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PES SS 1 Further Math 1st Term Exam 2025-2026
  • 1. 1.Which of the following expressions is equivalent to x³×x⁴?
A) X¹²
B) X-¹
C) X³+⁴
D) X⁷
  • 2. 2 If log⁡2(x)=3, what is the value of x?
A) 8
B) 2³
C) 3²
D) 6
  • 3. 3 Simplify x⁶/x²
A) x³
B) x⁸
C) x-⁴
D) x⁴
  • 4. 4 What is log⁡3(27) equal to?
A) 9
B) 3
C) 4
D) 81
  • 5. 5 Which expression represents (x⁴)³?
A) x⁴³
B) x⁷
C) x¹
D) x¹²
  • 6. 6 If log⁡a(x)=2 and log⁡a(y)=3, what is log⁡a(xy)?
A) 1
B) 5
C) 6
D) 23
  • 7. 7 Simplify x−³×x⁵
A) x²
B) x-¹⁵
C) x-²
D) x⁸
  • 8. 8 What is the value of log⁡5(125)?
A) 15
B) 3
C) 25
D) 5
  • 9. 9 Which expression is equivalent to (2³)⁴?
A) 2⁷
B) 2¹²
C) 2²⁴
D) 2³⁴
  • 10. 10 If log⁡2(8)=3, then 2³ equals:
A) 6
B) 4
C) 8
D) 16
  • 11. 11 Simplify (x²y³)²
A) x⁴y⁵
B) x⁵y⁶
C) x²y⁹
D) x⁴y⁶
  • 12. 12 What is log⁡4(64)?
A) 3
B) 6
C) 16
D) 8
  • 13. 13 What is the relationship between ax=b and log⁡a(b)=x?
A) They are equivalent expressions
B) They are inverse expressions
C) They are unrelated expressions
D) They are opposite expressions
  • 14. 14 If xn=1, what must be true about n?
A) n must be positive
B) n must be negatice
C) n can be any number
D) n must be zero
  • 15. 15 Which is equivalent to xa×xb?
A) xa-b
B) xab
C) xa+b
D) xa/b
  • 16. 16.Log 24 base 3 + Log 15 base 3 - Log 10 base 3, equals?
A) 2+ 4Log2 base 3
B) 4Log⅓ base 6
C) Log⅚
D) Log¾
  • 17. 17. If a¹=n, then?
A) Log 1 base a =n
B) Log n base a =1
C) an=1
D) Log a base n=1
  • 18. 18. If 52x+1 + 52x =150. Find the value of x.
A) 31.25
B) 5
C) 37.25
D) 37.65
  • 19. 19. Surds are?
A) Rational numbers
B) Irrational numbers
C) Cardinal numbers
D) Portal numbers
  • 20. 20. Which of the following is not an example of an irrational number?
A) 4/√3
B) √3/4
C) 3
D) √3
  • 21. 21. √mn equals?
A) m ×√n
B) m²× n²
C) √m + √n
D) √m × √n
  • 22. 22. √(m/n) equals?
A) √m × √n
B) √m ÷ n
C) 1/√n × √m
D) √m/√n
  • 23. 23. Simplify √75
A) 6√7
B) 3√5
C) 5√3
D) 9√2
  • 24. 24. Simplify √80
A) 5√4
B) 4√5
C) 3√2
D) 5√3
  • 25. 25. Similar surds are?
A) Surds that have the same number.
B) Surds that don't have square root
C) Surds that have the same roots
D) Surds that cannot be decided by each other
  • 26. 26. Simplify √50 - √18 + √32
A) 5√8
B) 2√3
C) 3√2
D) 6√2
  • 27. 27. Which of the following surds cannot be rationalized?
A) 2/√2
B) √3/√2
C) 2/√3
D) √3/2
  • 28. 28. The conjugate of a+√b is?
A) a²-b
B) a-√b
C) √a+√b
D) √b+a
  • 29. 30. A binary operations is commutative, if?
A) Null
B) a+b=a-b
C) a*b=b*a
D) a×b=a×b
  • 30. 31. A binary operation is associative, if?
A) a*b*c=a*c
B) c*a=a*b
C) (a*b)*c=a*(b*c)
  • 31. 32. If a binary operation is defined on set of real numbered by: a*b=a+2b, what is 2*3?
A) 8
B) 3
C) 9
D) 4
  • 32. 33. Log 100
A) 2
B) 1
C) 3
D) 0
  • 33. 34. Log 0.0001
A) 4
B) 3
C) -4
D) -3
  • 34. 35. Log 0.1
A) -1
B) 0
C) 1
D) -2
  • 35. 37. Log 0.01
A) 1
B) 2
C) -1
D) -2
  • 36. 38. Log 100000
A) -5
B) -4
C) 5
D) 4
  • 37. Log (10×0.1)
A) -1
B) 0.5
C) 0
D) 1
  • 38. 40 log (10÷0.1)
A) 0
B) 2
C) 1
D) -2
  • 39. 39. 2log10
A) -2
B) 1
C) 2
D) -1
  • 40. 40. 2log2 (4)
A) 2
B) 4
C) 1
D) 3
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