Maths-Gr10-March-2022-QP-and-Memo_hlayiso.com_.pdf

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Downloaded from hlayiso.com NSC- Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. - This question paper consists of 5 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test March 2022 NSC- Grade 10 QUESTION 1 rovided as possible answers to the following questions. n and write only the letter (A - D) next to the question number, for ative single digit integer, which of the following is NOT a possible value of C. 10 D. 12 (2) 1.2 An irrational number that lies between 5 and 6 is: A. B. ✓20+8 C. ✓20x8 D. 2,r (2) 1.3 Simplify the following: ( -3x 2y 5.:�y 2 + xy) = A. -15x2 /-3x2 y B. -15x3y3 -3x3y C. 3 3 - 15xy-xy 3 3 2 D. -15x3 y3 +xy (2) 1.4 1 2 The formula for the volume of a cone is V = - 1rr h. The radius, r , of the cone may be 3 expressed as: A. Jgh B. *' ✓3:h C. h D. 1� (2) 3 1rh Copyright Reserved Please turn over

Downloaded from hlayiso.com NSC- Grade 10 a - Ls If (a +27)=(at+3\(a’ +ma+9) , then m equals: A. -9 B. -3 c. 9 D 3 Q) 1.6 Factorise the following: 4x° —3x-27= A. (2x+9)(2x —3) B (2x -9)(2x +3) c. (4x +9)(x—3) D (4x —9)(x+3) (2) 2 a 17 Simplify the following. ————— = a & 95x 125 A x i) B x+5 25, Cc x-5 25 x D. aa 2 2 : @) 18 If it is given that y’ =50 and x* =10 , determine the value of Nera A. 5 B. 25 (e 50 Dz 250 (2) 1.9 Which quadrilateral is equiangular but not always equilateral? A. rectangle B. parallelogram Cc. rhombus Dz. square (2) el) Which of the statements below is false? A. All parallelograms are quadrilaterals. B. All rectangles are parallelograms. Cc. All squares are rhombuses. Dz. All rectangles are squares. (2) [20] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 Common Test March 2022 NSC- Grade 10 QUESTION 2 21 Determine the product of the following and simplify fully: (a+2)(a@’ —2a+8) (2) 2.2 Factorise the following expressions fully: 2210 yy (2) 222 ft e.| e), (3) 23 Simplify the following expressions fully: 1g” x 6” x 36"? 2.3.1 poy (4) Oe) 232 Yor? vty y-4 yty (4) 2.4 A picture is framed using four rectangular pieces of wood, as shown in the diagram below. Find the area of the picture, in terms of x. Give your answer in simplified form. Bay eee 5x +2 a (3) [18] Copyright Reserved Please turn over

Downloaded from hlayiso.com NSC- Grade 10 QUESTION 3 3.1 Solve for x in each of the following equations: eile = + = 2 (4) x+2 x-4 3.1.2 5°445* =626 (3) 3.2 Solve for x : -6<$2x-2<10. Illustrate your answer on a number line if x is a real number. (3) 3.3 Solve simultaneously for a and b: 4a-—b=5 -3a+4b=19 (6) [15] Give reasons for your statements in the answers to QUESTIONS 4 and 5. QUESTION 4 4.1 In the diagram below, AABC is drawn with ABO C,=10x , C,=y , § =78°, F=4x and d=z Calculate, with reasons, x, y and z. (4) 4.2 A parallelogram has two pairs of opposite sides parallel and equal. Name 3 other quadrilaterals that have these same properties. (3) (7] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 7 Common Test March 2022 NSC- Grade 10 QUESTION 5 In the diagram below, KL=LN=NM=EN and KNO K f L E Use the diagram above to prove the following: 5.1 M,=R GB) 52 AKLN = AMNL (4) 53 KLMN isa parallelogram. (3) 54 LME=90° (5) [15] TOTAL: 75 Copyright Reserved

Downloaded from hlayiso.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA DIRECTORATE: . EXAMINATION & ASSESSMENT Private Bag X01, EAST. END, 4018 Provincial Examination Administrati Malgate Building, 72 Stalwart Simelane Street. Durban, 4000 16/03/2022 TO: THE CHIEF INVIGILATOR OF ALL SCHOOLS OFFERING: MATHEMATICS NATIONAL SENIOR CERTIFICATE: COMMON TEST MARCH 2022: GRADE 10 ERRATA Please take note of the following change: PAGE | NUMBER ERROR CORRECTION 6 4l AABC is drawn with ABU AB // ST. 7 Question 5 | In the diagram below, In the diagram below, Instruction | KL=LN=NM=EN and KL=ILN=NM=EN and KNo KN / LM Kindly ensure that candidates are informed of the Errata. Ge tl fs — DATE “MR C. KHUMALO PROVINCIAL EXAMINATIONS AND ASSESSMENT SERVICES GROWING KWAZULU-NATAL TOGETHER

Downloaded from hlayiso.com o NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS COMMON TEST MARCH 2022 MARKING GUIDELINE MARKS: 75 TIME: 1½ hours This memorandum consists of 6 pages.

