Mathematics Grade 9 P2 Free State November 2025 Paper & Memo

ersloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock education Department of Education FREE STATE PROVINCE ees — — = : ———— eK a a Se SES Eee ere eR ET MATHEMATICS PAPER 2 MOCK NOVEMBER/DECEMBER TEST 2025 wee ee ee ee ee eS eS ee a ee eee — — — — = MARKS: 75 TIME: 15 Hours 1|Page ae Sea See

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock INSTRUCTION AND INFORMATION TO LEARNERS Read the following instructions carefully before answering the questions. ds Answer ALL the questions. Bi Clearly show ALL calculations. 3. Answer ONLY will not necessarily be awarded full marks. 4. You may use an approved scientific calculator (non-programmable and non-graphical) unless stated otherwise. If necessary, round answers off to TWO decimal places, unless stated otherwise. Write neatly and legibly. ALL diagrams or figures are NOT drawn to scale. Answer ALL questions’on the question paper. © PN wo Circle ONLY the letter for the CORRECT ANSWER, e.g. If the correct answer in 1, is D, you should only circle

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock QUESTION 1 Circle ONLY the letter for the CORRECT ANSWER, e.g. If the correct answer in 1, is D, you should only circle 1. Which line is perpendicular? (1) E F B 70° /209 450 45° A D é A ED 1. AD ™ B ED + FD : | c ED 1 CD - —_ D ED BD 2: What is the size of NSR? (1) Q P y 0 L . au >M bs N R A 100° B 80° c 40° D 20°

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 3. What is the relationship between 21 and 22? (1) A Adj. supplementary 2S B Adj. on the straight line c Co-interior Zs, AB||CD D Complementary Zs 4. What is the value of m? (1) A D 68° 469N Ff / im 44° 46° 68° 0 oOo WD PY 66°

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 5. What is the length of QP? (1) Q P D E po 40 cm 50cm 50 cm R F 30cm 40 cm 50cm 60 cm oa 0 oOo WD D> PQRS us a rhombus. Which of the following statement is CORRECT? (1) Q R APQT = APST APTR = AQTS AQTS = APST 0 ao WwW PY APTR = APST

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock fe oo oOo WD PF 50 ao WwW YD ABCE is a parallelogram with C = 90°. Calculate, with reasons, the size of oy ze E 2 7m B C D 16° a a 105° a 32° | 45° In a quadrilateral, each of two angles has a measure of 115°. If the measure of a third angle is 70°. What is the measure of the remaining angles? 60° 70° 130° 140° What is the value of x if AB|| CD? (1) (1) (1)

ensloaded from Stanmorephysics.com Mathematics Paper 2 Mock E 108° G D / \ L A 108° B 104° c 54° = D 52° bes 10. What is the size of m?- eS | m 58° y+45° 2 \ %, A 113° B 106° c 87° D 58° QUESTION 2 Nov/ Dec 2025 [10]

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 2.1 In the diagram below, AB is perpendicular to BC and ABD = 60°. Calculate, with reasons, the value of an angle indicated by the small letter (m) in the diagram. A A D anorepig. B "c Statement ‘eason 2.2 Calculate the value of the unknown angles indicated by small letter.(x) Statement 0 ison — (2) (3)

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 2.3 AB and CD are straight lines cut by transversal ST. Calculate, with reasons, (3) the value of x and hence show that AB|| CD. Statement

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 2.4 Calculate, with reasons, the values of an angle indicated by the small letter. (10) NB! You should NOT repeat the reasons. Answers must be in alphabetically order. 7 \ \._, 120° 110° Statement Reason [18]

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock QUESTION 3 3.4. In. AABC, calculate, with reasons: A (4) 3.1.2 The length of AC (1)

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 3.2. AABC = AEDC, BCD and ACE are staright lines. Find the unknown angle and side marked in the diagram a Statement

ewnloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 3.3 In the diagram below, DE||AC, BD= 4, DA = 8 and BE = 8. fava oe = ine } ¥ pif 3.3.1 (5) Statement 3.3.2 Find the length of EC. (5)

ewnloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 3.4 PQRS is a parallelogram. PQ = QT = TRand PT =8 cm. S P 3.4.1 Calculate Q (2) Statement 3.4.2 Calculate R (2) Statement Reason 3.4.3 Calculate S Statement Reason

ewnsloaded from Stanmorephysics.com Mathematics Paper 2 Mock 3.5. Consider APQS and ARSQ. Prove that APQS = ARSQ en Nov/ Dec 2025 Statement (5) [30]

