 2 x 3.3.2 24x 2 4 x 30x 5 5x3x4 x 6 x 1 3x ONE mark for multiplication sign, factorise5x5 6 x 1 4x 3 5 512x 25Copyright reserved(5)1 2 11x xy x 2 y 22441 x 2 x y xy 2 ONE mark each term4 3.4(3)(4)(4)[27]Please turn over

MARKING GUIDELINE-5MATHEMATICS N1T930(E)(A1)TQUESTION 44.14.24.34( y 3) 6 y 2( y 4)4 y 12 6 y 2 y 8 2 y 12 2 y 8 2 y 2 y 8 12 4 y 20 44 y 5 (5)4x 4 24 4x 24 4 4x 28 x 7 (4)1 2gt33 p gt 2 3p t2 gp t Copyright reserved3p g(3)[12]Please turn over

MARKING GUIDELINE-6MATHEMATICS N1T930(E)(A1)TQUESTION 55.1xy-41-31,33-22-140 4Scale: 1 cm 1 unit ONE mark for correct scale in both axisOne mark for indicating y-axis and x-axis(8)5.2Rectangular hyperbola (1)5.3No y-intercept (1)5.42 and 4 Copyright reserved(1)[11]Please turn over

MARKING GUIDELINE-7MATHEMATICS N1T930(E)(A1)TQUESTION 66.14 x 6 x 2 x 1800 12x 1800 1212x 15 6.2800 x x 1800 2 x 1800 80 0 2 x 1000x 50 0 6.3 20 2 152 x 2 x 2 (20) 2 (15) 2 x 2 400 225 x 175x 13,229 (3 x 3)[9]QUESTION 77.17.1.12 sin 30 3 cos 60 1 1 2 3 2 2 1 1 121 225 27.1.2(2) 4 cos 300 (sin 450 ) cos 450 3 1 1 4 2 2 2 3 1 2 2 1 3 7.2(2)Perimeter 4L 4(6 cm) 24 cm Copyright reserved(2)Please turn over

MARKING GUIDELINE7.3-8MATHEMATICS N1T930(E)(A1)TV L b h 200 125 90 2 250 000 m3 2 250 cm3 (2)[8]TOTAL:Copyright reserved100

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