Mathematics Grade 9 P2 November GP 2020 Question Paper (Eng)

Downloaded from hlayiso.com GAUTENG DEPARTMENT OF EDUCATION PROVINCIAL EXAMINATION NOVEMBER 2020 GRADE 9 MATHEMATICS (PAPER 2) NAME OF LEARNER: _____________________________________________________ GRADE: _____________________ TIME: 1 hour MARKS: 50 10 pages + 1 formula sheet P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 1) 2 GRADE 9 INSTRUCTIONS AND INFORMATION: 1. Answer ALL the questions. 2. Question 1 consists of FIVE multiple choice questions. You must circle the letter of the correct answer in the QUESTION PAPER. 3. Answer questions 2 – 4 in the spaces provided. 4. Clearly show all calculations, diagrams and graphs that you have used in determining your answers. Answers ONLY will not necessarily be awarded full marks. 5. Diagrams are not necessarily drawn to scale. Reasons MUST always be given for statements made when answering geometry questions. 6. The teacher will lead you through the practice question before you start the test. 7. Approved scientific calculators (non-programmable and non-graphical) may be used, unless otherwise stated. 8. Write neatly and legibly. Practice Question Circle the letter of the correct answer. 1. Complete: 𝐴̂ is an obtuse angle, because … A 0° < 𝐴̂ < 90°. B 180° < 𝐴̂ <360°. C 90° < 𝐴̂ <180°. D 𝐴̂ = 180°. You have done it correctly if you circled C. P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 3 GRADE 9 QUESTION 1 FOUR options are provided as possible answers to the following questions. Circle the letter next to the correct answer in the QUESTION PAPER. 1.1 ̂ C = 63°, CB extended to E, Ĉ = 54°, AB extended to D ∆ABC with AC extended to F, BA ̂ A = 𝑥°. and EB F A 63° 54° C 𝑥 1 3 B E D Complete: The size of 𝑥 = ... A 54°. B 63°. C 117°. D 126°. (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 4 GRADE 9 1.2 Which statement below about kite DEFG is TRUE? D E O G F A Two pairs of adjacent sides are equal in length. B Diagonals bisect each other. C Two pairs of opposite sides are parallel. D Diagonals are equal in length. 1.3 The rectangular prism below has a length of 8 cm, breadth of 3 cm and height of 4 cm. The volume of the prism is __________. 4 cm 3 cm 8 cm A 15 cm3 . B 48 cm3 . C 96 cm3 . D 56 cm3 . (1) 1.4 What type of triangle is ∆ABC below? A B C A Equilateral triangle B Scalene triangle C Right-angled triangle D Isosceles triangle P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 5 GRADE 9 1.5 XY  YZ and XK  KY X K Y Z Which statement is correct? A ∆XYK ≡ ∆ZYK B ∆XYK ≡ ∆XYZ C ∆ZYK⦀∆XYK D ∆XYK⦀∆XYZ (1) [5] QUESTION 2 Answer the following questions in the spaces provided. 2.1 ̂ B = 60°, BĈD = 45°, ̂ AB ∥ CD ∥ EF, CA B = 𝑥, 𝐴̂1 = 𝑦 and ̂ D=𝑧. S 1 𝑦 A 2 𝑥 B 60° 1 2 45° C 3 D 𝑧 E F 2.1.1 Determine, with reasons, the value of 𝑥. Statement Reason (1) P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 6 GRADE 9 2.1.2 Determine, with reasons, the value of 𝑦. Statement Reason Ĉ1 + 60° + 45° = 180° _____________________________ Ĉ1 =__________ AĈD = Ĉ1 + Ĉ2 = __________________ AĈD = y _____________________________ 𝑦 = _________ (5) 2.1.3 Determine the value of 𝑧. Statement Reason 𝑧 = ________________________ corresponding ∠𝑠 and EF ǁ CD (1) 2.2 Given: KN = KL, KL ⫽ NM  L̂ =2x + 20°and M = 3x – 35° L M 2𝑥 + 200 K N 2.2.1 Calculate the value of 𝑥 with reason/s. Statement Reason KL̂N = KN ̂L _______________________- ∴ KL̂N = __________ KL̂N = LN ̂M _______________________________ _______________________ sum of internal ∠𝑠 of ∆ ∴ 𝑥 = _______ (5) P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 7 GRADE 9 2.2.2 Hence, calculate the size of NL̂M. Statement Reason (2) [14] QUESTION 3 Answer the following questions in the spaces provided. 3.1 In the diagram below, ABCD is a square and PBRD is a parallelogram. A P D 1 3 2 1 2 1 2 2 1 3 B R C Complete to prove that ∆ABP ≡ ∆CDR. Statement Reason AB = _______________________ _______________________ PB = _______________________ _______________________ ̂ A = _______________________ _______________________ ∴ ∆ABP ≡ _________________ _______________________ (4) P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 8 GRADE 9 3.2 Given: ∆STR ⫴ ∆XYZ X R 𝑦 15 10 S 4 3 Y 𝑥 Z T 3.2.1 Write down the proportional sides of the two similar triangles above, by completing the statement. Statement Reason ST = = proportional sides of ⫴ ∆𝑠 XY (2) 3.2.2 Hence, calculate the value of 𝑥 and 𝑦. (5) [11] P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 9 GRADE 9 QUESTION 4 Answer the following questions in the spaces provided. 4.1 MNST is a parallelogram. NR = 9 mm, RS = 30 mm and MR = 12 mm. M T 12 mm N 9 mm R 30 mm S Calculate: 4.1.1 The area of ∆MNR. (3) 4.1.2 The perimeter of MNST. (5) P.T.O.

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 10 GRADE 9 4.2 A circular hole with a diameter of 14 cm is drilled through a rectangular block of wood. The dimensions of the wooden block are 30 cm by 20 cm by 10 cm. 17m 14 1 10 cm 20 cm 30 cm 4.2.1 Determine the volume of the wooden block. (3) 4.2.2 Determine the volume of the wooden block that remained after the hole was drilled. 22 Use 𝜋 = 7 . (6) 4.2.3 Determine the outer surface area of the wooden block before the hole was drilled. (3) [20] TOTAL: 50 END

Downloaded from hlayiso.com MATHEMATICS (PAPER 2) 11 GRADE 9 FORMULA SHEET Perimeter Area Rectangle 2(𝑙 + 𝑏) 𝑙×𝑏 Circle 2𝜋𝑟 𝜋𝑟 2 1 Trapezium 𝑆1 + 𝑆2 + 𝑆3 + 𝑆4 (𝑠𝑢𝑚 𝑜𝑓 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 𝑠𝑖𝑑𝑒𝑠) × ℎ 2 1 Triangle 𝑆1 + 𝑆2 + 𝑆3 𝑏 ×⊥ ℎ 2 Volume Rectangular prism 𝑙×𝑏×ℎ Cylinder 𝜋𝑟 2 × h 1 Triangular prism 𝑏 ×⊥ ℎ × 𝐻 2 Outer Surface Area Rectangular prism 2(𝑙 + 𝑏) × 𝐻 + 2 × 𝑙 × 𝑏