Mathematics Grade 10 KZN March Test 2025 Paper & Memo

Testpapers.co.za KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE a a “ " uo " “u u “ a uo « | 5 MARKS: 75 TIME: 12 hours This question paper consists of 5 pages. Copyright Reserved Please Turn Over | pyng L

Math =~ - March 2025 Common Test Testpapers.co.za INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 3 questions. yl Answer ALL the questions. 3. Number the answers numbering system used in this question paper. 4. Clearly show ALL cale answers. raphs, etc. which you have used in determining your Ss Answers only will NOT} ded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. if necessary, round oif answers correci io TWO decimai piaces, uniess siated oitierwise. & Wiiie nicaiiy aiid iegidiy, Copyright Reserved Please Turn Over

a , March 2025 Common Test Testpapers.co.za QUESTION 1 fala) Ll arzefo 7 59} , choose the value of x from the given set that will make the () qd) (a) 1.2 Between which twd eonsed joes V170 lie? Show all working details without the use of a 1 ; (2) 1.3 Simplify the followi ies (2) 13.2 (5-4x)’ (2) 3 2 1 a ar ape ar & 10773 - 4 Se a « 1.4 Factorise the following expressions fully: 1.4.1 2x7-18 (2) 1.4.2 §+125a° @) GB) Q) (2) G) [31] Copyright Reserved Please Turn Over

Math« Testpapers.co.za 2.2 the value of b. 23 Given: -9<-2x+3<5 2.3.1 Solve for x . 232. Represent the solution of 2.3.1 on a number line. 2.4 Solve for x and y simultaneously: 2x-y=17 4y+3x=9 Copyright Reserved March 2025 Common Test (2) (3) (3) (4) (5) (4) (2) (2) (4) 229] Please Turn Ove.

Mathematics rf Teilpapers.caze March 2025 Common Test QUESTION 3 Su - Ren, “ ri In the diagram below, APQR is a right-angled triangle, Q=90°, P=0, PQ=5 units and-PR=13 units. ut 3.1.1 Determine the numerical value of: (a) QR (2) (b) cosé () (c) cotd (1) (d) secQRP (1) 3.1.2 Write down the trigonometric ratio that is equal to ee ¢ (1) 3.2 If A=34° and B=53°, use your calculator to evaluate the following (correct to TWO decimal places). 3.2.1 cos(B-A) (2) 3.2.2. sin?B Q) 3.3 Without using a calculator, determine the value of: cosec45° . sin60° sin 45° . cos30° (5) TOTAL: ey Copyright Reserved

Testpapers.co.za KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE 75 This marking guideline consists of 9 pages. Copyright Reserved Please turn over

Testpapers.co.za Mathematics ij March 2025 Common Test NSC Marking Guideline QUESTION 1 1.1.1) 9 vA 5 Q) 1.1.2. | ¢ A f a) 1.1.3 [0 vA (a) 12 | S769 < V170 < Vi96 YA_ square root of perfect sq. vA answers 13.1 | (x-2y)(x? +244 Hx +2? y+4ay? —2x° ys VA removing brackets =x-8 ye ULL MARKS | Y CA answer (2) 1.3.2 (5—4x)" =(5-4x)(5-4x) =25~20x—20x+16x? vn — ts =25-40x+16x° ma ANSWER ONLY: FULL MARKS (2) 13.8 3 2 1 YA (x+3)(x-3) YA numerator ¥YCA_ simplification YCA answer (4) Copyright Reserved Please turn over

Testpapers.co.za Mathematics NSC Marking Guideline March 2025 Common Test Same genta ge gate _ Seats geen at vA __ prime bases ¥YCA_ removing brackets YCA simplification =57'25 i = ¥CA answer (4) 1.4.1 | 2.7 -18 = 2(x? -9) YA common factor = 2(x-3)(x+3) ¥CA answer (2) VA (2+5a) YA -10a VA (Avon 25a") (3) YA grouping vA (x? +5) YCA (x2) G3) TS.1 | 9~ 1 > al 3 vA answer Q) 135.2. | g* =9°* =(2') vA (2') =(3)' =27 VA answer (2) Copyright Reserved Please turn over

