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Quick answer key with short working

Q29 is not visible in the photo, so I haven’t guessed it. Send that part if you need it.

Chapter 1 — Integers, powers and roots

• 1. \(7\) — \(-8+15=7\)
• 2. \(-8\) — \(6-14=-8\)
• 3. \(-5\) — \(-12+7=-5\)
• 4. \(-4\) — \(-9-6+11=-4\)
• 5. \(-56\)
• 6. \(54\) — negative × negative = positive
• 7. \(-9\)
• 8. \(-9\) — \(45\div(-5)=-9\)
• 9. \(800\) — \(400+600-200\)
• 10. \(1500\) — \(50\times30\)
• 11. \(17\) — \(24-15+8\)
• 12. \(13\) — \(36\div6+7\)
• 13. \(11\) — \(25-2\times7\)
• 14. \(6\) — \(24\div4\)
• 15. \(1,2,3,5,6,10,15,30\)
• 16. \(9,18,27,36,45\)
• 17. \(23,29,31,37\)
• 18. \(12\)
• 19. \(24\)
• 20. Yes. Digit sum \(4+3+5+6=18\), divisible by 9. \(4356\div9=484\).
• 21. \(2\) and \(8\). The number must be even and its digit sum must be divisible by 3. \(522\div6=87\), \(528\div6=88\).
• 22. \(63\) — \(36+27\)
• 23. \(15\)
• 24. \(6\)
• 25. \(-3^\circ C\) — \(-6+11-8=-3\)

Chapter 2 — Expressions

• 26. a) \(7\) b) \(5\) c) \(2\)
• 27. \(3y=18\) and \(2a+1=9\) are equations.
• 28. \(6n\) somoni
• 30. \(12ab\)

More expressions

• 31. \(p^4q^2\)
• 32. \(5x,\ -x,\ 9x\)
• 33. \(7a\)
• 34. \(4x+10y\)
• 35. \(5p-3q\)
• 36. \(4m-3\)
• 37. \(\frac{7x}{2}\) or \(3.5x\)
• 38. \(2(5a+2a)=14a\) cm
• 39. \(4p\times3q=12pq\) cm²
• 40. \(4x+24\)
• 41. \(15a-10\)
• 42. \(6p+12q\)
• 43. \(-2x-14\)
• 44. \(-12y+15\)
• 45. \(12a-6b+18\)
• 46. \(5x+12\)
• 47. \(5p+18\)
• 48. \(4x-7y\)
• 49. Area \(=4(2x+5)=8x+20\) cm²; Perimeter \(=2((2x+5)+4)=4x+18\) cm
• 50. Mistake: only \(x\) was multiplied by 3. Correct: \(3(x+4)=3x+12\).

Key rules to remember

• Subtracting a negative means adding: \(-12-(-7)=-12+7\).
• For \(\times\) and \(\div\): same signs give positive, different signs give negative.
• Use BIDMAS/PEMDAS: brackets, indices, multiplication/division, then addition/subtraction.
• Like terms need the same variable part: \(5x\) and \(9x\) are alike, but \(2x^2\) is not like \(3x\).
• Expanding brackets: multiply every term inside the brackets by the outside number, including signs.

Quick checks: Q9 actual \(805\) vs estimate \(800\); Q10 actual \(1488\) vs estimate \(1500\).