LP Maths Grade 8 June 2022 QP and Memo

Downloaded f rom St anmorephysics. com SEKHUKHUNE SOUTH DISTRICT GRADE 08 MATHEMATICS TEST 02 TERM 2 DATE : JUNE 2022 MARKS :60 DURATION : 1, 5 HRS This question paper consists of 6 pages. 1 GRADE 08 TEST 2022

Downloaded f rom St anmorephysics. com INSTRUCTIONS AND INFORMATION 1. Answer ALL questions in this question paper. 2. A non-programmable calculator may be used. 3. Show ALL calculations clearly. 4. Show all units where applicable. 5. Number the answers correctly according to the numbering system used in this question paper. 6. Write neatly and legibly. 2 GRADE 08 TEST 2022

Downloaded f rom St anmorephysics. com QUESTION 1 Whole numbers and integers. 1.1 From the list numbers of below, choose a number that; 8 13 14 18 24 49 77 1.1.1 Is a multiple of 2 and 3 (1) 1.1.2 Is a perfect square (1) 1.1.3 Is a prime number (1) 1.1.4 Is a factor of 24 (1) 1.1.5 Is the square root of 169 (1) 1.1.6 Is the highest Common Factor of 48 and 72 (1) 1.2 A list of words is provided bellow. Use your knowledge of properties of whole numbers to select the correct word for the following. Commutative property, Associative property, Distributive property, Identity of zero, Identity of one. 1.2.1 𝑟 + (𝑠 + 𝑡) = 𝑠 + (𝑟 + 𝑡) (1) 1.2.2 14𝑥 × 0 = 0 (1) 1.2.3 𝑚 × (𝑛 + 𝑝) = (𝑚 × 𝑛) + (𝑚 × 𝑝) (1) 1.3 Determine the HCF of 8 and 180 using prime factorisation (tree diagram). (3) 1.4 A library buys 638 new books. Each shelf in the library can take 32 books. How many shelves are needed. (2) 1.5 Decrease R60 in the ratio 4:5 (2) 1.6 Calculate the following and say whether it is true or false: (3) (−3)3 > (−125) [19] QUESTION 2 Common and decimal fractions. 2.1 Calculate the following. 2.1.1 3 −5 (3) 2.1.2 4 ÷2 (3) 2.1.3 168,2÷ 2,9 + 1,4 (2) 3 GRADE 08 TEST 2022

Downloaded f rom St anmorephysics. com 2.2 Round the following : 2.2.1 17,702 to nearest whole number. (1) 2.2.2 20,345 to two decimal paces . (1) [10] QUESTION 3 Laws of exponents 3.1 Simplify the following 3.1.1 𝑎 × 𝑎3 × 𝑥 × 𝑥 × 𝑎2 (2) 3.1.2 (𝑥63×𝑐×22)0 (1) 3.1.3 (𝑥3𝑦)4 × 2𝑥3 ( 2) 3.1.4 √25𝑎 𝑐 (2) 3.1.5 × × (3) [10] QUESTION 4 Numeric and geometric patterns and Relationships 4.1 Study the following sequence and answer the questions that follow: 𝟏, 𝟑, 𝟓, 𝟕, 𝒂, 𝒃 4.1.1 Give the values of 𝑎 𝑎𝑛𝑑 𝑏. (2) 4.1.2 Determine the general term (Tn =…) to describe the above pattern. (2) 4.1.3 Use the general term to find T12 of the sequence. (2) 4 GRADE 08 TEST 2022

Downloaded f rom St anmorephysics. com 4.1 Study the following geometric pattern and answer the following questions. 4.2.1 Fill in the missing numbers in the table below: Figure 1 2 3 4 5 Number of small 1 4 9 𝒂 𝒃 triangles (2) 4.2.2 Write down the general term, 𝑇𝑛, of the number sequence formed by the number of (2) small triangles in the above pattern. 4.3 Find the values of 𝒂, 𝒃, 𝒄 𝒂𝒏𝒅 𝒅. Input (x) (𝒅𝒐 𝒏𝒐𝒕 𝒄𝒐𝒑𝒚 𝒕𝒉𝒆 𝒅𝒊𝒂𝒈𝒓𝒂𝒎) Output 12 b a 6 𝒙 −3 −−𝟐 c 𝟑 −4 27 7 (4) 4.4 Given the following general term: 𝑻𝒏 = 𝒏𝟑 − 𝟏 (2) Create a three terms sequence. [16] 5 GRADE 08 TEST 2022

Downloaded f rom St anmorephysics. com QUESTIONS 5 Algebraic expressions (language) 5.1 Given below is an algebraic expression, answer the following questions based on it: 𝟑𝒙𝟐 + 𝒙𝟒 − 𝟐𝒙 + 𝟏 5.1.1 How many terms are given in the expression? (1) 5.1.2 What is the degree of this expression? (1) 5.1.3 Give the constant term of this expression. (1) 5.1.4 Give the coefficient of 𝑥. (1) 5.2 Write an algebraic expression that will symbolize each of the following. 5.2.1 Six more than the product of five and a number. (1) 5.2.2 The product of ten and the sum of two different numbers (2) [7] TOTAL MARK [60] 6 GRADE 08 TEST 2022

