Mathematics Grade 9 P2 Free State November 2022 QP

GRADE 9 MATHEMATICS PAPER 2 NOVEMBER 2022 TIME: 1 HOUR 30 MINUTES TOTAL: 60 This question paper consists of 14 pages.

Grade 9 FS/ November 2022 Mathematics Paper 2 INSTRUCTIONS AND INFORMATION Read the instructions carefully. 1. Answer ALL the questions. 2. Write neatly and legible. 3. Number your answers exactly as questions are numbered. 4. Give reasons for each statement in QUESTION 1 to QUESTION 3. 5. Show ALL working. 6. You may use an approved scientific calculator (non-programmable and non-graphical). 7. Diagrams are NOT necessarily drawn to scale. Copyright reserved Page 2 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 QUESTION 1 1.1 In the diagram FG ⟂ GH. Find the value of 𝑥 (3) G H ሺ2𝑥 − 9ሻ0 𝑥 F Statement Reason 1.2 ̂G = 2𝑝 + 300 . Calculate the m = 1100 and CE In the diagram below, AB ‖ CD, ̂ (3) size of 𝑝. H A F B 𝑚 C D 2𝑝 + 30 0 E G Statement Reason Copyright reserved Page 3 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 1.3 Determine the value of a and b in alphabetical order. All reasons must be given (4) 1.3.1 U Q 800 𝑎 𝑏 1200 S V 600 R T Statement Reason 1.3.2 Determine the value of the variable in the diagrams Give reasons for (3) your. A 0 B 105 a C D E Statement Reason Copyright reserved Page 4 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 1.3.3 Determine the value of the variable in the diagrams Give reasons for (2) your statements E F 1060 𝑥 G H Statement Reason 1.3.4 Determine the value of the variable in the diagrams Give reasons for (2) your statements 𝑎 430 Statement Reason [17] Copyright reserved Page 5 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 QUESTION 2 2. Determine the value of 𝑥. All reasons must be given (4) 2.1 𝑦 380 𝑥 Statement Reason 2.2 The quadrilateral below is a square. Determine the value of 𝑥 and 𝑦 in (4) alphabetical order. All reasons must be given. 𝑦 𝑥 Statement Reason Copyright reserved Page 6 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 QUESTION 3 3.1 Give one minimum condition for congruent triangles (1) 3.2 Line segment QR is parallel to line segment ST. Complete the following proof (3) that ∆QRU⫼∆TSU R Q U T S In ∆QRU and ∆TSU Statement Reason ̂ T = QT RQ ̂S Alt angle QR ‖ ST ̂S QR = ___________ _____________________________ Vert. opp. angles __________ = ̂S TU ∴ ∆QRU ⫼∆TSU Equal angles or AAA Copyright reserved Page 7 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 3.3 Proof that : ∆ABD ≡ ∆CED (4) B A D C E Statement Reason In ∆ABD and ∆CED [8] Copyright reserved Page 8 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 QUESTION 4 4.1 Point Aሺ1 ; 5ሻ is plotted on the Cartesian Plane below. • 𝐀ሺ1 ; 5ሻ 4.1.1 Translate point A, 3 units to the right and then 5 units down. (1) 4.1.2 Write down the new coordinate of point A. (1) ____________________________________________________ ____________________________________________________ Copyright reserved Page 9 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 4.2 Draw ∆ABC with vertex coordinates of Aሺ−𝟑 ; 𝟓ሻ , Bሺ−𝟔 ; 𝟑ሻ and Cሺ−𝟐 ; 𝟑ሻ 4.2.1 Draw the image of ∆ABC, if is translated using the rule (1) ሺ𝑥 ; 𝑦ሻ ⟶ ሺ𝑥 + 3 ; 𝑦 − 7ሻ. 4.2.2 Reflex ∆ABC about the 𝒚 − 𝐚𝐱𝐢𝐬. (1) Copyright reserved Page 10 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 4.3 In the given diagram, ∆ABC is enlarged through the origin by a factor of 2 to form its image ∆A′ B′ C′ . 𝐂′ 𝐂ሺ𝟐 ; 𝟓ሻ 𝐀′ 𝐁′ 𝐀ሺ𝟐 ; 𝟏ሻ 𝐁ሺ𝟓 ; 𝟏ሻ 4.3.1 Determine the coordinates of the vertices of ∆A′ B′ C′ (3) _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ 4.3.2 Determine the lengths of the sides of ∆𝐀′ 𝐁 ′ 𝐂 ′ . (3) ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ [10] Copyright reserved Page 11 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 QUESTION 5 5.1 Calculate the perimeter of the diagram. (2) 22 𝑚 9𝑚 15 𝑚 8𝑚 ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 5.2 The quadrilateral below is a trapezium. Find the area and the perimeter of the (2) diagram below. 11 𝑐𝑚 9 𝑐𝑚 8 𝑐𝑚 17 𝑐𝑚 Perimieter = ______________ Area = _____________ Copyright reserved Page 12 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 5.3 The perimeter of a rectangle is 46 cm. If the length = ሺ2𝑥 + 5ሻ cm and the (3) breadth= ሺ𝑥 + 6ሻ cm, calculate the area of the rectangle. ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 5.4 Calculate: 1,12 𝑘𝑚2 = _________________𝑚2 (1) ____________________________________________________ ____________________________________________________ ____________________________________________________ 5.5 A carton that is the shape of a (3) rectangular prism is 30 𝑐𝑚 long, 20 𝑐𝑚 wide and 10 𝑐𝑚 high. 10 𝑐𝑚 Calculate the surface area of the carton. 20 𝑐𝑚 30 𝑐𝑚 ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ 5.6 A cylinder has a radius of 7 𝑐𝑚 and height of 10 𝑐𝑚. ‘n Silinder het ‘n radius van 7cm en ‘n hoogte van 10cm. 5.6.1 Calculate the volume of the cylinder. (if 𝜋 = 3,14ሻ (2) Bereken die volume van die silinder (as 𝜋 = 3,14ሻ ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ Copyright reserved Page 13 of 14 Please turn over

Grade 9 FS/ November 2022 Mathematics Paper 2 5.6.2 Find the total surface area of a closed cylinder. (3) ____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________ (1) 5.6.3 If the dimensions are doubled, what would the total surface area be? ____________________________________________________ ____________________________________________________ [16] TOTAL [60] Copyright reserved Page 14 of 14 Please turn over