Mathematics Grade 10 IEB June 2019 Question Paper

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Downloaded from hlayiso.com Page 1 of 5 St John’s DSG Grade 10 Mathematics June Examination 2019____________________________________________ QUESTION 1 1.1 Indicate whether the following are Rational or Irrational: 1.1.1 0, 8̇ 1 1.1.2 26 1.1.3 2𝜋 1.1.4 −√3 (2) 1.2 Arrange the following in descending order: 3 4 √3 ; √2 ; √2 ; √2 (1) 1.3 Represent 𝑥 ∈ (−3 ∶ 6 ] in Set Builder Notation and on a number line. (4) [7] QUESTION 2 2.1 Given the sequence 17; 26; 35; … … … 2.1.1 Give the next 2 terms of the sequence. (1) 2.1.2 Calculate the 25th term. (3) 2.2.1 Is a sequence increasing or decreasing if the common difference is a negative? (1) 2.2.2 Which of the following rules will give a decreasing sequence: Tn = - 2n + 4 or Tn = 2n - 27 (1) 2.3. Given the sequence 16; 8; 4; 2; … … … Find the nth term (3)

Downloaded from hlayiso.com Page 2 of 5 St John’s DSG Grade 10 Mathematics June Examination 2019____________________________________________ 2.4 Determine the value of 𝒑 in the arithmetic sequence below: −27 ; 𝒑 ; −43 ; … … (3) 2.5 A programme for preparing runners for the Comrades Marathon suggests running 12 𝑘𝑚 in the first week of training and increasing this distance by 4 𝑘𝑚 each week for the next 25 weeks. Determine: 2.5.1 The formula to determine the distance run in any one of the weeks of training. (3) 2.5.2 The week in which 92 𝑘𝑚 should be run? (2) 2.5.3 By how far will the distance run in the 10th week of training exceed 42,2𝑘𝑚, which is the distance of a standard marathon? (2) [19] QUESTION 3 Fully factorise the following: 3.1 𝑎5 − 4 𝑎3 𝑏4 (3) 3.2 27𝑎3 + 8𝑏 3 (2) 3.3 2𝑥𝑦 − 6𝑎𝑏 − 3𝑎𝑦 + 4𝑏𝑥 (3) [8] QUESTION 4 4.1 Simplify the following: 2 4.1.1 1 + (2) 𝑎 2𝑎 + 4 3𝑎−6 4.1.2 ÷ (4) 𝑎2 − 4 𝑎2 − 4𝑎 + 4 𝑝+𝑞 𝑝−𝑞 4.2 𝐼𝑓 𝑿 = 𝑝 − 𝑞 𝑎𝑛𝑑 𝒀 = 𝑝 + 𝑞 Determine the following in terms of 𝑝 and 𝑞: 𝟑 (𝑿 – 𝒀) (4) [10]

Downloaded from hlayiso.com Page 3 of 5 St John’s DSG Grade 10 Mathematics June Examination 2019____________________________________________ QUESTION 5 Simplify the following and give your answers with positive exponents: 2 − 𝑥 10 5 5.1 (𝑦−5) (3) 6𝑎−2 . 33𝑎+1 5.2 (3) 18𝑎 7 . 5𝑚 + 5𝑚+1 5.3 (3) 5𝑚−1 − 5𝑚 [9] QUESTION 6 Solve for 𝑥 6.1 4 − 2(2𝑥 − 5) = −(𝑥 − 5) (2) 6.2 𝑑𝑥 − 𝑒𝑞 = 𝑓𝑥 (2) 1 𝑥−1 6.3 = (4) 𝑥+3 −3 6.4 −7 < 2 − 3𝑥 ≤ 5 (3) 2 1 6.5 3𝑥 + 5𝑥 = (4) 81 [15] QUESTION 7 Plane A takes off from King Shaka International Airport heading towards Cape Town International Airport. At the same time plane B takes off from Cape Town International Airport heading towards King Shaka International Airport flying 20𝑘𝑚/ℎ slower than plane A. The airports are 1634𝑘𝑚 apart and the planes meet after 54 minutes. Calculate the distance from King Shaka International Airport at which they meet and the speed of the planes. [6] QUESTION 8 Simplify the following correct to two decimal places: 8.1 𝑠𝑖𝑛 35° (1) sin 50° 8.2 (1) cos 50° 8.3 𝑡𝑎𝑛2 37° (2) [4]

Downloaded from hlayiso.com Page 4 of 5 St John’s DSG Grade 10 Mathematics June Examination 2019____________________________________________ QUESTION 9 Solve the following equations to solve for 𝑥 correct to one decimal place. 9.1 sin 𝑥 = 0,33 (1) 9.2 2 cos 𝑥 = 1,64 (1) 9.3 tan( 𝑥 − 15°) = 1,529 (2) [4] QUESTION 10 If 13 𝑠𝑖𝑛 𝜃 + 5 = 0 and 𝜃 𝜖 [90° ; 270°], calculate with the aid of a diagram, but without using a calculator, the value of cos 𝜃 + sin 𝜃. [7] QUESTION 11 Without the use of a calculator and showing all working Prove that 𝑠𝑖𝑛2 30° + 𝑐𝑜𝑠 2 30° = 1 [5] QUESTION 12 In a rugby game, Justin has been awarded a penalty kick. The rugby posts are 6𝑚 high and Justin is standing 20𝑚 from the centre of the posts. 12.1 Will Justin be able to kick the ball over the posts if he kicks the ball at an angle of 15°? (3) 12.2 What is the minimum angle (𝜃) at which Justin must kick the ball in order to score? (3) [6]

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