Advanced mathematics

The derivative of x³ with respect to x is:

• 1 3x
• 2 x⁴ ÷ 4
• 3 3x²
• 4 x²

The integral of 2x with respect to x is:

• 1 2 + c
• 2 x² + c
• 3 2x² + c
• 4 x + c

The roots of x² − 5x + 6 = 0 are:

• 1 −1 and 6
• 2 2 and 3
• 3 1 and 6
• 4 −2 and −3

The sum of the first 10 terms of an arithmetic progression with first term 2 and common difference 3 is:

• 1 160
• 2 150
• 3 155
• 4 145

The value of log₂ 32 is:

• 1 16
• 2 4
• 3 6
• 4 5

The value of sin 30° is:

• 1 1/2
• 2 √2/2
• 3 1
• 4 √3/2

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

• 1 −5
• 2 11
• 3 5
• 4 8

The slope of the line through (1, 2) and (3, 8) is:

• 1 6
• 2 3
• 3 4
• 4 2

The limit of (sin x) ÷ x as x approaches 0 is:

• 1 1
• 2 ∞
• 3 −1
• 4 0

The number of different arrangements of 4 distinct letters is:

• 1 12
• 2 24
• 3 8
• 4 16

The sum to infinity of the geometric series 1 + 1/2 + 1/4 + … is:

• 1 3/2
• 2 1
• 3 2
• 4 4

The distance between the points (0, 0) and (6, 8) is:

• 1 14
• 2 10
• 3 7
• 4 12

The derivative of cos x with respect to x is:

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

The integral of 3x² with respect to x is:

• 1 x³ + c
• 2 6x + c
• 3 x² + c
• 4 3x³ + c

The limit of (x² − 4) ÷ (x − 2) as x approaches 2 is:

• 1 0
• 2 ∞
• 3 2
• 4 4

Which expression equals cos 2θ?

• 1 1 − 2 sin²θ
• 2 1 + 2 sin²θ
• 3 2 sin θ cos θ
• 4 sin²θ − cos²θ

The 12th term of an arithmetic progression with first term 5 and common difference 4 is:

• 1 45
• 2 53
• 3 48
• 4 49

The 8th term of the geometric progression 3, 6, 12, … is:

• 1 192
• 2 96
• 3 768
• 4 384

The value of log₁₀ 1000 is:

• 1 10
• 2 100
• 3 3
• 4 2

If log₃ x = 4, then x is:

• 1 81
• 2 12
• 3 64
• 4 7

If A has rows (1, 2) and (0, 1), then A² has rows:

• 1 (1, 4) and (0, 1)
• 2 (1, 2) and (0, 1)
• 3 (2, 4) and (0, 2)
• 4 (1, 4) and (0, 2)

The inverse of the matrix with rows (2, 1) and (1, 1) has rows:

• 1 (1, 1) and (1, 2)
• 2 (2, −1) and (−1, 1)
• 3 (1, −1) and (−1, 2)
• 4 (−1, 1) and (1, −2)

The distance of the point (3, 4) from the origin is:

• 1 5
• 2 25
• 3 7
• 4 12

The midpoint of (2, 4) and (6, 10) is:

• 1 (4, 7)
• 2 (3, 5)
• 3 (4, 6)
• 4 (8, 14)

The equation of the circle with centre at the origin and radius 5 is:

• 1 x + y = 25
• 2 x² − y² = 25
• 3 x² + y² = 25
• 4 x² + y² = 5

The focus of the parabola y² = 8x is:

• 1 (8, 0)
• 2 (4, 0)
• 3 (0, 2)
• 4 (2, 0)

The number of diagonals of a hexagon is:

• 1 15
• 2 12
• 3 9
• 4 6

The value of 6C3 is:

• 1 18
• 2 10
• 3 20
• 4 30

The probability that the sum of two dice is 7 is:

• 1 7/36
• 2 1/12
• 3 1/7
• 4 1/6

Two fair coins are tossed. The probability of at least one head is:

• 1 3/4
• 2 1/4
• 3 1/2
• 4 2/3

The modulus of the complex number 3 + 4i is:

• 1 5
• 2 √7
• 3 7
• 4 25

The product (2 + 3i)(2 − 3i) is:

• 1 −5
• 2 4 + 9i
• 3 −13
• 4 13

The discriminant of x² − 6x + 9 = 0 is:

• 1 −36
• 2 36
• 3 18
• 4 0

The product of the roots of 2x² − 5x + 3 = 0 is:

• 1 2/3
• 2 −3/2
• 3 3/2
• 4 5/2

The solution of |x| < 3 is:

• 1 x > −3
• 2 −3 < x < 3
• 3 x < 3
• 4 x < −3 or x > 3

The sum of the coefficients in the expansion of (1 + x)⁴ is:

• 1 8
• 2 32
• 3 16
• 4 4

The dot product of (1, 2, 3) and (4, −5, 6) is:

• 1 12
• 2 0
• 3 21
• 4 −12

The sum of the integers from 1 to 20 is:

• 1 210
• 2 420
• 3 200
• 4 190

The value of the integral of x from 0 to 1 is:

• 1 0
• 2 1/2
• 3 1
• 4 2

The derivative of e²ˣ with respect to x is:

• 1 e²ˣ ÷ 2
• 2 2xe²ˣ
• 3 e²ˣ
• 4 2e²ˣ

The angle in radians equal to 180° is:

• 1 π
• 2 2π
• 3 π/2
• 4 π/4