Mathematics Grade 10 April Test 2021 Paper & Memo

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Downloaded from hlayiso.com NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. il This question paper consists of 6 questions. 2. Answer ALL the questions. ch Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. 4 Answers only will NOT necessarily be awarded full marks. 5 You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. c Diagrams are NOT necessarily drawn to scale. 8. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 3 KZN/March 2021 : NSC “QUESTION 1 Ll Determine the product of the following and simplify fully: 11 ab? (20 +40) (2) 1.1.2 (x-2)(x? +2x+8) (3) 1.2 Factorise the following expressions fully: 1210 2x? +7x-4 (2) 122 ax-ay-b’x+by (3) 1.2.3. 125-27m5 (2) ile} Simplify the following expressions fully: 13.1 25xty*x (5x*y°) G) fs 132 +7xt+10 x+2 (4) x+5 5 9.3"? 45,3" 1330 4 a @) [23] QUESTION 2 2.1 Solve for x in each of the following equations: 2.1.1 1-Sx=6 (2) 212 (x+2)(x-4)=0 (2) 14+2 213 g=—— @) x 214 3.7°'4+7=154 (3) 2.2 Solve for x : 3(2x+4)-3(x-3)<0. Represent your answer in interval notation. (3) oe Solve for x and y simultaneously: 4x-2y=6 2y+3x=8 (5) [18] Copyright Reserved Please turn over

Downloaded from hlayiso.com NSC QUESTION 3 3 1 Simplify the following expression: x-2 x+4 ti | 3 6 -2 3.1.2 | Hence, determine the value of x if: ae = =. 32 Without using a calculator, simplify the following expression fully: 2021 1-2020° Give reasons for your statements in the answers to QUESTIONS 4, 5 and 6. QUESTION 4 4.1 In the diagram below, F = 2x, €,= 75°, €,=2x—15° and B, =135°. A E af, F iz 2x 135° Tee f 2x - 15° Cc 3 4.1.1 Determine the value of x. 4.1.2 Determine if EF //GH. Motivate your answer. (3) (2) QB) [8] (3) (3) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 KZN/March 2021 NSC 42 In the diagram below, square ACDE has an area of 256 cm? and AB = BC. B A * C 4 ; E , D 4.2.1 Determine the length of AC. (Let AC =x) 4.2.2 Hence, determine the length of AB. (Correct to TWO decimal places). QUESTION 5 5.1 The angles of a certain quadrilateral are in the ratio 2:3:4: 6. Calculate the size of the largest angle. 5.2 Complete the statements below for the properties of a rhombus: (write the question number and missing word / term only) \21 Opposite anglesare. 5.2.2 Allsidesare........ and, opposite sides are parallel to each other. 5.2.3. Diagonals bisect each other at ........ degrees. (3) (3) [12] (2) qd) qd) dd) | Copyright Reserved. Please turn over

Downloaded from hlayiso.com NSC By) The diagonals of rhombus PQRS intersect at T. | $, = 2x and BP, = 3x +20° Pd S ‘ R 5.3.1 State the value of Q, , in terms of x. qd) 5.3.2 Hence, calculate the value of x. (3) 19] QUESTION 6 In the diagram below, ABCD and EFCD are parallelograms. A B D Cc Prove that AFDE isa parallelogram. [5] TOTAL: 75 Copyright Reserved

