Mathematics Grade 10 Free State March Test 2022 Paper & Memo

Downloaded from hlayiso.com education Department of Education FREE STATE PROVINCE Downloaded at testpapers.co.za [ GRADE 10 ] II II II II This question paper consists of 4 pages Copyright reserved Please turn over

Downloaded from hlayiso.com INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 4 questions. 2. Clearly show ALL calculations, diagrams, graphs, etc. that you have used to determine your answers. 3. Answers only will NOT necessarily be awarded full marks. � If necessary, round off answers to TWO decimal places, unless stated�rwise. v�· 4. 5. Diagrams are NOT necessarily drawn to scale. ♦ �� 6. You may use an approved scientific calculat�,on-programmable and non-graphical), unless stated otherwise. �'\ � 7. An information sheet with formulae is included �'fend of the question paper. 8. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com QUESTION 1 1.1 Show that 0,75 is rational number. (1) 1.2 Round 34,4678 off to two decimals (1) 1.3 Consider the following numbers: .fi5; ✓ -7; 1r Which one of the following numbers is: 1.3.1 Irrational (1) 1.3.2 Rational (1) 1.3.3 Non-real (1) 1.4 Determine two positive integers between which 53 lies. (2) 0� 1.5 Simplify completely ♦ 1.5.1 3x{2x-4xy) (2) 1.5.2 (x-3) 2 (2) 1.5.3 (2r - p)(3r 2 -4rp + p 2 ) (3) [14] QUESTION 2 2.1 Factorize completely 0 2.1.1 2x -82 �, (2) 2.1.2 °' \"c�oe- 3qy x' -4x+3 (2) 2.1.3 *� 2 px+ (3) 2.2 Simplify 270-9 27x 2 +18x +12 (4) [12] Copyright reserved Please turn over

Downloaded from hlayiso.com QUESTION 3 3.1 Solve for x 3.1.1 (2x+1)(x- 3)=0 (2) 3.1.2 3 x =1 (2) 3.1.3 - 4 � 3x-1� 5 (represent your answer graphically) (4) 3.1.4 g2 x+3 = 27x+5 (4) 3.2 Solve for x and y simultaneously 2x- y = -1 and x + 2y = 12 (4) [16] QUESTION4 4.1 Find the values of x, y and z in the diagram below. Give a reason for each statement. y X z (5) 4.2 EFGH is a rhombus in which the diagonals EG and FH intersect at M. FEH = 100 ° E .---..------------. H 100 ° M F G Find the value of: 4.2.1 FEM (2) 4.2.2 EFM (2) [9] TOTAL: 50 Copyright reserved Please turn over

Downloaded from hlayiso.com MARCH TEST 22 education Department of Education FREE STATE PROVINCE ( GRADE 10 ] � �------�-------- -------------------------�� � � II II 11 .: II RANDUM II II II MARCH TEST II II II ,�� II " �------------------- ------------------------�� #/ MARKS: 50 TIME: 1 HOUR

Downloaded from hlayiso.com MARCH TEST 22 QUESTION 1 1.1 0 ,75 75 ✓ i.=-' - =- . 75 ' 100 ✓ ',J 100 OR �� �.� r�J I\�r4 �✓ 4 (1) \ 1.2 ✓ answer 34,46w= 34,47 (1) ,� •.. 1.3- - 1.3.1 tr ✓ answer (1) 1.3.2 ✓25 ✓ answer (1) 1.3.3 µ ✓ answer (1) 1.4 Find two positive integers between which 53 lies. ✓25 < £3 < 56 ✓ 5<-✓33<6✓ ✓ ffs < -J3'i < 56 :. 53 lies between Sand 6 ✓ answer (2) 1.5 1.5.1 3x(2x-4xy) distribution law =6x 2 -12x 2 y ✓ 6x 2 ✓-12x 2 y (2) 1.5.2 (x-3) 2 ✓ (x-3)(x-3) =(x-3)(x-3) ✓ ✓ x 2 -6x+9 =X 2 -6X+9 ✓ (2) 1.5.3 2 (2r- p)(3r -4rp + p ) 2 3 ✓ 6r 3 -8r 2 p+2rp =6r 3 -8r2 p + 2rp-3r 2 p +4rp- p 2 = 6r3 -11r 2 p+6rp 2 - p 3 ✓-3r p+4rp- p3 ✓-11r 2 p and +6rp 2 (3) [14] QUESTION 2 2.1 2.1.1 2x 2 -8 ✓ HCF of 2 ✓ brackets =2(x2 -4)✓ (2) =2(x+2)(x-2)✓ 2.1.2 x 2 -4x+3 ✓✓ Factors =( X - 3)( X -1) ✓ ✓ (2)

Downloaded from hlayiso.com MARCH TEST 22 2.1.3 2 px +3qx -2 py- 3qy =(2px-2 py)+( 3qx- 3qy)✓ =2 p(x-y) + 3q(x-y) ✓ =(2y+3q)(x-y)✓ ✓Grouping OR ✓Common factor for =(2px+3qx)+(-2py-3qy)✓ two brackets ✓answer =x (2p+3q)-y( 2p +3q) ✓ = (x-y)(2p+3q)✓ (3) 2.2 27x 3 -8 ✓✓Factorising numerator 27x 2 +18x +1 2 ✓Factorising ( 3x-2)(9x 2 +6x+4) denominator = ✓✓ 2 3 (9x +6x+4) ✓answer 3x-2 ( 4) =-- ✓ 3 [11] QUESTION 3 3.1 Solve for x: 3.1.1 ( 2 X +1) ( X- 3) =0 ✓x = - -1 or ✓ x = 3 ( 2x +1)=0 or (x- 3)=0 1 x =--✓ or x=3 ✓ 2 (2) 3.1.2 3 x =1 3 x=3 0 X=0 (2) 3.1.3 -4�3x-1�5 -4+1�3x �5+1 ✓simplification -3�3x�6✓ -1�X �2 ✓ ✓ ✓-1 • ✓ • ✓ 2 ✓graphical � � -1 2 representation (4) 3.1.4 g 2x+3 =27 x+S 3 2 (2 x+3) =3 3(x+5) ✓ ✓same base 3 2 x+6 =3 3x+l5 ✓ ✓simplifying ✓equating exponents 4x+6=3x+1 5 ✓

Downloaded from hlayiso.com MARCH TEST 22 X=9 ✓ ✓answer (4 ) 3.2 2x-y =-1.........(1) and x + 2y = 12 ..........(2) X=-2y+12 ...........(3) ✓Making x subject of Substitute equation 3 into equation 1 the formula Eq 1: 2(-2y +12)-y=-1 ✓ ✓Subt eq 3 into 1 -4y+ 24-y=-1 -Sy =-25 y=5 ✓ ✓y=5 Eq 3: X=-2(5)+12 X= 2 ✓ ✓x=2 (4) [16] QUESTION 4 4.1 Statement x =34' (Corrsp Ls =)✓ ✓S&R y=78 (Alt Ls=)✓ ✓S&R z= 180-112✓ (Int L of � or aL s on straight line are suppl)✓ ✓S ✓R z= 68" ✓ ✓answer (5) 4.2 4.2.1 FEM =50 ✓ (Diagonals of rhombus bisect at the vertex ✓S L s)✓ ✓R (2) 4.2.2 EFM =180-(50+90) (sum of L s in � )✓ ✓s ✓R EFM= 40 ° ✓ (2) [9]

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