FS Maths Grade 8 MOCK June 2024 QP only

FS/June 2024 Grade 8 GRADE 8 MATHEMATICS MOCK PAPER JUNE 2024 Gr 8 MATHEMATICS MARKS: 60 TIME: 1HOUR This question paper consists of 15 excluding cover pages. Copyright reserved Please turn over

FS/June 2024 Grade 8 INSTRUCTIONS AND INFORMATION TO THE LEARNERS 1. Write neatly and legibly. 2. Clearly show ALL steps which you used in determining the answer. 3. An approved calculator (non-programmable and non-graphical) may be used unless stated otherwise. 4. Diagrams are NOT necessarily drawn to scale. 5. Round off to TWO decimal places, unless stated otherwise. 6. In the multiple-choice questions, circle only the letter for the correct answer, e.g. If the correct answer in 1 is D, you should only circle D . There is only one correct answer in each question. Copyright reserved 1 Please turn over

FS/June 2024 Grade 8 EXAMPLE Multiple choice questions Circle only the letter for the correct answer. If the correct answer in 1 is D, you should only circle D . PRACTICE QUESTION 1. 204 is equal to 104 A. 20 B. 2 C. 8 D. 16 ANSWERS A = 𝟐 × 𝟏𝟎𝟒 C = 24 × 104 1 𝟏𝟎𝟒 104 = 𝟐 × 𝟏𝟎𝟒 − 𝟒 = 24 = 𝟐 × 𝟏𝟎𝟎 =2 ×4 = 𝟐𝟎 incorrect = 8 incorrect B = 𝟐 × 𝟏𝟎𝟒 D = (2 ×10 )4 𝟏𝟎𝟒 104 =𝟐 24 × 104 = 104 = 𝟐 incorrect = 24 = 2 × 2 × 2 × 2 = 𝟏𝟔 correct Your answer is correct if you corcled D. Copyright reserved 2 Please turn over

FS/June 2024 Grade 8 QUESTION 1 Multiple choice questions Circle only the letter for the correct answer. 1. Express (3𝑎)4 in simplified form. (1) A. 12𝑎 B. 16𝑎4 C. 7𝑎4 D. 84𝑎4 Copyright reserved 3 Please turn over

FS/June 2024 Grade 8 2. Which expression that is equivalent to the expression shown below: (1) 7𝑎 + 5(4𝑎 − 7) A. 27𝑎 − 35 B. 27𝑎 − 7 C. 7𝑎 − 13 D. −20𝑎 3. Simplify: (18 ÷ 3) + (9 × 2) − 6 = (1) A. 18 B. 102 C. 27 D. 21 Copyright reserved 4 Please turn over

FS/June 2024 Grade 8 4. 1 1 1 − 8 × 8 is equal to (1) 8 A 0 B 1 16 C 1 64 D 7 64 5. Which list is made up of multiples of 8? (1) A 1 ; 8 ; 40 B 8 ; 16 ; 32 C 16 ; 22 ; 28 D 8 ; 14 ; 24 [5] Copyright reserved 5 Please turn over

FS/June 2024 Grade 8 QUESTION 2 2.1 Complete: 0 (1) = __________________________ 100 2.2 Consider the number: 240 2.2.1 Write the number as the product of its prime factors in an (1) exponential form. ______________________________________________________ ______________________________________________________ 2.2.2 If A = 24 × 32 , B = 22 × 32 × 72 and C = 22 × 3 × 53 . Determine (2) the LCM and HCF. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ Copyright reserved 6 Please turn over

FS/June 2024 Grade 8 2.3 Express 0,5 m : 20 cm in its simplest form. (1) ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ 2.4 The ratio of oranges to pears in a shop is 3 : 2. If there are 210 fruits in a (2) shop, how many pears are there? ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ [7] Copyright reserved 7 Please turn over

FS/June 2024 Grade 8 QUESTION 3 Simplify the following WITHOUT the use of a calculator. Show ALL steps. 3.1 3−(−8) (2) −6 ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ 3.2 3 3 (−√1) + 8 − 66 (2) ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ 3.3 (−5)2 − (−12) − 10 (3) 25 ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ Copyright reserved 8 Please turn over