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock QUESTION 4 414 ABCD is a rectangle with D, = 32°,AB =BE=5cm A D 32° Ld f 4.1.1 Find the length of the unknown side DC. - Statement 4.1.2 Calculate the value of the unknown E; Statement Reason (1) (1

ewnloaded from Stanmorephysics.com Mathematics Paper 2 Mock 4.2. Atriangular prism is given. 14cm 4.2.1 Find the length of AC. Nov/ Dec 2025 Statement Reason 4.2.1 Calculate the surface area of the triangular prism. (1) (2)

ewnloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 4.3. PQRS is a rectangle of length (2x — 1) cm and width (x + 2) cm. Ifasquare (4) - of side 6 cm is cut from the corner P, show that the area of the shaded “region is (2x? + 3x — 38) cm (x + 3)cm Q [9]

ensloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock QUESTION 5 5.1 Study the diagram, NOT drawn to scale below. At the left of this shape is a semicircle with diameter of 4 cm. 4cm 80m 6cm 5.1.1 Convert mm to cm | 5.1.2 Determine the perimeter of the shape Statement Reason (5)

ewnloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Paper 2 Mock 15.13 The total area of the shape 5.2 Study the diagram below and calculate, correct to two decimal places where necessary the area of the shaded region. [Hint: h = 6 cm| 12cm (3)

evsloaded from Stanmorephysics.com Mathematics Paper 2 Mock Nov/ Dec 2025 TOTAL [75] [8]

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline QUESTION 1 ais iw} + A SOS o ON DOD oO FF WwW DN 000 > > >O.> > a = ° < QUESTION 1 (1) (1) (1) (1) (1) (1) (1) (1) (1) (1) TOTAL [10] 2.1 In the diagram below, AB is perpendicular to BC and ABD = 60°. Calculate, with reasons, the value of an angle indicated by the small letter (m) in the diagram. A ry | 60° m m = 30° ¥ Compl. Zs ¥ Statement: 1 mark Reason: 1 mark (2)

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline 2:2 Calculate the value of the unknown angles indicated by small letter.(2) Statement: 1 mark Reason: 1 mark Answer: 1 mark 0979 = 200 278° 2 = 419 # 2.3. ABand CD are straight line: value of x and hence show that AB|| CD. i 5x + 70° A B E\2x + 5° versal ST. Calculate, with reasons, the 3x—410 C R. D T 2x +59 = 3x-10°Y Alt. 2s AB|] CD. ~ 2 = 159° OR Statement: 1 mark — - Reason: 1 mark yoy Adj. suppl Zs ¥ Answer: 1 mark ox=159 Vv (3) (3)

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline 2.4 Calculate, with reasons, the values of an angle indicated by the small letter. NB! You should NOT repeat the reasons. Answers must be in alphabetically order. I B D k= 50° W alt. 2s AB|| CD. ~ Statement: 1 mark Reason: 1 mark (10) 1 = 180° — 120° co-int. 2s AB|| CD. Statement: 1 mark =eor Reason: 1 mark m = 110° ¥ corres. ZsAB||CD. ¥ Statement: 1 mark Reason: 1 mark n= 110° vert.opp Zs ¥ Statement: 1 mark = Reason: 1 mark 0= 70 ¥ adj. suppl 2s ¥” Statement: 1 mark Reason: 1 mark Here, the examiner wanted to check whether the learners understand all REASONING used in angles relationships with parallel line (XFUN)

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline QUESTION 3 3.1 In AABC, calculate, with reasons: 3.1.1. The size of x /an size of the interior angles. 180°—20° i A or S xetvy 1 iw Statement: 2 marks Reason: 1 mark Answer: 1 mark =20° ¥ 3.1.2 The length of AC B=x+10° € = 2x — 10° A=5x+20° = 20° + 10° = 2(20°) — 10° = 5(20°) + 20° = 30° = 30° = 120° Statement & reason: (1) The length of IsoscelesA ¥ 41 mark AC = 20cm

3.2 ®Oewnloaded from Stanmorephysics.com Mathematics Mock Marking Guideline Nov/Dec 2025 AABC = AEDC, BCD and ACE are staright lines. Find the unknown angle and side marked in the diagram AABC = AEDC ¥ = 359°V Since SAS ¥ ED = AB “c=2cmv Statement: 1 mark Reason: 1 mark Answer: 1 mark Reason: 1 mark Answer: 1 mark (5)

