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Here is a Grade 8 Mathematics question paper covering the topics you requested, followed by its memo. --- GRADE 8 MATHEMATICS ASSESSMENT Total Marks: 50 Instructions: 1. Answer all questions. 2. Show all your calculations clearly. 3. Write neatly and legibly. --- Section A: Number System (12 Marks) Question 1 1.1 Classify each number as Natural (N), Whole (W), Integer (Z), or Rational (Q). Write all applicable classifications. a) 7 (1 mark) b) -3 (1 mark) c) 0.25 (1 mark) d) sqrt(16) (1 mark) 1.2 Arrange the following numbers in ascending order: (2)/(3), 0.6, -1.5, 1, -(1)/(2). (4 marks) 1.3 Find the Highest Common Factor (HCF) of 36 and 48. (2 marks) 1.4 Calculate: -8 + 3 × (-4) - 10 ÷ 2. (2 marks) --- Section B: Ratio and Rates (12 Marks) Question 2 2.1 Simplify the following ratios: a) 24 : 36 (2 marks) b) 1.5 m : 50 cm (2 marks) 2.2 Divide R180 in the ratio 2:3:4. (3 marks) 2.3 Increase 75 in the ratio 7:5. (2 marks) 2.4 A car travels 180 km in 2 hours. How far will it travel in 3.5 hours at the same average speed? (3 marks) --- Section C: Exponents (13 Marks) Question 3 3.1 Evaluate: a) 3^3 - 2^4 (2 marks) b) (-5)^2 + 1^5 (2 marks) 3.2 Simplify using exponent laws: a) x^6 × x^2 (1 mark) b) (y^9)/(y^3) (1 mark) c) (m^4)^3 (1 mark) d) 2a^0 + (3b)^0 (2 marks) 3.3 Simplify: (2x^3y^2)^3 (4 marks) --- Section D: Algebraic Expressions (Product) (13 Marks) Question 4 4.1 Find the product of the following: a) (5a)(3b) (1 mark) b) (-2x^2)(4xy) (2 marks) 4.2 Expand and simplify: a) 3(x+4) (2 marks) b) -2y(y-5) (3 marks) c) (x+3)(x+7) (3 marks) d) (2m-1)(m+4) (2 marks) --- --- MEMORANDUM --- Section A: Number System (12 Marks) Question 1 1.1 Classify each number as Natural (N), Whole (W), Integer (Z), or Rational (Q). a) 7 N, W, Z, Q b) -3 Z, Q c) 0.25 Q d) sqrt(16) N, W, Z, Q 1.2 Arrange the following numbers in ascending order: (2)/(3), 0.6, -1.5, 1, -(1)/(2). Step 1: Convert all numbers to decimal form for easy comparison. (2)/(3) ≈ 0.667 -(1)/(2) = -0.5 The numbers are approximately: 0.667, 0.6, -1.5, 1, -0.5. Step 2: Order the decimal values from smallest to largest. -1.5, -0.5, 0.6, 0.667, 1 Step 3: Write the original numbers in ascending order. -1.5, -(1)/(2), 0.6, (2)/(3), 1 1.3 Find the Highest Common Factor (HCF) of 36 and 48. Step 1: List the factors of each number. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Step 2: Identify the common factors and the highest among them. Common factors: 1, 2, 3, 4, 6, 12 The highest common factor is 12. 12 1.4 Calculate: -8 + 3 × (-4) - 10 ÷ 2. Step 1: Perform multiplication and division from left to right. -8 + (3 × (-4)) - (10 ÷ 2) -8 + (-12) - 5 Step 2: Perform addition and subtraction from left to right. -8 - 12 - 5 -20 - 5 -25 --- Section B: Ratio and Rates (12 Marks) Question 2 2.1 Simplify the following ratios: a) 24 : 36 Step 1: Find the greatest common divisor (GCD) of 24 and 36, which is 12. Step 2: Divide both parts of the ratio by the GCD. (24)/(12) : (36)/(12) 2 : 3 b) $1.5 m