FS/June 2024 Grade 8 3.4 9 −1 7 + √0,36 (3) 12 24 ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ [10] QUESTION 4 4.1 Arrange the following decimal fraction in ascending order: (1) 2.7 ; 0.55 ; 0.75 ; 0.12 ; 0.302 ______________________________________________________ ______________________________________________________ 4.2 This is George’s monthly expenditure. 1. Spend 0,625 of his money on rent. 2. Spend 30% of his money on transport costs. 12 3. Spend 50 of his money on groceries 4.2.1 If George earns R15 500 per month, calculate the total amount of (1) money George spends on rent, transport, and groceries. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ Copyright reserved 9 Please turn over

FS/June 2024 Grade 8 4.2.2 On what item does George spend the most money? (1) ____________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ 4.2.3 If George saves the rest of his money, what percentage of money (2) does he save? ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ [5] QUESTION 5 5.1 Simplify the following expressions WITHOUT the use of a calculator. Show ALL steps. 5.1.1 𝑘8 (1) 𝑘6 ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ Copyright reserved 10 Please turn over

FS/June 2024 Grade 8 5.1.2 (42 )4 (2) 48 ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ 5.1.3 −3𝑎𝑏 3 × −5𝑎3 𝑏 3 (1) ______________________________________________________ ______________________________________________________ 5.2 Write 683 000 000 in scientific notation. (2) ______________________________________________________ ______________________________________________________ ______________________________________________________ [6] QUESTION 6 6.1 Write down the next term of the following pattern: 6.1.1 1 ; 4 ; 16 ; … (1) ______________________________________________________ ______________________________________________________ ______________________________________________________ Copyright reserved 11 Please turn over

FS/June 2024 Grade 8 6.1.2 5; 10 ; 15 ; … (1) ______________________________________________________ ______________________________________________________ 6.2 Study the diagram below and answer the questions that follows. 6.2.1 How many matchsticks are added to form subsequent pattern? (1) _____________________________________________________ _____________________________________________________ 6.2.2 Describe the pattern formed by the matchsticks in words. (2) ____________________________________________________ _____________________________________________________ _____________________________________________________ 6.2.3 Determine the number of matchsticks required in the 𝑛𝑡ℎ pattern (1) in the form 𝑇𝑛 = ⋯ ____________________________________________________ _____________________________________________________ 6.2.4 How any matchsticks will be in the 15th picture? (2) ____________________________________________________ _____________________________________________________ [8] Copyright reserved 12 Please turn over

FS/June 2024 Grade 8 QUESTION 7 7.1 Study the flow diagram below. Input (𝑥) output (𝑦) (3) 𝐀________ 𝟏𝟑 𝟒𝒙 − 𝟕 𝟐𝟏 𝐁 ________ 𝟏𝟎 𝐂 __________ Determine the values of A, B and C. A ____________ B ____________ C ____________ 7.2 Use the table below to answer the questions that follows 𝒙 𝟎 −𝟏 𝟐 𝟓 𝒏 𝒚 13 3 17 𝒎 8 2 4 4 4 7.2.1 Write down the relationship between 𝑥 𝑎𝑛𝑑 𝑦 in the form 𝑦 =… (1) 𝑦 = ________________ 7.2.2 Calculate the values of m and 𝑛. (1) 𝑚: ______________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ Copyright reserved 13 Please turn over

FS/June 2024 Grade 8 𝑛: (1) ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ [6] QUESTION 8 8.1 Express the following statement as an algebraic expression: (2) “The difference between 5 and twice a number” ______________________________________________________ _____________________________________________________ 8.2 Given the expression: −4𝒂𝟓 + 𝟐𝒂𝟒 𝒃 − 𝒂𝟑 𝒚𝟐 + 𝟐𝒂𝟐 𝒃𝟐 − 𝒂𝒃𝟒 − 𝟏𝟎 𝟑 8.2.1 How many terms are there in the expression? (1) ______________________________________________________ ______________________________________________________ 8.2.2 What is the value of the constant term? (1) ______________________________________________________ ______________________________________________________ 8.2.3 Write down the coefficient of 𝒂𝟑 𝒚𝟐 term. (1) ______________________________________________________ ______________________________________________________ Copyright reserved 14 Please turn over

