{ “instructions”: “Answer all 40 questions. Simplify algebraic answers fully. Where an answer contains a negative index, rewrite it using positive indices unless the question says otherwise. Work carefully: later questions may require two or more laws of indices.”, “sections”: [ { “title”: “A. Powers and Roots”, “questions”: [ { “type”: “short_answer”, “prompt”: “Calculate 4².”, “answers”: [“16”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Calculate 5³.”, “answers”: [“125”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Calculate 3⁴.”, “answers”: [“81”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Calculate 2⁵.”, “answers”: [“32”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Calculate 2⁶.”, “answers”: [“64”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Calculate 2⁷.”, “answers”: [“128”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Find √81.”, “answers”: [“9”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Find ∛125.”, “answers”: [“5”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Find the fourth root of 81.”, “answers”: [“3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Find the fifth root of 32.”, “answers”: [“2”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Find the sixth root of 64.”, “answers”: [“2”], “marks”: 1 } ] }, { “title”: “B. Fractional Indices”, “questions”: [ { “type”: “short_answer”, “prompt”: “Evaluate 64^(1/3).”, “answers”: [“4”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Evaluate 81^(1/4).”, “answers”: [“3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Evaluate 32^(1/5).”, “answers”: [“2”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Evaluate 64^(1/6).”, “answers”: [“2”], “marks”: 1 }, { “type”: “multiple_choice”, “prompt”: “Which expression is equivalent to a^(1/3)?”, “options”: [“√a”, “∛a”, “a³”, “1/a³”], “answer”: “∛a”, “marks”: 1 } ] }, { “title”: “C. Core Laws of Indices”, “questions”: [ { “type”: “short_answer”, “prompt”: “Simplify p³ × p⁵.”, “answers”: [“p^8”, “p8”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify q⁹ ÷ q⁴.”, “answers”: [“q^5”, “q5”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (x³)⁴.”, “answers”: [“x^12”, “x12”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify m⁰.”, “answers”: [“1”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify r¹.”, “answers”: [“r”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Write x^(-3) using positive indices.”, “answers”: [“1/x^3”, “1/x3”], “marks”: 1 }, { “type”: “true_false”, “prompt”: “When multiplying powers with the same base, the indices are added.”, “answer”: true, “marks”: 1 }, { “type”: “true_false”, “prompt”: “When dividing powers with the same base, the indices are multiplied.”, “answer”: false, “marks”: 1 } ] }, { “title”: “D. Mixed Laws of Indices”, “questions”: [ { “type”: “short_answer”, “prompt”: “Simplify p³ × p⁵ ÷ p².”, “answers”: [“p^6”, “p6”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify q⁷ ÷ q² × q³.”, “answers”: [“q^8”, “q8”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (x³)² × x⁴.”, “answers”: [“x^10”, “x10”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (a⁴)³ ÷ a⁵.”, “answers”: [“a^7”, “a7”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify p⁵ × p^(-2).”, “answers”: [“p^3”, “p3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify q² ÷ q⁵ using positive indices.”, “answers”: [“1/q^3”, “1/q3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (x^(-2))³ using positive indices.”, “answers”: [“1/x^6”, “1/x6”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (p²q³)(p⁴q²).”, “answers”: [“p^6q^5”, “p6q5”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify p⁷q⁵ ÷ p³q².”, “answers”: [“p^4q^3”, “p4q3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (p²q³)².”, “answers”: [“p^4q^6”, “p4q6”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (x³y²)(x^(-1)y⁴).”, “answers”: [“x^2y^6”, “x2y6”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify x²y⁵ ÷ x⁴y² using positive indices.”, “answers”: [“y^3/x^2”, “y3/x2”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (a³b²)² ÷ a⁴b.”, “answers”: [“a^2b^3”, “a2b3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (p²q^(-1))³ using positive indices.”, “answers”: [“p^6/q^3”, “p6/q3”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (x²y³)³ ÷ x⁴y⁵.”, “answers”: [“x^2y^4”, “x2y4”], “marks”: 1 }, { “type”: “short_answer”, “prompt”: “Simplify (p³)² × p⁴ ÷ p⁵.”, “answers”: [“p^5”, “p5”], “marks”: 1 } ] } ] }