FSc mathematics

The derivative of sin x is:

• 1 −cos x
• 2 −sin x
• 3 cos x
• 4 tan x

The integral of cos x with respect to x is:

• 1 tan x + c
• 2 sin x + c
• 3 −sin x + c
• 4 cos x + c

The sum of the roots of 2x² − 6x + 1 = 0 is:

• 1 1/2
• 2 3
• 3 6
• 4 −3

The value of (1 + i)² is:

• 1 −2i
• 2 1 + 2i
• 3 2i
• 4 2

The coefficient of x² in the expansion of (1 + x)⁵ is:

• 1 5
• 2 15
• 3 10
• 4 20

The determinant of the matrix with rows (1, 2) and (3, 4) is:

• 1 −2
• 2 10
• 3 −10
• 4 2

The equation of the line with slope 2 that passes through the origin is:

• 1 y = 2x + 2
• 2 y = 2x
• 3 x = 2y
• 4 y = x + 2

The arithmetic mean between 4 and 16 is:

• 1 20
• 2 10
• 3 12
• 4 8

The limit of (1 + 1/x)ˣ as x approaches infinity is:

• 1 0
• 2 ∞
• 3 e
• 4 1

The radius of the circle x² + y² = 49 is:

• 1 3.5
• 2 14
• 3 7
• 4 49

The integral of 1/x with respect to x is:

• 1 −1/x² + c
• 2 x ln x + c
• 3 1/x² + c
• 4 ln |x| + c

The derivative of tan x with respect to x is:

• 1 −csc² x
• 2 cot x
• 3 sec² x
• 4 sec x tan x

The limit of (eˣ − 1) ÷ x as x approaches 0 is:

• 1 e
• 2 1
• 3 ∞
• 4 0

The sum of the first 10 odd numbers is:

• 1 55
• 2 90
• 3 100
• 4 110

The determinant of the matrix with rows (3, 1) and (2, 5) is:

• 1 15
• 2 −13
• 3 17
• 4 13

The coefficient of x³ in the expansion of (1 + x)⁶ is:

• 1 6
• 2 20
• 3 15
• 4 30

The distance between (1, 2) and (4, 6) is:

• 1 √7
• 2 7
• 3 25
• 4 5

The slope of the line 3x + 4y = 12 is:

• 1 3/4
• 2 −3/4
• 3 −4/3
• 4 4/3

The equation of the circle with centre (1, 2) and radius 3 is:

• 1 (x − 1)² + (y − 2)² = 3
• 2 x² + y² = 9
• 3 (x + 1)² + (y + 2)² = 9
• 4 (x − 1)² + (y − 2)² = 9

The value of tan 45° is:

• 1 1
• 2 √3
• 3 0
• 4 1/2

The product of the roots of x² − 7x + 10 = 0 is:

• 1 −7
• 2 10
• 3 −10
• 4 7

If 2ˣ = 32, then x is:

• 1 4
• 2 6
• 3 16
• 4 5

The value of log₂ 8 + log₂ 4 is:

• 1 5
• 2 6
• 3 4
• 4 12

The 20th term of the sequence 3, 7, 11, … is:

• 1 79
• 2 77
• 3 83
• 4 80

The number of different arrangements of the letters of the word MATH is:

• 1 16
• 2 12
• 3 24
• 4 4

A and B are independent events with P(A) = 0.3 and P(B) = 0.5. Then P(A and B) is:

• 1 0.8
• 2 0.15
• 3 0.35
• 4 0.2

The dot product of the vectors (2, 1) and (1, 3) is:

• 1 5
• 2 7
• 3 3
• 4 6

The area under the line y = x from x = 0 to x = 4 is:

• 1 4
• 2 8
• 3 2
• 4 16

If y = x³ − 3x, the value of dy/dx at x = 2 is:

• 1 9
• 2 3
• 3 12
• 4 6

The sum (3 + 2i) + (1 − 5i) is:

• 1 4 + 7i
• 2 4 + 3i
• 3 4 − 3i
• 4 2 + 7i

The value of sin 90° is:

• 1 1
• 2 √3/2
• 3 1/2
• 4 0

The set of all real numbers x with x² = 9 is:

• 1 {3, −3}
• 2 {3}
• 3 {−9, 9}
• 4 {9}