O.R.T.I November 2023 Mathematics grade 9 Paper 2

O.R.TAMBO INLAND DISTRICT SENIOR PHASE GRADE 9 NOVEMBER 2023 MATHEMATICS PAPER 2 MARKS: 75 TIME : 2 hours This question paper consists of 10 pages including annexure .

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District INSTRUCTIONS AND INFORMATION FOR LEARNERS 1. Read the instructions for each question carefully. 2. Answer all the questions. 3. Number your work exactly as questions are numbered. 4. Clearly show ALL the calculations, diagrams and graphs you have used in determining your answers 5. Your calculations must include reasons 6. You may use an approved scientific calculator (non-programmable and non-graphical). 7. Diagrams are NOT necessarily drawn to scale. 8. 9. 10. 2|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District QUESTION 1 1. In this question, 4 possible answers are given. Write only the correct answer next to the corresponding number. EXAMPLE: If the correct answer for 1.1 is A, write only answer as 1.1 A. 1.1 In the figure below 𝑥° = 50° because they are (1) A. Alternate angles B. Corresponding angles C. Adjacent angles D. Vertically opposite angles 1.2 The value of 𝑥 in the figure below is (1) A. 15 B. 20 C. 30 D. 60 1.3 When parallel lines are cut by a transversal, (1) A. All pairs of angles formed are always equal. B. Pairs of corresponding angles lie on opposite of a transversal. C. Pairs of co-interior angles are supplementary. D. Pairs of angles that lie above the parallel lines are acute angles. 1.4 ∆ABC drawn below is (1) A. A scalene triangle B. An equilateral triangle C. An isosceles triangle D. An obtuse angled triangle 3|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District 1.5 Which of the statements below defines a trapezium? (1) A. Pairs of opposite sides are parallel B. One pair of opposite sides is parallel C. All its angles are right angles D. Diagonals have always the same lengths 1.6 One of the statements below is not a property of a right angled triangle. (1) A. Has one angle a right angle B. The side that lies opposite the right angle is the hypotenuse. C. The line segment that bisects the right angle forms an acute angle on the hypotenuse. D. The two sides adjacent to the right angle are perpendicular 1.7 When two triangles are congruent, one of the conditions is incorrect (1) A. Two corresponding sides and an included angle are equal. B. Two corresponding angles and a corresponding side are equal. C. Corresponding angles are equal and corresponding sides are proportional. D. A right angle, hypotenuse and one other corresponding side are equal. 1.8 Which statement describes the transformation of line segment? A. Translated 5 units up B. Reflected in the Y- axis C. Translated 5 units down D. Reflected in the X- axis 1.9 The area of a circle with the radius of 2 cm is A. 5𝑐𝑚2 B. 12,56 𝑐𝑚2 C. 7,8 𝑐𝑚2 D. 10 𝑐𝑚2 4|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District 1.10 The volume of a rectangular prism drawn below is A. 15 𝑐𝑚3 B. 60 𝑐𝑚3 C. 96 𝑐𝑚3 D. 68 𝑐𝑚3 [10] QUESTION 2 2.1 Read the figure below and answer the questions that follow. 2.1.1 Calculate the size of 𝑥°? Give reasons for your answer. (2) 2.1.2 Determine with reasons the value of y. (4) 2.1.3 ̂B Hence, find the size of DA (2) 2.1.4 ̂ C and angle D? Give a reason for your What the relationship is between DA (2) answer. 2.1.5 ̂ B = AD FA ̂ E (Reason…………… (………… ; …………) (2) 2.2 Study the form of transformation drawn below and state the rule in the form (2) 5|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District 2.3 2.3.1 On the cartessian plane provided (ANNEXURE) at the end of the question (3) paper, draw kite SAMP with vertices S(1; −2) ; A(2; −1) ; M(3; −2) ; P(2; −5). Label the vertices and show the coordinates of each point. 2.3.2 Reflect the figure (kite) you have drawn along the y-axis and label it as (3) 𝑆 1 𝐴1 𝑀1 𝑃1. Show the coordinates of each point of the image. 2.3.3 What is the relationship between the coordinates of the object and the (1) coordinates of the image? [21] QUESTION 3 3.1 ABCD is a parallelogram with diagonal BD, AB is extended to E, AD̂ C = 2𝑥 + 23, 𝐷𝐵̂C= 66°, Study the diagram and answer the questions that follow. 3.1.1 The sum of the interior angles of a parallelogram is 360°. Then, calculate the (2) value of 𝑥. Give reason(s) where necessary. 3.1.2 Give with reasons the size of (i) CB̂E (2) ̂ (ii) ADB (2) 6|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District 3.1.3 Calculate with reasons the size of DB ̂E. Showing the relationship with its (4) opposite interior angles of a triangle. 3.2 ∆𝑃𝑄𝑂 and ∆SRO are right angled triangles with QO= RO, PQ ⊥ QR and SR ⊥ RQ Copy and complete the table below to show that ∆𝑃𝑄𝑂 ≡ ∆SRO. Statement Reason In ∆𝑃𝑄𝑂 and ∆SRO 3.2.1 … … = 𝑆𝑂̂𝑅 ………………….. (2) 3.2.2 QO= …… given (1) 3.2.3 𝑃𝑄̂ 𝑂 =S𝑅̂O …………………. (1) …………………. (1) ∴ ∆𝑃𝑄𝑂 ≡ ∆SRO 3.3 ∆𝑆𝑇𝑅 and ∆XYZ drawn below are similar triangles. 𝑇𝑆 (2) 3.3.1 Copy and complete 𝑋𝑌 = ⋯ … . = ⋯ … .. (reason) 3.3.2 Hence, calculate the length of side (i) YZ (2) (ii) TR (2) [21] 7|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District QUESTION 4 4.1 Study the trapezium ABCDE drawn below and answer the questions that follow. 4.1.1 Determine the perimeter of trapezium ABCDE (2) 4.1.2 Calculate the area of (i) ∆BCD. (3) (ii) trapezium ABCDE and convert your answer in meters (3) 4.2 In the figure below, the circle is enclosed in a shaded square with the length of the side = 6 𝑐𝑚. Calculate the area of the shaded part. Round off your answer to a whole. (5) NOTE: Use 𝜋 = 3,14 4.3 In the triangular prism drawn below, DE = 5 cm, FE = 4 cm, CE = 15 cm and DF⟘ FE 4.3.1 Calculate the volume (3) 4.3.2 Calculate the total surface area (4) 8|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District 4.4 Read the container drawn below and then calculate the volume of water in ml (3) that can fill the inside container. [23] END GOOD LUCK - ENJOY THE FESTIVE SEASON. 9|Page

November 2023 November 2023 Mathematics Grade 9 Paper 2 O.R.T.I.District NAME:_____________________________________ QUESTION 2.3.1 ANNEXURE 10 | P a g e