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline 3.3 In the diagram below, DE||AC, BD= 4, DA = 8 and BE = 8. In ABAC and ABDE BAC = BDE ¥ Statement: 1 mark (5) a a Reason: 1 mark ACB = BED ¥ Statement: 1 mark Reason: 1 mark «» ABAC || ABDE AA ¥ Condition: 1 mark Similarly ABC = DBE | Common 3.3.2 Find the length of EC BE BD Prop: 2 mark EC DA om Re Subst: 1 mark Simpl: 1 mark Answer: 1 mark Baty EC 8 EC = 8x8 /

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline 3.4 PQRS is a parallelogram. PQ = QT = TRand PT =8cm. 3.4.1. Calculate Q Statement: 1 mark (2) Reason: 1 mark 3.4.2 Calculate R Co-int Zs PQ|ISR v Statement: 1 mark (2) Reason: 1 mark 3.4.3 S= 60° V¥ Opp Zs of parm v Statement: 1 mark (2) Reason: 1 mark

3.5 ®Oewnloaded from Stanmorephysics.com Mathematics Mock Marking Guideline Q In APQS and ARSQ Consider APQS and ARSQ. Prove that APQS = ARSQ mo ite 8, =Q,¥ given ¥ Qs=saq Common side . APQS = ARSQ SAS ¥% Nov/Dec 2025 Statement: 1 mark Reason: 1 mark Statement: 1 mark Reason: 1 mark Condition: 1 mark (5) [30]

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline QUESTION 4 41 ABCD is a rectangle with D, = 32°, AB = BE =5cm A D 4.1.1 bk Fr olf tangle are= v Statement & Reason: 1 ba timorephysics.com mark 4.1.2 Calculate the value of the unknown E; E, = 58° ZssumofA/int Zsofad ¥ Statement & Reason: 1 mark (1) (1)

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline 42 A " _ is given. 14cm 4.2.1 Find the length of AC 6 10 cm 10cm 6cm| 8cm § z g § = + s = 6cm 8 cm 10cm 6cm 10 cm

4.3 ®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline — ah Pythagoras Length of AC: 1 mark (1) = +7100 ‘AC? = 10cm AC=10cm ¥ 4.2.2 Calculate the surface area of the triangular prism. Area of AABC = 5(8 cm)(6 cm) = 24 cm? Area of ADEF = 5(8 cm)(6 cm) = 24 cm? Area of ACFD = (14 cm) Calculation: 1 mark (2) Surface area of triangulai Answer. face = 244+ 24+ 112+ 84 = 384cm? Vv PQRS is a rectangle of length (2x — 1) cm and width (x + 2) cm. If a square of side 6 cm is cut from the corner P, show that the area of the shaded region is (2x? + 3x — 38) cm 6 (x + 3)cm Q (2x —1)cm Ss R Area shaded region = area of rectangle — area of square = (2x-1)(x+2)-(6x6) ¥ Vv Sust: 2 marks = 2x? +3x-2-36 ¥ Simpl: 1 mark (4) 5 Answer: 1 mark = (2x2 4+3x-—38)cm Vv 19]

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline QUESTION 5 5.1 Study the diagram, NOT drawn to scale below. At the left of this shape is a semicircle with diameter of 4 cm. 5.1.1 Convert mm to cm Convert 80 mm to cm 80mm +10 =8cmv¥ Conv: 1 mark 5.1.2 Determine the perimeter of the shape 4cm xcm 80 m 6cm Value of x: 1 mark Length of the rectangle Pythagoras ¥ x=10cm (1) (1)

®Oewnloaded from Stanmorephysics.com Mathematics Mock Marking Guideline The arc of the semicircle has a length of: SAG: x4) =2mcm Perimeter = 27 +10+4 +6+8 = 34,28cm V¥ 5.1.3 The total area of the shape Area of the right— angled triangle (A) =5(8 x 6) = 24cm? = 2m cm” Total area of the shape = 24+40+2n v =70,28cm2 ¥ Nov/Dec 2025 Perimeter: 1 mark Total area: 2 mark (1) (2)

®ownloaded from Stanmorephysics.com Nov/Dec 2025 Mathematics Mock Marking Guideline 5.2 Study the diagram below and calculate, correct to two decimal places where necessary the area of the shaded region. [Hint: h = 6 cm] 12cm Area of 2 As = ai(5 4 24 em: 1 mark (3) 48 cm*: 1 mark Area of rectangle = 1 . Area of the shaded regio Acm2 v¥ Total area: 1 mark [9] Total [75]