Downloaded from hlayiso.com Mathematics o March 2022 Common Test NSC – Marking Guideline QUESTION 1 1.1 D  answer (2) 1.2 B  answer (2) 1.3 C  answer (2) 1.4 A  answer (2) 1.5 B  answer (2) 1.6 C  answer (2) 1.7 B  answer (2) 1.8 D  answer (2) 1.9 A  answer (2) 1.10 D  answer (2) [20] QUESTION 2 2.1 (a  2)(a 2  2a  8)  a3  2a 2  8a  2a 2  4a  16  expand  a  4a  16 3  simplification (2) 2.2.1 x3  y 9   x3   y 3    3   x  2y 3   x  y  x  xy  y  3 2 3 6   x  xy  4 y  2 3 6 (2) 2.2.2 f  e 1 e f  f  1  e  ef  common factors  1( f  1)  e(1  f )  1( f  1)  e( f  1)  common bracket (3)  ( f  1)(1  e)  answer OR f  e 1 e f  f  ef  e  1  f (1  e)  (e  1)  common factors  f (1  e)  1(1  e)  common bracket  (1  e)( f  1)  answer (3) OR Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics o March 2022 Common Test NSC – Marking Guideline f  e 1 e f  common factors  f  ef  e  1  common bracket  f (1  e)  (e  1)  answer (3)  f (1  e)  1(1  e)  (1  e)( f  1) 2.3.1 18m2  6 m  36m 2 22 m  2.33m (2.32 ) m2  (2.3)  m  (22.32 ) m 2   prime bases 22 m  2.33m 2m  2.32 m  4.2 m.3 m.22 m  4.32 m  4  raising powers  22 m  2.33m 2m  2 m  2 m  4 .32 m  4 m  2 m  4   simplification 22 m  2.33m  22 m  2 2 m.33m3m  answer  22 (4) 2.3.2 y2  y  2 y2  2 y  2  factors of y2  4 y y trinomial ( y  2)( y  1) y ( y  2)  difference of 2   squares ( y  2)( y  2) y ( y  1)  common factor 1  answer (4) 2.4 Students do not need to expand binomial x binomial Area  (6 x  3)(4 x  2)  (6 x  3) Area  (24 x 2  12 x  12 x  6) units 2  (4 x  2) Area  (24 x 2  24 x  6) units 2  A  lw (3) [18] QUESTION 3 Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics o March 2022 Common Test NSC – Marking Guideline 3.1.1 3 5  2 x2 x4  LCD LCD : ( x  2)( x  4) RESTR : x  2 or x  4  numerator 3( x  4)  5( x  2)  2( x  2)( x  4) 3x  12  5 x  10  2( x 2  2 x  8) 8 x  2  2 x 2  4 x  16 2 x 2  12 x  14  0 2( x  7)( x  1)  0  CA factors  x  7 or x  1  CA (4) x4 3.1.2 5  5  626x 5 x.54  5 x  626 5 x (54  1)  626  common factor 4 5 (5  1)  626 x 5 x  625  625 5 5x 4  answer x  4 (3) 3.2 6  2 x  2  10 4  2 x  12  4  2 x  12 2  x  6  2  x  6  number line / notation (3) 3.3 4a  b  5 ( Eq 1) 3a  4b  19 ( Eq 2)  Eq1  4 Eq 1  4  16a  4b  20  Adding eqs Eq 1  Eq 2 3a  4b  19 13a  39  a =3 a 3  substitution Sub a  3 in Eq 1 4(3)  b  5 b  7  b=7 (5) OR  b  4a  5  Sub Eq 3  Eq 2 Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics o March 2022 Common Test NSC – Marking Guideline 4a  b  5 ( Eq 1) 3a  4b  19 ( Eq 2) Eq 1 Eq 3 b  4a  5 Sub Eq 3 in Eq 2: 3a  4(4a  5)  19  a =3 3a  16a  20  19  substitution 13a  39  b=7 a 3 (5) Sub a  3 in Eq 1 4(3)  b  5 b  7 [15] Give reasons for your statements in the answers to QUESTIONS 4 and 5. QUESTION 4 4.1 10 x  78  4 x (ext  of ΔSTC) 6x = 78o x = 13o  S  R y = 180o – [78o + 4(13o)] (sum of  s ΔSTC) y = 50o  S/R OR y = 180o – (10  13o) ( sum of  s st . line) y = 50o  S/R z = 78o corresp  s; ST //AB   S/R (4) 4.2 Rhombus  answer Square  answer Rectangle  answer (3) [7] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics o March 2022 Common Test NSC – Marking Guideline QUESTION 5 5.1 Mˆ 1  Lˆ 2  s opp  sides   S/R but Nˆ  Lˆ 1 2 alt  s ; KN // LM   S/R Nˆ 1  Kˆ  s opp  sides   S/R  Mˆ  Kˆ 1 (3) 5.2 In ∆KLN and ∆MNL: 1. LN is common  S/R 2. Kˆ  Mˆ 1 (proved above)  S/R 3. Nˆ  Lˆ 1 2 alt s ; KN // LM  S/R  ∆KLN and ∆MNL (A; A; S)  S/R (4) 5.3 KL  NM ( given) KN  ML (congruent s proved above)  S  R  KLMN is a parallelogram. Reason: 2 Pairs of opp sides equal and parallel  S/R (3) 5.4 Mˆ 1  Mˆ 2  Lˆ2  Eˆ  180 ( sum s of NME )  S/R but Lˆ  Mˆ 2 1 (s opp  sides )  S/R and Eˆ  Mˆ 2 (s opp  sides )  S/R  Mˆ 1  Mˆ 2  Mˆ 1  Mˆ 2  180  substitution 2Mˆ  2Mˆ  180 1 2 2( Mˆ 1  Mˆ 2 )  180  Mˆ  Mˆ  90 simplification 1 2 ˆ  90  LME (5) [15] TOTAL: 75 Copyright Reserved Please turn over