General Mathematics I — android Past Questions

University of Ilorin MTH101: 39 questions.

Topics: Trigonometry Function of Angle, Set Theory and Venn Diagram, Binomial Theorem, Complex Number, Quadratic Equation, Number System, Sequence and Series

1. Given \( U = \{1,2,3,4,5,...,15\} \), \( A = \{1,2,3,4,5,6\} \), and \( B = \{2,5,7,13,5\} \), find \( n(A \cup B) \).
   1. 6
   2. 7
   3. 8
   4. 9
2. Given \( M = \{a,b,c,d,e,f\} \), \( P = \{b,c,k,f,i,j\} \), and \( N = \{e,f,h,i,j,g\} \), find \( M \cap (N \cap P) \).
   1. {b}
   2. {c}
   3. {f}
   4. {e}
3. Simplify \( \sin 5x + \sin 3x \).
   1. \( 2 \sin 4x \cos x \)
   2. \( 2 \sin x \cos 4x \)
   3. \( \sin 8x \)
   4. \( \cos 2x \sin 3x \)
4. Simplify \( \frac{1 - \tan^2 x}{1 + \tan^2 x} \).
   1. \( \sin 2x \)
   2. \( \cos 2x \)
   3. \( \tan 2x \)
   4. \( \cot 2x \)
5. Given \( x^2 - 4x + 3 = 0 \) with roots \( a \) and \( b \), find \( a^2 - b^2 \).
   1. 6
   2. 8
   3. 10
   4. 12
6. Expand \( (1 + 4x)^3 \).
   1. \( 1 + 12x + 48x^2 + 64x^3 \)
   2. \( 1 + 12x + 48x^2 + x^3 \)
   3. \( 1 + 4x + 16x^2 + 64x^3 \)
   4. \( 1 + 3x + 6x^2 + 4x^3 \)
7. Simplify \( (2 - i)^3 \).
   1. \( 2 - 11i \)
   2. \( 2 - 13i \)
   3. \( 8 - i \)
   4. \( 6 - 3i \)
8. Convert \( Z = (2, 45^\circ) \) to Cartesian form.
   1. \( \sqrt{2} + i \sqrt{2} \)
   2. \( 1 + i \)
   3. \( 2 + 2i \)
   4. \( 2 \cos 45^\circ + i 2 \sin 45^\circ \)
9. In the expansion of \( (3u + 2x)^4 \), what is the coefficient of \( u^3 x \)?
   1. 216
   2. 96
   3. 144
   4. 108
10. What is the expression for \( \sin 3A \)?
    1. \( 3 \sin A - 4 \sin^3 A \)
    2. \( 4 \sin^3 A - 3 \sin A \)
    3. \( \sin A \cos^2 A \)
    4. \( 3 \cos A - \sin A \)
11. If \( Z = -3 \), what is its polar form?
    1. \( (3, 0^\circ) \)
    2. \( (3, 180^\circ) \)
    3. \( (-3, 180^\circ) \)
    4. \( (3, -90^\circ) \)
12. Given \( P = \{a,b,c,d,e,d\} \) and \( Q = \{b,d,e\} \), with universal set \( U = \{a,b,c,d,...,i\} \), find \( P' \cap Q' \).
    1. \( \{g,h,i\} \)
    2. \( \{a,c\} \)
    3. \( \{f,g,h,i\} \)
    4. \( \{b,d,e\} \)
13. Natural Numbers are also known as _____.
    1. Counting Numbers
    2. Whole Numbers
    3. Integers
    4. Rational Numbers
14. The law \( (A \cup B)' = A' \cap B' \) is known as _____.
    1. De Morgan's Theorem
    2. Distributive Law
    3. Associative Law
    4. Commutative Law
15. Given \( x^2 - 2x + 4 = 0 \) with roots \( P \) and \( Q \), find \( P + iQ \).
    1. \( 1 + i \sqrt{3} \)
    2. \( \sqrt{3} + i \)
    3. \( 2 + i \sqrt{2} \)
    4. \( 1 + i \)
16. Find three consecutive terms of an A.P. whose sum is 3 and product is -15.
    1. -3, 1, 5
    2. -1, 1, 3
    3. 2, 3, 4
    4. -5, 0, 5
17. Find the sum of multiples of 3 between 3 and 100.
    1. 1683
    2. 1665
    3. 1700
    4. 1650
18. Find \( i^{17} \).
    1. \( i \)
    2. \( -i \)
    3. \( 1 \)
    4. \( -1 \)
19. If \( M = \{3,3\} \), find \( n(M) \).
    1. 1
    2. 2
    3. 3
    4. 0
20. Simplify \( \frac{\csc A}{\sec A} \).
    1. \( \cot A \)
    2. \( \tan A \)
    3. \( \sin A \)