FS/June 2024 Grade 8 8.3 Simplify the following expression: 8.3.1 2𝑥 − 4𝑦 − 𝑏 + 𝑦 − 4𝑥 + 3𝑏 (2) ______________________________________________________ ______________________________________________________ ______________________________________________________ 8.3.2 3 √100𝑘 8 𝑙16 + √729𝑘12 𝑙12 (3) ______________________________________________________ ______________________________________________________ ______________________________________________________ 8.4 Subtract 3𝑎 − 𝑏 − 𝑐 from 𝑎2 − 3𝑏 + 2𝑐 (3) ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ [13] GRAND TOTAL [60] Copyright reserved 15

FS/June 2024 Grade 8 GRADE 8 MATHEMATICS MOCK PAPER MARKING GUIDELINE JUNE 2024 Gr 8 MATHEMATICS MARKS: 60 TIME: 1HOUR This question paper consists of 15 excluding cover pages. Copyright reserved Please turn over

FS/June 2024 Grade 8 INSTRUCTIONS AND INFORMATION TO THE LEARNERS 1. Write neatly and legibly. 2. Clearly show ALL steps which you used in determining the answer. 3. An approved calculator (non-programmable and non-graphical) may be used unless stated otherwise. 4. Diagrams are NOT necessarily drawn to scale. 5. Round off to TWO decimal places, unless stated otherwise. 6. In the multiple-choice questions, circle only the letter for the correct answer, e.g. If the correct answer in 1 is D, you should only circle D . There is only one correct answer in each question. Copyright reserved 1 Please turn over

FS/June 2024 Grade 8 EXAMPLE Multiple choice questions Circle only the letter for the correct answer. If the correct answer in 1 is D, you should only circle D . PRACTICE QUESTION 1. 204 is equal to 104 A. 20 B. 2 C. 8 D. 16 ANSWERS A = 𝟐 × 𝟏𝟎𝟒 C = 24 × 104 1 𝟏𝟎𝟒 104 = 𝟐 × 𝟏𝟎𝟒 − 𝟒 = 24 = 𝟐 × 𝟏𝟎𝟎 =2 ×4 = 𝟐𝟎 incorrect = 8 incorrect B = 𝟐 × 𝟏𝟎𝟒 D = (2 ×10 )4 𝟏𝟎𝟒 104 =𝟐 24 × 104 = 104 = 𝟐 incorrect = 24 = 2 × 2 × 2 × 2 = 𝟏𝟔 correct Your answer is correct if you corcled D. Copyright reserved 2 Please turn over

FS/June 2024 Grade 8 QUESTION 1 Multiple choice questions Circle only the letter for the correct answer. 1. Express (3𝑎)4 in simplified form. (1) = 34 𝑎4 = 81𝑎4 OR = 3𝑎 × 3𝑎 × 3𝑎 × 3𝑎 = 81𝑥 4 A. 12𝑎 B. 16𝑎4 C. 7𝑎4 D. 81𝑎4 ✓ Copyright reserved 3 Please turn over

FS/June 2024 Grade 8 2. Which expression that is equivalent to the expression shown below: (1) 7𝑎 + 5(4𝑎 − 7) = 7𝑎 + 5(4𝑎 − 7) = 7𝑎 + 20𝑎 − 35 = 27𝑎 − 35 A. 27𝑎 − 35 ✓ B. 27𝑎 − 7 C. 7𝑎 − 13 D. −20𝑎 3. Simplify: (18 ÷ 3) + (9 × 2) − 6 = (1) = (18 ÷ 3) + (9 × 2) − 6 = 𝟔 + 18 − 𝟔 = 18 A. 18 ✓ B. 102 C. 27 D. 21 Copyright reserved 4 Please turn over

FS/June 2024 Grade 8 4. 1 1 − 8 × 8 is equal to 1 (1) 8 1 1 1 = 8 − (8 × 8) 1 1 =8− 64 1 8 1 = (8 × 8) − 64 8 1 = 64 − 64 7 = 64 A 0 B 1 16 C 1 64 D 7 ✓ 64 5. Which list is made up of multiples of 8? (1) 𝟖 ; 𝟏𝟔 ; 24 ; 𝟑𝟐 ; 𝟒𝟎 ; 48 ; … All these numbers are made up of multiples of 8 A 1 ; 8 ; 40 B 8 ; 16 ; 32 ✓ C 16 ; 22 ; 28 D 8 ; 14 ; 24 [5] Copyright reserved 5 Please turn over

