Mathematics Grade 11 Mpumalanga March Test 2025 Paper & Memo

Testpapers.co.za Downloaded from Stanmorephysics.com education DEPARTMENT: EDUCATION MPUMALANGA PROVINCE TIFICATE EXAMINATION MARKS: 50 TIME: 60 Minutes This question paper consists of 4 pages including the cover page.

Testpapers.co.za Newnlenckeck from Stanmoreghpsics.com CONTROLLED TEST 2025 Read the following instructions carefully before answering the questions. 1. 2. The questions paper consists of three questions: QUESTION | TO QUESTION 3. Answer ALL questions in all sections. Number the answers correctly according to the numbering system used in this question paper. Clearly show ALL cal sj graphs, etc, that you have used in determining your answers. Answers only will not ne awarded full marks. Write neatly and legibly.

Testpapers.co.za Newnlenckeck from Stanmoreghpsics.com CONTROLLED TEST 2025 QUESTION 1 1.1 Solve for x: Et x? -2x=8 (3) 1-2 4x? — x —2 =0 (answer correct to TWO decimal places) (3) 113 ( (4) 1.1.4 (5) 1.2 Solve simultaneo $ 4xt+y=7 and (6) 8 of a ™ 1.3. The roots of a quadratic equation arex = eet 3 Calculate the values of k for which the root(s) are equal (2) 14 — Given: (x+5)? =1-p? Calculate the values of p for which the roots of the equation are non-real (5) [28]

Testpapers.co.za Newnlenckeck from Stanmoreghpsics.com CONTROLLED TEST 2025 QUESTION 2 2.1 Simplify the following without using a calculator. Your answers must be free of negative exponent and irrational exponents. DAL | 322 ge! (5) Dgenel 212 (4) 22 Solve for x, withou 2.2.1 32=128 .- Sirs, (4) 222 © 1 (4) [17]

Testpapers.co.za Maewniencack from Stanmorerkprics.com CONTROLLED TEST 2025 QUESTION 3 3.1 In the diagram below, P (-6; 8) is a point in the Cartesian plane. A is the point on the positive x-axis. ZAOP=0. P(-6 ; 8) Determine, with the aid of a diagram, the following: Andel The length of OP. (2) 3.1.2 tand (1) 3.1.3 sind+cos0 (3) [6] TOTAL [50]

Testpapers.co.za Downloaded from Stanmorephysics.com education DEPARTMENT: EDUCATION MPUMALANGA PROVINCE -ERTIFICATE EXAMINATION MATHEMATICS GRADE 11 MARKS: 50

Testpapers.co.za Deuniondeck from Stanmorephpsics.com MEMORANDUM 2025 QUESTION 1 11.1 x? -2x=8 x? — 24820 Y Standard Form ) v Factors (+ 2k Y x values (3) =-2 orx=4 1.1.2 4x7 -x-2=0 v — _-CDtyCl—4 Substitution { vv Answers (3) x=0,84 or x= 113 x(x-1)26 x -x-620 Y Standard Form (x-3)(x+2)>0 oR < : > Y Critical Values -2 3 vv Answers (4) 2x+vxt+1=1 ia be ¥ Isolating the surd x+1=1-2x (Wx+1)? =(1-2x)? ¥ Squaring on both sides x+1=1-4x4+4x? Y Standard Form 4x° -5x=0 x(4x—5)=0 ¥ Common factor 5 5 x=0 or x# 4 Y Rejecting x = 4 (5)

Testpapers.co.za Daewntendeck from Stanmorephpsics.com MEMORANDUM 2025 1% 4xt+y=7 VET HAX crverrsveneen line ¥ Wekineytinaabjeal 3x? + Wy Hy? veer line2 substitute linel into line2: Y Substitution 3x? + 2nGh—4x) = (7 -— 4x)? 4x+y=7 and 3x?4+2. : 2 49 ~56x+16x2 Y Standard form Y Factors Y x values 7 =. =3 x 3 ory Substitute x=2 in y=7-—4x Substitute x=lin y=7-4x 7 y=7-42) y=7-4() 7 vers y= ¥_yvalues (6) 13 For equal roots :13-—2k =0 ¥ 13-2k=0 2k = 13 13 1 k=— or k=6- _B 2” 2 vY k= =) (2) i (x+5)° =1-p? ¥ Squaring both sides x+5=+4y1—p? x=5tji-p> For non —real roots : 1-p’ <0 p -1>0 p<-l0r p>l vx subject of the formula v l-p<0 v Y answer (5)

Testpapers.co.za MEMORANDUM 2025 p<-l0r p>l x? +10x+25 =1- p? x? +10x+24+ p> =0 b’ —4ac =100-4(1)(24 + p =4-4p’ For non-real roots: 4-4p’ <0 p-1>0 (p-I(p+l)>0 p<-lor p>l Y b-4ac=4-4p* ¥ 4-4p?<0 v Factors v Y answer [28]

Testpapers.co.za Daewnlondeck from Stanmorephpsics.com MEMORANDUM 2025 QUESTION 2 2.1.1 322 rr Sa Y Exponential Laws(Numerator) 32042 1330-1) 2933" B22 33-3 “63 ¥ Common Factor _ 32"(3? ay 6.37" 3"(9- Ji Y Simplification _ 27 63” 801 9 6 40 27 vv Answer (5) 212 B- V3) V3.6 _ 9-6V3 +3 V3.6 12-6v3 dhieeiGnivk = Multiplying out the numerator 3.6 6(2-V3)_ V6 ¥ Common Factor = ~<a V3N6 6 _ ¥63-V3) VB =V/2(2-¥3) OR 2V2-V6 vv Answer (4) 22:1 x sa 1 v3 =128 aur tae 32* =128 1 (2°)* =2” 5_ 7 v Equating the exponents x 7 a ¥ Answer (4)

Testpapers.co.za Dawntondecs from Stanmorephpsics.com MEMORANDUM 2025 222 1 = xt —3x*=10 =O Dayan (x4 —5)(x4 +2) =0 1 oot xr=S or x4 =—2 J 1 x=5* or x4 #-2 x= 625 v¥ Factors 1 Y Restriction ( x4 #-2) v Answer (4) Y Standard Form Y Factors 1 Y Restriction (x4 #-2) v Answer (4) [17] QUESTION 3 3.14 veyer Phythagorsus ¥ Substitution inti the Phythagorus (-6)'+ (8) =? r? =100 v Answer (2) r=10 3.1.2 8 4 MAO = =—5 Y Answer (1) 3.1.3 sin 0 + cosO 2 + (- 4) ¥¥ Substitution 10 10 8 6 _1 Y Answer (3) 10 10 5 [6]