Education REPUBLIC OF SOUTH AFRICA SENIOR CERTIFICATE GRADE 10 SRR See ceescoEaas ¢ fepeseseuee See eeeeeseeeeseesesss MARKS: = 75 TIME: 1% hours This memorandum consists of 7 pages. Copyright Reserved KwaZulu-Natal Department of Education RESESESR ESSE. : MATHEMATICS . : COMMON TEST : : MARCH 2021 i : MARKING GUIDELINE : cf : Please tum over Downloaded from hlayiso.com 2 KZN/March 2021 Mathematics NSC - Markimg Guidelines QUESTION ! eet at? (-2a2 + 4b) yee =—2a0°b? + 4ab* vo 4ab* Q) V2 (x-2)(x? +2x+8) Dy? + 8x 237 4-16 ¥ = . =x +4y—16 oe B) ee ee ae yarn =(2x-1Nx+4) ae )) (2) 122 | @x-ay—b'x+by ae Y common factors ¥(a-8) V =x(a~bYa+b)-y\a-b) (a~ a+b) =(a-b)[x(a+b)-y] =(a-bYax+bx-y) ce G) 123) Fi 125-27 oe =(5~3m\25+15m+ 9m") Yo (25415m49m2) Q) [ee eta vo sty ¥ simplification of indices 1 ee xy 3) Es2eee SET tlO x42 xts OS ¥¥% both factors _ (+5) 042) 9 a x45 x+2 x+2 7 4 = 7 (4) 133 | 9.37453" each IS H5.3" as 3-33 oa 3 (8145) 31-3) ¥ _ factorisation of 3° 28 2 v 4) =-43 Ge (4) te {23} Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 4 KZN/March 2021 NSC — Marking Guidelines dx—-2y=6 Eql 2y+3x=8 Eq2 Flea a ‘ te stitution of (ig ae 2 into (/:q 2) ys2x-3 Sub Eq3 into Eq2: | 2(2x~-3)+3x=8 x=2 4x—643x=8 Tx=l4 x=2 substitution of x =2 x=2: 4(2)-2y=6 Subx=2 (2)-2y (5) i) | = vel i [18] QUESTION 3 F aE = BT [Sal | xn2_ x44 a a 6 Ux-2)_ (x44) ico -x-4 answer @) 312 substitution of answer from 3.1.1 ca (2) 32 2021 1-2020° = 2021 (1=2020)(1+ 2020) factorisation ____2021 *2019)(2021) simplification --—_L 2019 answer (3) [8] Mathematics 3 KZN/March 2021 NSC - Marking Guidelines QUESTION 2 ae Pan Y simplification Answer only: 2/2 Q xe-l ¥__answer 21.2 | (x4.2)(x-4)=0 w=72 or x=4 vv _answers (2) 2.13 1+2x g= x gralt2x Vv gronLHs gx-2y=1 xg-2)=1 ve factorisation 1 ) Me answer Q) 214 13.7475 154 3.77 =147 a ell malt 3 3 T1349 ei Y prime base x-1=2 = ¥ answer : G) 22 [ Hax+4)-3x-30<0 6x+12—3x+9<0 - fo simplification 3r421<0 : 3x<-21 eT Yo x<-7 s.xe(—01-7) Y__answer (3) 23 | 4x-2y=6 Egil 2y+3x=8 Eq2 Egl+£q2: 7x=14 v Egl+ Eq2 (elimination) x=2 Yo Ix=l4 Subx=2: 4(2)-2y=6 Vx? -2y=-2 y substitution of x=2 ye v (5) OR Copyright Reserved Please turn over Copyright Reserved Please tun over

Mathematics: = KZN/March 2021 NSC ~ Marking Guidelines QUESTION 4 at eee (ext Zof : 135° = 2x-+75° 2x =135°-75° 2x = 60° = 30° answer (3) 44.2 | G =2(30°)-15° ‘ C, =45 By + C, = 135° + 45° = 180° statement 2 EFO (co-int Zs supplementary) reason OR 2(30°)- 15° 45° é, 45° EBC = 45° (Zsonstraight line) oC, = EBC statement 2 &FO (alternate Zs equal) Teason 6) ae < YY trea of 2 ACKAE : B : x7 =256cm" A Cc answer E D (3) Copyright Reserved Piease tun over Mathematics Downloaded from hlayiso.com 6 NSC - Marking Guidelines KZN/March 2021 4.2.2 | Inf AB= BC (given) and AB +BCh= AC? (pythag) |) gp 2AB =16° v AB =128 AB=8 Yom AB=11,3lom 4 ca (3) L— (12) QUESTION 5 5.1 2x + 3x+4x+ 6x = 360° (sum of Zs in quad) 15x = 360° — v — xvalue «. largest angle =6x24° = 144° v_ca Q) 5.2_[ 5.2.1 |equal v answer (| 322 [equal 7 answer @ v answer, aw) (523 [90 Copyright Reserved Please turn over

- Downloaded from hlayiso.com Mathematics 7 KZN/March 2021 NSC ~ Marking Guidelines 53 Pp Q s LO R 33.1 |G =2x (angles opp=sides) “4 y «ty 532 7 SIR F=90° ) (diags of rhombus) a sir ind : Q 3x+20° +90°42x= 180° : me ¥ answer | 3) OR \ B= 3x 20° (diags of rhombus) ¥ SR Ind oS Oo [ 65-4404 2420 = 180° lox = 140° i: ¥__answer (3) [9 QUESTION 6 A B E. D fe ED= FC (opp sides of parm EFCD =) vs AF = FC (diags of parm ABCD) vy SIR ED= AF ada but EDD vy oSR AFDEis a parallelogram i _ Rk 15] (2 opposite sides equal and parallel) TOTAL: 75 Copyright Reserved Please tum over