FS/June 2024 Grade 8 QUESTION 2 2.1 Complete: 0 (1) =0✓ answer 100 2.2 Consider the number: 240 2.2.1 Write the number as the product of its prime factors in an (1) exponential form. 𝟐𝟒𝟎 = 𝟐𝟒 × 𝟑 × 𝟓 ✓ answer 2.2.2 If A = 24 × 32 , B = 22 × 72 and 3 × 53 . Determine the LCM and (2) HCF. Factors 2 2 2 2 3 3 2 2 7 7 3 5 5 5 LCM 2 2 2 2 3 3 5 5 5 7 7 = 𝟖𝟖𝟐 𝟎𝟎𝟎 ✓ answer HCF 2 2 3 = 𝟏𝟐 ✓ answer OR LCM = 𝟐𝟒 × 𝟑𝟐 × 𝟓𝟑 × 𝟕𝟐 = 𝟖𝟖𝟐 𝟎𝟎𝟎 ✓ HCF = 𝟐𝟐 × 𝟑 = 𝟏𝟐 ✓ Copyright reserved 6 Please turn over

FS/June 2024 Grade 8 2.3 Express 0,5 m : 20 cm in its simplest form. (1) 0,5 𝑚 = 50 𝑐𝑚 50 𝑐𝑚 ∶ 20 𝑐𝑚 =5∶2✓ answer 2.4 The ratio of oranges to pears in a shop is 3 : 2. If there are 210 fruits in a (2) shop, how many pears are there? 3+2= 5 3 ∴ Oranges: × 210 5 = 126 ✓ answer Pears: 210 – 126 = 84 ✓ answer OR 2 Pears: 5 × 210 = 84 ✓ [7] QUESTION 3 Simplify the following WITHOUT the use of a calculator. Show ALL steps. 3.1 (−3)−(−8) (2) −6 −3 + 8 = ✓ simplify −6 5 = −6 ✓ answer 3.2 3 3 (−√1) + 8 − 66 (2) = −1 − 66 + 8 ✓ associative = −59 ✓ answer Copyright reserved 7 Please turn over

FS/June 2024 Grade 8 3.3 (−5)2 − (−12) − 10 (3) 25 25 = 25 + 12 − 10 ✓ method = 1 + 12 − 10 ✓ associative =3✓ answer 3.5 9 −1 7 + √0,25 (3) 12 24 18 31 6 = 24 − 24 + 24 ✓ simplify 18 6 31 = 24 + 24 − 24 ✓ associative 24 31 = 24 − 24 7 = − 24 ✓ answer [10] QUESTION 4 4.1 Arrange the following decimal fraction in ascending order: (1) 2.7 ; 0.55 ; 0.75 ; 0.12 ; 0.302 0.12; 0.302; 0.55; 0.75; 2.7 ✓ answer 4.2 This is George’s monthly expenditure. 1. Spend 0,625 of his money on rent. 2. Spend 30% of his money on transport costs. 12 3. Spend of his money on groceries 50 4.2.1 If George earns R15 500 per month, calculate the total amount of (1) money George spends on rent, transport, and groceries. Rent: 15 500 × 0,625 = R9 687.50 30 Transport: 100 × 15500 = 𝑅4 650 13 Groceries: 50 × 15500 = R4 030 Total = 9 687,50 + 4 650 + 4 030 = R18 367.50 ✓ answer Copyright reserved 8 Please turn over

FS/June 2024 Grade 8 4.2.2 On what item does George spend the most money? (1) On rent ✓ answer 4.2.3 If George saves the rest of his money, what percentage of money (2) does he save? 18 367,50 × 100 = 118,5% ✓ answer 15500 He is overspent by 18,5%. ✓ answer [5] QUESTION 5 5.1 Simplify the following expressions WITHOUT the use of a calculator. Show ALL steps. 5.1.1 𝑘8 (1) 𝑘6 𝑘2 ✓ answer 5.1.2 (42 )4 (2) 48 48 = 48 ✓ method =1 ✓ answer 5.1.3 −3𝑎𝑏 3 × −5𝑎3 𝑏 3 (1) = 15𝑎4 𝑏 6 ✓ answer 5.2 Write 683 000 000 in scientific notation. (2) 6,83 ✓ × 𝟏𝟎𝟖 ✓ 6,83 ✓ 108 ✓ [6] Copyright reserved 9 Please turn over

