Maths-Grade-10-March-2023-QP-and-Memo_hlayiso.com_.pdf

Downloaded from hlayiso.co Downloaded from Stanmorephysics.com WAS KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE | MARKS: 75 TIME: 1% hours Copyright Reserved Please Turn Over

Downloaded from hlayiso.com MathenBiownloaded from Stanmorephysi¢s.com March 2023 Common Test INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This questi 2. Answer A. 3. Number the answers correctly according to the numbering system used in this ont pa per consists of 4 questions. i pealtiay LL ath ie questions. question paper. 4. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. 9. Write neatly and legibly. Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Materstnloaded from Stanmogephysics.com QUESTION 1 Ll Ifxe {-2; 2; 4;5} ,choose the value of x from the given set that will make the expression of as be: 4-x 1.1.1 ration 1.1.2 unde; 1.1.3 irrational 1.1.4 non-real Between which two consecutive natural numbers does 4/40 lie. Show all your working out 1.2 and do so without the use of a calculator. 1.3 Factorise the following expressions fully; 13.1 x4—16 (13.2 62°y—10zy+15z—25 1.4 Simplify the following expressions fully; 1.4.1 (m—4n)(m? +4mn+16n?) 2 1.4.2 [2 - 3) x 2 143 2 a w=] ox-1 x 4+x41 15 . Determine without the use of a calculator: QUESTION 2 2.1 Solve for x: 21.1 3x? =5x+12 1 x-1 2.1.2 (3) = 128 2 Copyright Reserved 2023 2022 -1 March 2023 Common Test () (1) (1) (2) (2) (3) (2) (2) (5) (2) [22] (3) (3) (3) Please Turn Over

Downloaded from hlayiso.com Mathewnloaded from Stanmoreplysicgs.com March 2023 Common Test 2.2 Solve the inequality —3<1-2x<7 Hence, illustrate your answer on a number line if x is a real number. (4) 2.3 Solve for x and y simultaneously if: x+3y+5=0 » (5) 3x-2y=-4 ' 2.4 The product © numbers x and y is 60 and their sum is 15. Show that i + 1 = ; : (5) x y [23] QUESTION 3 3.1 In AABC, €=90°and B=9, AC =7 units, BC = Sunits and AB = /74 units. A 7 c 5 V74 °8 B Use the diagram above to write down the value of : (Leave your answer in surd form) 3.1.1 cos? qd) 3.1.2 cotO (1) 3.1.3 cosec?@ (2) 3.1.4 Hence or otherwise, determine the size of 9 (correct to TWO decimal places). (2) Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Matherp¥ewnloaded from Stanmagephysi¢s-com March 2023 Common Test 3.2 In the diagram below, O(x; y) is a point in the second quadrant. ROQ= @ and 13sin 0 =12. y Q(x) t <—1_0 < Vs o> R x . Make use of the diagram above to: 3.2.1 determine the value of x. (2) 3.2.2 calculate the value of sec 0 . Q) 3.2.3 calculate the value of StanO +1 (2) (11) QUESTION 4 4.1 Solve for x where 0° < x <90’ ,in each of the following equations. Give your answer correct. to TWO decimal places. 4.1.1 tan3x=5,75 (2) 4.1.2 cosec (x-35°)=7,814 (3) cos(2x+10° 4.1.3 o0s(2x +10") 9 150 (3) 4.2 If A=70° and B=40" ,use your calculator to evaluate the following(correct to ONE decimal place). 4.2.1 tan(A+B) (2) 4.2.2 sin?A (2) 3B 4.2.3 — 3/2sec 9 (2) 4.3 Without the use of the calculator, showing all your working, determine the value of: cot? 60’. tan 45°.sin 30° cos 60° \ 6) [19] TOTAL [75] Copyright Reserved