Downloaded f rom St anmorephysics. com SEKHUKHUNE SOUTH DISTRICT GRADE 08 MATHEMATICS TEST 02 TERM 2 MARKING GUIDELINE DATE : 07 JUNE 2022 MARKS :60 This Marking guideline consists of 5 pages. 1 GRADE 08 TEST 01 MEMO 2022

Downloaded f rom St anmorephysics. com QUESTION 1 Whole numbers and integers. 1.1 1.1.1 18 0r 24  (1) 1.1.2 49  (1) 1.1.3 13  (1) 1.1.4 8 (1) 1.1.5 13  (1) 1.1.6 24  (1) 1.2 1.2.1 Associative property  (1) 1.2.2 Identity of zero (1) 1.2.3 Distributive property  (1) 1.3 Determine the HCF of 8 and 180 using prime factorisation (tree diagram). 8 180 2 4 2 90 2 2  2 45 3 15 3 5 HCF: 2 × 2 = 22 = 4  (3) 1.4 1 𝑆ℎ𝑒𝑙𝑓 ∶ 32 𝐵𝑜𝑜𝑘𝑠  Simplify : 1 MARK 𝑥 ∶ 638 𝑏𝑜𝑜𝑘𝑠 Answer : 1 MARK 638 ∴ 𝑥 = 32 = 19,9375 ≈ 20 𝑠ℎ𝑒𝑙𝑓𝑠  (2) 1.5 Decrease R60 in the ratio 4:5 Simplify : 1 MARK 4 Answer : 1 MARK 𝑅60 × 9  = 𝑅48  (2) 1.6 −27  > −5  Calculation:−27 and −5 False ( −5 is greater than −27)  Conclusion : 1 MARK (3) 2 GRADE 08 TEST 01 MEMO 2022

Downloaded f rom St anmorephysics. com [19] QUESTION 2 Common and decimal fractions. 2.1 2.1.1 1 5 Conversion( Mixed number) : 36 − 58 1MARK 19 45 = −  6 8 𝐿𝐶𝐷 = 24 (4)(19)−(3)(45)) =  Simplify: 1 MARK 24 Answer 1 MARK 76−135 = 24 59 =−  24 (3) 2.1.2 1 2 Conversion( Mixed number) : 4 8 ÷ 2 11 1MARK 33 24 = ÷  Simplify: 1 MARK 8 11 Answer 1 MARK 33 11 = ×  8 24 121 (3) =  72 2.1.3 = 58 + 1,4  (2) = 59,4  2.2 Round the following : 2.2.1 18  (1) 2.2.2 20,35  (1) [10] QUESTION 3 Laws of exponents 3.1 Simplify the following 3.1.1 𝑎6 × 𝑥 2  Product law: MARK (1) 3.1.2 1 (1) 3 GRADE 08 TEST 01 MEMO 2022

Downloaded f rom St anmorephysics. com 3.1.3 Power product law:1 MARK 12 4 3 (𝑥 𝑦 ) × 2𝑥  Answer : 1 MARK 2𝑥15 𝑦 4  (2) 3.1.4 √25𝑎4 𝑐 8 5𝑎2 𝑐 4  (1) 3 2 3.1.5 3𝑦 𝑎 𝑦 × 𝑦 4 × 𝑎2 3𝑦 3 𝑎2  𝑦 5 𝑎2 3−5 2−2 3 3𝑦 𝑎  = 𝑦2  (3) [8] QUESTION 4 Numeric and geometric patterns and Relationships 4.1 Study the following sequence and answer the questions that follow: 𝟏, 𝟑, 𝟓, 𝟕, 𝒂, 𝒃 4.1.1 𝑎=9  𝑏 = 11  (2) 4.1.2 𝑇1 = 2(1) − 1 = 1 𝑇2 = 2(2) − 1 = 3  𝑇𝑛 = 2𝑛 − 1  (2) 4.1.3 𝑇12 = 2(12) − 1 = 23  (2) 4.2 4.2.1 Fill in the missing numbers in the table below: 𝑎 = 16  𝑏 = 25  (2) 4.2.2 𝑇𝑛 = 𝑛2  (2) 4.3 Find the values of 𝒂, 𝒃, 𝒄 𝒂𝒏𝒅 𝒅. 𝑎 = 24  𝑏=2  𝑐 = −3  𝑑 = −6  (4) 4.4 𝑻𝒏 = 𝒏𝟑 − 𝟏 (2) 𝟎; 𝟕; 𝟐𝟔  [16] 4 GRADE 08 TEST 01 MEMO 2022

Downloaded f rom St anmorephysics. com QUESTIONS 5 Algebraic expressions (language) 5.1 5.1.1 4 ( FOUR) TERMS  (1) 5.1.2 4th degree (FOUR)  (1) 5.1.3 1  (1) 5.1.4 −2  (1) 5.2 5.2.1 5𝑥 + 6 𝑜𝑟 5 × 𝑥 + 6  (1) 5.2.2 10(𝑥 + 𝑦)  (2) 10𝑥 + 10𝑦  [7] TOTAL MARK [60] 5 GRADE 08 TEST 01 MEMO 2022