Testpapers.co.za Mathematics NSC Marking Guideline March 2025 Common Test 15.3] (4y (is) rest =i i YA 24 =(2")" =(3)" =3" ¥CA _ simplification 1 = 31 YCA answer (3) Amorephysies.com [31] QUESTION 2 2.1.1 | 3x(x-8)=0 vA x=0 or x=8 VA 2) 2.1.2 | 7x? -5x-2=0 (7x+2)(x-1)=0 YA factors 2 xe or x=1 YCAVCA G3) 2.1.3. | 3*-729=0 34 =729 35-4 _ 36 vA __ prime base 5x-4=6 5x=10 YCA simplification y=2 YCA answer GB) Copyright Reserved Please turn over

Testpapers.co.za Mathematics March 2025 Common Test NSC Marking Guideline 2.1.4 BE | 2x?-=128 a x7 =64 YA __ division by 2 ieee} 6x (2 xs GI_ 6) YA x reciprocal of exp. x=Q" 4 L YCA 2 16 ¥CA answer OR 3 2x? =128 a am YA division by 2 28) gl) i YA x reciprocal of exp. “6 ¥CAYCA answer (4) YA common factor ¥CA simplification YCA division by Fy YCA prime bases ¥CA answer (5) i Na fesart (¢ —2a -a°V fa +2a*)—(a’ -2a% )] =b el +a ol el -a°+2a™ ‘)= b vA factorising YCA _ simplification YCA _ simplification YCA answer Copyright Reserved Please turn over

Mathematics Testpapers.co.za NSC Marking Guideline March 2025 Common Test OR (a'+2a*) -(a'-2a°) =6 a°+4+4a° -(a°-4+4a° =6 vA a°+4+4a° $ 6.6 <6 YA a°-4+44a° BNE See a al ¥CA _ simplification 8=b YCA answer (4) 2.3.1 | -9s5=2x+3<5 -9-35-2x<5-3 SIRS eae YA simplification wol<x $6 ¥CA answer (2) 2.3.2, YCA critical values i— at =e vCA O@ (2) 2.4 2X YAH DTarcrecsereeed equation | 4y+3x=9... equation 2 vA ti y=2x-17.. i a 6 substitute equation 3 into equation 2 4(2x-17)+3x=9 ¥CA substitution 8x-68+3x=9 11x=77 sgpieel YCA value of x substitute x — value into equation 3 y=2(7)-17 y=3 YCA value of y OR Copyright Reserved Please turn over

Testpapers.co.za Mathematics March 2025 Common Test NSC Marking Guideline DRE YSN oecreecsseeed equation 1 AY PBK EO... ccsssee equation 2 beg 2) equation 3 2 substitute equation 3 into equation 2 4y+3(2417)-9 8y+3y451=18 lly =-33 y= substitute y—value into equation 4y+3x=9.. substitute x— value into equation 1 2(7)-y=17 y=3 YA equation 3 ¥CA_ substitution YCA value of YCA value of x YA 4y=8x-68 YCA equating YCA value of x YCA value of y (4) [29] Copyright Reserved Please turn over

Mathematics Testpapers.co.za NSC Marking Guideline March 2025 Common Test QUESTION 3 3.1.1a | PR?=QR?+QP’ — Pythag 2 if 2 ied 13°= QR’ +5 vA correct substitution (QR? = Vi3? 3? y QR=12 CA answer ANSWER ONLY:FULL MARKS ude : (2) 3.1.1b 5 vA cos 0 = — 13 - dd) ade enlllne St es 12 > da) 311d secre = 13 CA 12 z ad) 212 sing = QR OR cosQrp = 2k # PR PR da) al cos(53°-34°) YA _ correct substitution YCA = 0,95 PENALISE HERE FOR ROUNDING (2) 3.2.2 | sin? B =(sin 53°) YA correct substitution =0,64 YCA (2) 3.3 2 3 v Z aN A cosec45° =—— 2B vA sin ase wz 2 2 YA cos30°= RE 2 2 2 3 i ing per YCA . simplification nD ° 22 ¥CA answer Copyright Reserved Please turn over

Mathematics Testpapers.co.za NSC Marking Guideline March 2025 Common Test elo v2 YCA simplification Pp. 1 =2 ¥CA answer - - (5) Biafmorephysies.com [15] TOTAL: | 75 Copyright Reserved Please turn over