- 1. 1. What is the diameter of a circle of area 77cm²? ( Take π = 22/7)
A) √2/7 cm
B) 7 cm
C) 3 ½ cm
D) 7√2 cm
- 2. 2. An arc of a circle of radius 8cm substends an angle of 85⁰ at the centre of the circle. Find the length of the major arc. (Take π = 22/7)
A) 272.45 cm
B) 289.62 cm
C) 11.87 cm
D) 38.41cm
- 3. 3. The angle of a sector of a circle of radius 5.5 cm is 60⁰. What is the perimeter of the sector? ( Take π = 22/7)
A) 30.25 cm
B) 5. 76 cm
C) 16.76 cm
D) 11.26 cm
- 4. 4. Find the value of SinA + CosA if CosA = 3/5
A) 1.5
B) 5.0
C) 7.0
D) 1.4
- 5. 5. Express 1 + cos 30⁰ ÷ 1 - sin 30⁰ in surd form
A) 2 + √3
B) √3 - 2
C) 2√3 + 2√2
D) 2 √3 + √2
- 6. 6. The tangent of 135⁰ has the value
A) -½
B) 1
C) -1
D) ½
- 7. 7. Find the values of x, for which 2cos x + 1 = 0, 0⁰ ≤ x ≤ 360⁰
A) 120⁰, 240⁰
B) 90⁰, 270⁰
C) - 60⁰, 60⁰
D) 0⁰, 180⁰
- 8. 8. Find the value of z in the diagram above
A) √3
B) 6√3
C) 3√3
D) 2√3
- 9. 9. Given the statements: p: the subject is difficult q: I will do my best. Which of the following is equivalent to `` Although the subject is difficult, I will do my best``?
A) p~q
B) p ^ q
C) pvq
D) ~pvq
- 10. 10. What is the negation of the sentence " John is older than me"
A) John is not older than me
B) John is my age mate
C) John is younger than me
D) John is neither older than me
- 11. 11. Which of the following is a valid conclusion from the premise: " Nigerian footballers are good footballers"?
A) Joseph is a good footballer therefore he is a Nigerian footballer
B) Joseph plays football in Nigeria therefore he is a good footballer
C) Joseph is a Nigerian footballer therefore he is a good footballer
D) Joseph plays good football therefore he is a Nigerian footballer
- 12. 12. If p, q, r stands for; p: Birds fly; q: The sky is blue; r: The grass is green. What is the symbolic representation of: If the grass is green and the sky is not blue then the birds do not fly?
A) (r v ~q) <---> ~ p
B) (r ^ ~ q) ---> ~ p
C) (r ^ ~ q) <---> ~ p
D) (r ^ q) ---> ~ p
- 13. 13. A cone is formed by folding a major sector of a circle having angle 220⁰ at the he centre. Calculate the circumference of the base of the cone of the diameter of the circle is 14cm, correct to 1 decimal place.
A) 4.3cm
B) 5.5cm
C) 26.9cm
D) 30. 0cm
- 14. 14. Calculate the volume of a cone with radius 3cm and perpendicular height 3.5cm (Take π = 22/7)
A) 3.3cm³
B) 33.0cm³
C) 66.0cm³
D) 65.0cm³
- 15. 15. Find the total surface area of a cone radius 7cm and slant height 8cm.
A) 77cm²
B) 56cm²
C) 330cm²
D) 110cm²
- 16. 16. Find the volume of a right pyramid of square base 6cm and 42cm height
A) 504cm³
B) 678cm³
C) 572cm³
D) 324cm³
- 17. 17. Find the dimensions of a rectangle whose perimeter and area are 46cm and 112cm² respectively
A) 17cm by 6cm
B) 12cm by 6cm
C) 14cm by 9cm
D) 16cm by 7cm
- 18. 18. The area of a circle is 81πcm². Find the diameter of the circle.
A) 13cm
B) 9cm
C) 18cm
D) 7cm
- 19. 19. In the diagram above, ML//PQ and NP//QR. If <LMN = 40⁰ and <MNP = 55⁰, find <PQR
A) 40⁰
B) 25⁰
C) 15⁰
D) 35⁰
- 20. 20. The values of three angles at a point are 3y - 45⁰, y + 25⁰ and y⁰. Find the value of y.
A) 58⁰
B) 40⁰
C) 76⁰
D) 68⁰
- 21. 21. In the diagram, /XR/= 4cm, /RZ/= 12cm, /SR/=n, /YZ/= m and SR//YZ. Find m in terms of n.
A) m = 3n
B) m = 5n
C) m = 4n
D) m = 2n
- 22. 22. In the diagram above, name the triangle which is congruent to ∆XYZ
A) ∆TYS
B) ∆TYZ
C) ∆XYS
D) ∆XYZ
- 23. 23. Which of the following triangles are congruent?
A) I and IV only
B) II and III only
C) II and IV only
D) I and II only
- 24. 24. What is the ratio x : y in the figure above?
A) 3 : 7
B) 3 : 4
C) 4 : 3
D) 4 : 7
- 25. 25. Find the value of x in the diagram
A) 50⁰
B) 70⁰
C) 80⁰
D) 60⁰
- 26. 26. In the above figure, BA//DE. Reflex <CDE = 320⁰, <CBA =50⁰. Find the value of x.
A) 320⁰
B) 130⁰
C) 140⁰
D) 270⁰
- 27. 27. What is the value of m in the diagram?
A) 40⁰
B) 30⁰
C) 20⁰
D) 50⁰
- 28. 28. In proving the congruence of two triangles, which of the following is NOT important?
A) Three angles
B) Two sides and the included angles
C) Right-angle, hypotenuse and another side
D) Two angles and a side
E) Three sides
- 29. 29. Sin 30⁰ = Cos 60⁰ =
A) 0.5
B) 0.5
C) 1/2
D) 1/2
- 30. 30. Cosine falls on which quadrant?
A) 4th
B) Four
C) 4
D) Fourth
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