MATH-March-QP & Memo-2019-Gr10_hlayiso.com_.pdf

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Mathematics Downloaded from hlayiso.com Common Test March 2019 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. i. oe This question paper consists of & questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, ete. 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 education Department: Education PROVINCE OF KWAZULU-NATAL NATIONAL SENIOR CERTIFICATE: COMMON TEST: MARCH 2019 TO: THE CHIEF INVIGILATOR OF ALL SCHOOLS OFFERING MATHEMATICS: GRADE 10 ERRATA Please take note of the following change: Page ERROR CORRECTION Page 6 | In the diagram below PO =Q = MN, In the diagram below PQ =QM = MN, (Q 8.2) | QMP PNand... | OM // PN and ... Kindly ensure that candidates are informed of the Errata. Qnchece 4 la hag Ms E. COEJZEE DATE ASSISTANT DIRECTOR PROVINCIAL EXAMINATION ...Championing Quality Education-Creating and Securing a Brighter Future

Downloaded from hlayiso.com Mathematics Common Test March 2019 NSC QUESTION 1 Ll Factorise the following expressions fully: ML 62 +7x~=20 @) 1.12 eae aed &) 1.2 Simplify the following expressions fully: 121 (2x43)(5-x) (3) 12.2 (xv ~3)(x7 8 +3" +9) Q) 1.2.3 Zeet gx-3 aa 4) 4s*-° ( {14] QUESTION 2 Determine, without the use of a calculator, the value of x in each of the following: 2.1 (x=3)(x +2) =0 (2) 2.2 11x3°**! = 297 G) 23 4x? ~3%~1 x41 aaa S94 nn ee (5) 4x41 x =x+1 24 ah =V (2) [12] QUESTION 3 3.1 Rewrite 0.45 as a common fraction, in simplest form. qd) Ee) Given : where vER cm | For which value(s) of x is P undefined? (2) 3.2.2 If x = 7, determine between which two integers P lies. (2) 3.3 The larger of two consecutive integers is represented by x +3. Determine an expression which represents the smaller integer. (1) (6] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test March 2019 NSC QUESTION 4 4.1 Solve for y and y simultaneously: 4x = 10-31 (5) ¥t2xr=6 4.2 The following inequality is given: -9 s 2x +3<5: where +ER 4.2.1] Solve for x in the inequality. (3) 4.2.2 Represent your answer to QUESTION 4.2.) on a number line. (1) 4.2.3 Write your answer to QUESTION 4.2.1 in interval notation. (1) 4.3 The mean of three numbers is 25. The second number is four less than twice the first. The third number is two more than four times the first. (Hint: Let the smallest number be x) Calculate the numerical value of the smallest number. (4) {14} QUESTION 5 Study the diagram below and calculate the unknown angles w. x. y and 2. Give reasons for your statements. [4] B QUESTION 6 6.1 Complete the following statements: 6.1.1 A quadrilateral with two pairs of adjacent sides equal isa .... (1) 6.1.2 A quadrilateral with both pairs of opposite sides parallel is a .... (1) 6.2 Which quadrilateral has diagonals that always bisect its angles and also bisect each other? (1) 6.3 Given the following three quadrilaterals: a rectangle, a rhombus and a kite. Which of these quadrilaterals do not have perpendicular diagonals? (1) [4] Copyright Reserved Please turn over

Downloaded from hlayiso.com Common Test Ma Mathematics NSC Give reasons for your statements in QUESTIONS 7 and 8. QUESTION 7 tal In the sketch below, EFGH is a parallelogram. FRE =75° : EFK =4x : FGK =2x and KGH =3x. F G = H TAA Calculate the value of x. (3) 712 Calculate the size of GHE. @) F2 In the diagram ABCD is a parallelogram with diagonals intersecting at P. AY and CX are drawn such that BY = DX. A B D Cc Prove that AYCX is a parallelogram. (3) 8] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test March 2019 NSC QUESTION 8 8.1 The sketch below shows rectangle ABCD with points F and £ drawn such that AFCE is a rhombus. A F B al D E Cc If it is further given that AB =|6cm and BC =12cm, calculate the length of CF . (7) 8.2 In the diagram below PQ =QM = MN, OM PPN and LPN = LNP. L 8.2.1 Show that MP bisects P . (Hint: let P =x) (3) 8.2.2 Prove that APRN ||| AORM. G) [13] TOTAL: 1 Copyright Reserved

Downloaded G1t 10 from hlayiso.com ·rv11t-TH 1 ML-1T Mathematics Common Test March 2019 • GRADE 10 MEMORANDUM education QUESTION 1 Department Education I .I.I 6x' +7x-20 PROVINCE OF KWAZULU-NATAL =(3x-4 X 2x+5) ✓(2x+5) ✓(3x-4) (2) l.1.2 xJ +x1-x-l ♦•••••••••••••••••••••••••••••••aaaaaaaaaaaaas• ♦ = x2 (x+1)-l(x+ I) ✓ common hracket ,: • ✓ factors MATHEMATICS =(x2 -l)(x+l) ✓ diff. of two squares = (x-l)(x+l)(x+l) COMMON TEST 1.2.1 (3) (2x+3X5-x) = )0x-2x2 +l5-3x MARCH 2019 ✓ -2x2 =-2x2 +7x+l5 ✓ +7x MARKING GUIDELINE ✓ +15 �������-�·-···········�--�······�-······�---··�· � � l.2.2 (xy3 -3)(x2 y6 +3xy3 +9) =(:X:/-27) ✓ xl y' (3) ✓ -27 (2)' NATIONAL 1.2.3 32>-1 .s•-l SENIOR CERTIFICATE 45•-2 )2•-1 ,5•-l = 2 -2 ✓ base as prime factors ( ) (3 _5y (32 .5) GRADE10 32,-1 _5•-l 32,-•.5•-l ✓ simplification MARKS: 75 = )2;t-l-2x+4_5x-J-x+2 ✓ adding and suhtracting =J3 .S-l indices 27 =- 2 ✓ 3·'•.5-I or 5- 5 (4) 1141 These marking guideline consists of 10 pages. Copyright Reserved Please turn over

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