FS/June 2024 Grade 8 QUESTION 6 6.1 Write down the next term of the following pattern: 6.1.1 1 ; 4 ; 16 ; … (1) 25 ✓ answer 6.1.2 5; 10 ; 15 ; … (1) 20 ✓ answer 6.2 Study the diagram below and answer the questions that follows. 6.2.1 How many matchsticks are added to form subsequent pattern? (1) 3 matchsticks ✓ answer 6.2.2 Describe the pattern formed by the matchsticks in words. (2) From picture 1 add 3 matchsticks ✓ to get the next picture ✓ 6.2.3 Determine the number of matchsticks required in the 𝑛𝑡ℎ pattern (1) in the form 𝑇𝑛 = ⋯ Tn = 3𝑥 + 1 ✓ answer 6.2.4 How any matchsticks will be in the 15th picture? (2) 𝑇15 = (3 × 15) + 1 ✓ substitution = 46 ✓ answer [8] Copyright reserved 10 Please turn over

FS/June 2024 Grade 8 QUESTION 7 7.1 Study the flow diagram below. Input (𝑥) output (𝑦) (3) 𝐀________ 𝟏𝟑 𝟒𝒙 − 𝟕 𝟐𝟏 𝐁 ________ 𝟏𝟎 𝐂 __________ Determine the values of A, B and C. A 5 ✓ B 7 ✓ C 33 ✓ answer 7.2 Use the table below to answer the questions that follows 𝒙 𝟎 −𝟏 𝟐 𝟓 𝒏 𝒚 13 3 17 𝒎 8 2 4 4 4 7.2.1 Write down the relationship between 𝑥 𝑎𝑛𝑑 𝑦 in the form 𝑦 =… (1) 1 13 𝑦 = 2𝑥 + 4 ✓ answer 7.2.2 Calculate the values of m and 𝑛. (1) 1 𝑚 = 2 (5) + 4 13 (1) 10 13 = + 4 4 23 = 4 ✓ answer Copyright reserved 11 Please turn over

FS/June 2024 Grade 8 1 13 8 = 2𝑛 + 4 13 𝑛 8− 4 = 2 19 ∴ 𝑛= 4 ✓ answer [6] QUESTION 8 8.1 Express the following statement as an algebraic expression: (2) “The difference between 5 and twice a number” 2𝑥 − 5 ✓ 8.2 Given the expression: −4𝒂𝟓 + 𝟐𝒂𝟒 𝒃 − 𝒂𝟑 𝒚𝟐 + 𝟐𝒂𝟐 𝒃𝟐 − 𝟑 − 𝟏𝟎 𝒂𝒃𝟒 8.2.1 How many terms are there in the expression? (1) 6 terms ✓ 8.2.2 What is the value of the constant term? (1) −10 8.2.3 Write down the coefficient of 𝑎𝑏 2 term. (1) 3 1 −3 ✓ 8.3 Simplify the following expression: 8.3.1 2𝑥 − 4𝑦 − 𝑏 + 𝑦 − 4𝑥 + 3𝑏 (2) = 2𝑥 − 4𝑥 − 𝑏 + 3𝑏 − 4𝑦 + 𝑦 ✓ = −2𝑥 + 2𝑏 − 3𝑦 ✓ Copyright reserved 12 Please turn over

FS/June 2024 Grade 8 8.3.2 3 √100𝑘 8 𝑙16 + √729𝑘12 𝑙 24 (3) = 10𝑘 4 𝑙 8 + 9𝑘 4 𝑙 8 ✓ ✓ 4 8 = 19𝑘 𝑙 ✓ 8.4 Subtract 3𝑎2 − 𝑏 − 𝑐 from 𝑎2 − 3𝑏 + 2𝑐 (3) Horizontally: 𝑎2 − 3𝑏 + 2𝑐 − (3𝑎2 − 𝑏 − 𝑐) = 𝑎2 − 3𝑏 + 2𝑐 − 3𝑎 + 𝑏 + 𝑐 ✓ = 𝑎2 − 3𝑎2 − 3𝑏 + 𝑏 + 2𝑐 + 𝑐 ✓ = −2𝑎2 − 2𝑏 + 3𝑐 ✓ VERTICALLY 𝑎2 − 3𝑏 + 2𝑐 3𝑎2 − 𝑏 − 𝑐 −𝟐𝒂𝟐 − 𝟐𝒃 + 𝟐𝒄 ✓ ✓ ✓ [13] GRAND TOTAL [60] Copyright reserved 13