Downloaded from hlayiso.com Downloaded from Stanmorephysics.com } KWAZULU-NATAL PROVINCE EDUCATION RE IC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE This marking guideline consists of 5 pages. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathemaownloaded from Stanmorephysics. com Common Test March 2023 GRADE 10 Marking Guideline QUESTION 1 1.1.1 | x=2 = Y answer (1) 1.1.2 | x=4 = v answer (1) 1.1.3 | x=-2 Ilan v answer (1) 1.1.4] x=5 lon Y answer (1) 1.2 | 3/97 <3faoezea Y radical form =3<340 <4 Y answer (2) 1.3.1 | = (x? -4)(x? +4) Y both factors = (x-2)(x+2)(x? +4) Y both factors (2) 1.3.2 = 2zy(3z—-5)+5(3z-5) ¥ Yeach term =(2zy+5)(3z-5) V answer (3) 1.4.1 | =m +4m’n+16mn? —4m’n-16mn’ —64n* ¥ simplification =m —64n" v answer (2) =m n | Answer only: full marks ] 1.4.2 [2 32 3) ¥ expansion =| 2x-2 |} 2x-2 x x 9 v answer = 4x’ -12+ (2) x 1.4.3 x? —4x 1 2 Y factorisation of difference of © (x=1)(x? +x +1) x-1 xe 4x41 cubes x? —4x—x° —x-1-2(x-1) v v finding the LCD and the = (x-1) ( EX +1) simplification of the numerator — -5x-1-2x+2 ~ (x-1) ( RC EX+ 1) Y simplification _ 1-7x (x=1)(x? +x+1) v answer (5) 1S | 2022+1 Y factorising a denominator (2022-1)(2022 +1) -t1 v answer 2021 OR (2) 1.5 | Let 2022 be: x pg __xtl © (x=1)(x+1) Y factorisation -1 (2) 2021 v answer [23] Copyright Reserved Please turn over

Mathemaownloaded from Stanmorephysics.com Downloaded from hlayiso.com 10 Marking Guideline Common Test March 2023 QUESTION 2 2.1.1 | 3x?—5x-12 ¥ standard form v ae (3x-+4)(x- factorisation x=—“or x v answer @) 2.1.2 (2) -7 ¥ exponential form 21 =27 ¥ simplification x=-6 v answer (3) 2.1.3] yi 239 Y dividing x=(2°) v (2°) x=2* x=16 v answer (3) 2.2 | -4<-2x<6 Y transposingY dividing -3< BSx<2 Y answer e————_© * 3 2 ¥ number line (4) 2.3 | X43V4+5 =O (1 BX = 2Y = —4aecccsseeeee (2) From equation (1) X= BY —Sreccseeeneeee > (3) ¥ making x the subject of the Substitute eq. (3) into eq. (2) oe tion 3(-3y-5)-2y=-4 Y simplification —9y-15-2y=-4 y=-l v y-value x= -3(-1)-5 v x-value x=-2 (5) (-2;-1) OR X+ BV 45 =Oeecsseeecccees (1 3x = 2Y SA (2) ¥ multi by -3 Add eq. (2) and eq. (3) ¥ eliminating x Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathemapownloaded from Stanmorephysics. com Common Test March 2023 GRADE 10 Marking Guideline -lly=11 Y simplification y=-l v y-value x+3(-1)+5 V x-value x=-2 (5) (-2;-1) 2.4 | Let the first number be: x and the second number be: y XV =60 ..eeeeeeeeeee >(1) ¥ equation 1 Xt VHS veces. >(2) equation 2 we wm . hele reciprocals is Y adding reciprocals x yo ox V finding the LCD since x+y=15 and xy=60 -1.1°15 1 oy y 60 4 Y substitution -. the sum of their reciprocals is +. (5) [23] QUESTION 3 3.11] 9-2 cos’= 74 v answer (1) 312] a5 cote= 7 Y answer (1) 3.1.3 2 Y substitution cosec? 6 = () =/4 v answer (2) 7 49 | Answer only: full marks _ | 314) p-d v74 Vv 0=54,46° answer (2) 3.2.1) 2 (73) 2 Y substituti x =(13) —(12 Pythagoras (3) (2) (tage) v substi a (2) a re 3.2.2 | SCOT Vans (1) 3.2.3 12 ¥ substitution Stan +1=5| -— |+1=—11 Vanswer (2) [11] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathemapownloaded from Stanmoreph ysics. com Common Test March 2023 GRADE 10 Marking Guideline QUESTION 4 4.1.1 | 3x=80,13" ¥ 80,13" x=26,71 v answer nl | Answer only: full marks | (2) 4.1.2 1 14 y—i sin(x—35° sin(x-35") Y¥ cross multiplication sin(x—35°) =—+— , 7,814 v answer x= 42,35" (3) 4.13 | cos(2x+10°)=0,477 ¥ cos(2x+10°)=0,477 2x+10=61,51 ¥Y 2x+10=61,51° x=25,76 Y answer (3) 4.2.1 | — tan (70° + 40") Y substitution v answer (2) =-2,7 | Answer only: full marks | 4.2.2} (2. apo? ¥ substitution 7 (sin 70 ) Y answer (2) 4.2.3 ¥ substitution v answer (2) 4.4 2 v(%) v(1) “(2) “(3) ¥ answer (5) [19] TOTAL: 75 Copyright Reserved