Grade 10 Mathematics: Question Paper 2

Transcription

1 Matematics(NSC)/Grade 10/ P2 6 Exemplar Grade 10 Matematics: Question Paper 2 MRKS: 100 TIME: 2 ours QUESTION Give te co-coordinates of, te new co-ordinates ofte point (-2; 5) if: It is reflected about te x-axis (1) It is reflected about te y-axis (1) It is reflected about te line y = x (2) 1.2 Given te points (-3; 2), (5; -1) and C(2; p), calculate: Te lengt of te line segment. (2) Te co-ordinates of M, te midpoint of te line segment. (2) Te value of p if te gradient of C is 2. (3) 1.3 In C below, = 53,14 and C = 20 metres. 20 m 53,14 C Calculate te value of. (2) Hence, express C in terms of tan53,14. (2) 1.4 Te base of te rectangular prism below as a lengt 18 cm a breadt xcm. Te eigt of te prism is 5 cm. 5 cm 18 cm x cm Calculate te folowing in terms of x: Te volume of te prism. (2) Te new breadt of te prism, if te volume of te prism is doubled, but te lengt and te eigt remain te same. (1) 1.5 Te ages of te people in te Jackson family are as folows: 63; 32; 34; 64; 32; 27; Determine te mean. (2) Determine te mode. (1) Determine te median. (2) Determine te upper quartile. (2) [25]

2 Matematics(NSC)/Grade 10/ P2 7 Exemplar QUESTION 2 C as co-ordinates (-4; 2), (1; 2) and C(-1; 6), and C = 5 units 2.1 Determine te lengts of and C (3) 2.2 W at kind of triangle is C. Give a reason for your answer. (2) 2.3 Explain wy C cannot be rigt angled. (5) 2.4 If D is te point (x; y) suc tat E(2 1 4 ; 7) is te midpoint of CD. Determine te co-ordinates of D. (3) 2.5 Sow tat te quadrilateral CD is a trapezium. (5) [18] QUESTION 3 In te diagram below tere are 4 triangles (labeled s 1 4) tat are saded in grey and 1 triangle ( C) saded in wite. y x C 3.1 Copy and complete te following statements by filling in a 1, 2, 3, or a 4: is te reflection of in te y-axis (and vice versa). (2) is te reflection of in te x-axis (and vice versa). (2) is te reflection of in te line y = x (and vice versa). (2) 3.2 Te wite triangle, C, as co-ordinates (-3;0); (-5;-1) and C(-4; -4) Describe te transformation tat as occurred from 3 to C. (2) If C is reflected along te line y = x, draw C on te grid provided and write down te co-ordinates of eac point. (6) [14]

3 Matematics(NSC)/Grade 10/ P2 8 Exemplar QUESTION 4 candle maker makes candles wit a radius, r and a eigt, referred to as Type. See te diagram below. r r Type Type Te candle maker also makes two oter types of candle: Type and Type C. 4.1 Type candles ave te same radius and double te eigt of te Type candle. Express te volume of wax needed to make Type candles in terms of te volume of wax needed to make Type candles. (2) 4.2 Type C candles ave te same eigt and double te radius of te Type candle. Express te volume of wax needed to make Type C candles in terms of te volume of wax needed to make Type candles. (2) 4.3 Wat will be te impact on te eigt if e wants to make a candle wit te same volume of wax as te Type candle, but wants it to ave alf te radius. (2) 4.4 Te candles are transported by packing eac candle into a rectangular box. Sown in te diagram above. If te radius of a Type candle is cm and te eigt is 11cm, calculate te area of cardboard needed to make up boxes for te Type candles. (3) [9]

4 Matematics(NSC)/Grade 10/ P2 9 Exemplar QUESTION 5 Te diagram below is a roug, un-scaled plan of te front structure of a ouse and garage. 1,4m 3 H O U S E G R G E 2,9 m 5.1 Calculate te value of. (4) 5.2 Calculate te pitc of te ouse roof (sown as on te diagram). (4) 5.3 Calculate te widt of te ouse (sown as lengt on te diagram). (3) 5.4 Wat would be te impact on if te pitc of te garage roof was canged to be 15. Sow your working. (4) [15]

5 Matematics(NSC)/Grade 10/ P2 10 Exemplar QUESTION 6 Skype is a free Voip (voice over internet protocol) solution wic allows you to instant message or talk to people all over te world. Skype as experienced rapid growt since its launc in ugust Te table below sows te Real Skype Users (approx 10% of tose registered on skype) in 9 sub-regions. RealUsers: Sub-Regional Europe/Mid East/frica W.Europe E.Europe/Mid East frica Subtotal 2,054,568 3,467,114 2,311,409 7,833,108 mericas (Nort/Sout) US Canada S.merica Subtotal 2,801, ,817 4,706,325 8,424,525 sia/pacific us/nz/jap/tal/s.kor Cina India/Oter Subtotal 1,760,401 2,112,482 1,267,489 5,140,372 Total real users 21,398, Draw a pie cart to illustrate usage by sub-regions in te sia/pacific region. (5) 6.2 Calculate te number of degrees required to draw te frica section of a pie cart sowing all of te Total real users. (2) 6.3 Wic sub-region makes up approximately 2 9 of te Total real users? (2) 6.4 How muc do people talk on skype for in a day?elow is a istogram sowing results in a sample group of 150 university students and te number of words spoken by eac on skype on one particular day. (Please note tat te information sown ere is not official skype statistics and does not claim to be a true representation of te actual skype usage trends). Skype usage in a sample of 150 university students 40 No.of students to <4 4 to <8 8 to <12 12 to <16 16 to <20 20 to <24 24 to <28 28 to <32 32 to <36 36 to <40 Number of tousands of words used in te day Wat is te range? (1) Wat is te modal group? (1) Wic group contains te median value? (2) Calculate te estimated mean?(sow all your calculations and give your answer to te nearest word). (5) [19] End of Paper