    4. \( \cos A \)
21. What is the expansion for \( a^3 + b^3 \)?
    1. \( (a + b)^3 - 3ab(a + b) \)
    2. \( (a - b)^3 + 3ab(a - b) \)
    3. \( a^3 + b^3 + 3ab \)
    4. \( (a + b)(a^2 - ab + b^2) \)
22. In the expansion of \( (1 + 4x)^5 \), what is the coefficient of \( x^3 \)?
    1. 160
    2. 320
    3. 640
    4. 1280
23. Simplify \( 2(\cos^2 A + \sin^2 A) \).
    1. 1
    2. 2
    3. 0
    4. \( \cos 2A \)
24. Given \( (X + P^2)^2 + 3P - 2 = 0 \) has equal roots, find \( P \).
    1. 1
    2. 2
    3. 0
    4. -1
25. What is \( A \cap A \)?
    1. \( A \)
    2. \( \emptyset \)
    3. \( U \)
    4. \( A' \)
26. Convert \( Z = (2, 25^\circ) \) to rectangular form.
    1. \( 2(\cos 25^\circ + i \sin 25^\circ) \)
    2. \( 2 \cos 25^\circ + i 2 \sin 25^\circ \)
    3. \( \cos 25^\circ + i \sin 25^\circ \)
    4. \( 2 + i 25 \)
27. Given \( A = \{2,4,5,1\} \), what is the cardinality of the set?
    1. 4
    2. 5
    3. 3
    4. 2
28. Find the third term in the expansion of \( \sqrt{1 + 2x} \).
    1. \( -\frac{1}{2}x^2 \)
    2. \( \frac{1}{2}x^2 \)
    3. \( -x^2 \)
    4. \( x^2 \)
29. Simplify \( \tan A + \cot A \).
    1. \( 2 \csc 2A \)
    2. \( \sec A \csc A \)
    3. \( \sin 2A \)
    4. \( \cos 2A \)
30. Simplify \( (\cos A - \sin A)(\cos A + \sin A) \).
    1. \( \cos 2A \)
    2. \( \sin 2A \)
    3. \( \tan 2A \)
    4. \( \cot 2A \)
31. If \( \sin A = \frac{a}{b} \), what is the value of \( \tan A \)?
    1. \( \frac{a}{\sqrt{b^2 - a^2}} \)
    2. \( \frac{a}{b^2 - a^2} \)
    3. \( \frac{b}{\sqrt{b^2 - a^2}} \)
    4. \( \frac{a^2}{b} \)
32. Rational and irrational numbers belong to which set of numbers?
    1. Real Numbers
    2. Integers
    3. Natural Numbers
    4. Whole Numbers
33. If \( A \cap B = \{\} \), it means \( A \) and \( B \) are _____.
    1. Disjoint
    2. Equal
    3. Subsets
    4. Complements
34. Simplify \( \cos 4x - \cos 2x \).
    1. \( -2 \sin 3x \sin x \)
    2. \( 2 \sin 3x \cos x \)
    3. \( \cos 6x \)
    4. \( \sin 2x \)
35. Given \( x^2 + kx + 10 = 0 \) with roots \( a \) and \( b \), and \( a^2 + b^2 = 29 \), find \( k \).
    1. 7
    2. 5
    3. -7
    4. -5
36. Given \( x^2 + kx - 10 = 0 \) with roots \( a \) and \( b \), and \( a^2 + b^2 = 29 \), find \( k \).
    1. 3
    2. -3
    3. 7
    4. -7
37. Expand \( (x + 2y)^5 \).
    1. \( x^5 + 10x^4 y + 40x^3 y^2 + 80x^2 y^3 + 80x y^4 + 32y^5 \)
    2. \( x^5 + 5x^4 y + 10x^3 y^2 + 10x^2 y^3 + 5x y^4 + y^5 \)
    3. \( x^5 + 2x^4 y + 4x^3 y^2 + 8x^2 y^3 + 16x y^4 + 32y^5 \)
    4. \( x^5 + 10x^4 y + 20x^3 y^2 + 40x^2 y^3 + 80x y^4 + 32y^5 \)
38. Expand \( (1 - x)^{1/2} \) to the third term.
    1. \( 1 - \frac{1}{2}x - \frac{1}{8}x^2 \)
    2. \( 1 + \frac{1}{2}x + \frac{1}{8}x^2 \)
    3. \( 1 - \frac{1}{2}x + \frac{1}{8}x^2 \)
    4. \( 1 - x + x^2 \)
39. What is the expression for the Idempotent Law in set theory?
    1. \( A \cup A = A \) and \( A \cap A = A \)
    2. \( A \cup \emptyset = A \)
    3. \( A \cap \emptyset = \emptyset \)
    4. \( A \cup U = U \)

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