HSSC mathematics

The derivative of ln x with respect to x is:

• 1 ln x ÷ x
• 2 1/x
• 3 eˣ
• 4 x

The integral of eˣ with respect to x is:

• 1 eˣ⁺¹ + c
• 2 x eˣ + c
• 3 ln x + c
• 4 eˣ + c

The solutions of x² − 9 = 0 are:

• 1 3 only
• 2 3 and −3
• 3 0 and 9
• 4 9 and −9

The number of ways to choose 2 people from 5 is:

• 1 25
• 2 5
• 3 20
• 4 10

The eccentricity of a circle is:

• 1 0
• 2 1
• 3 Greater than 1
• 4 Between 0 and 1

The domain of f(x) = √(x − 2) is:

• 1 All real numbers
• 2 x > 0
• 3 x ≤ 2
• 4 x ≥ 2

The derivative of x² sin x is:

• 1 2x cos x
• 2 2x sin x − x² cos x
• 3 2x sin x + x² cos x
• 4 x² cos x

The sum of the integers from 1 to 100 is:

• 1 10100
• 2 5050
• 3 5100
• 4 5000

The magnitude of the vector 3i + 4j is:

• 1 25
• 2 5
• 3 7
• 4 12

The value of cos 60° is:

• 1 1/2
• 2 1
• 3 0
• 4 √3/2

The derivative of sin 2x with respect to x is:

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

The integral of sin x with respect to x is:

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

The limit of (1 − cos x) ÷ x² as x approaches 0 is:

• 1 2
• 2 0
• 3 1/2
• 4 1

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

• 1 6
• 2 8
• 3 4
• 4 7

The period of the function sin x is:

• 1 4π
• 2 2π
• 3 π
• 4 π/2

The value of 10C2 is:

• 1 100
• 2 90
• 3 45
• 4 20

The number of terms in the expansion of (a + b)⁸ is:

• 1 7
• 2 16
• 3 8
• 4 9

The eccentricity of the ellipse x²/25 + y²/9 = 1 is:

• 1 3/5
• 2 5/3
• 3 16/25
• 4 4/5

The slope of the tangent to y = x² at x = 3 is:

• 1 2
• 2 6
• 3 9
• 4 3

The area of the triangle with vertices (0, 0), (4, 0) and (0, 6) is:

• 1 12
• 2 6
• 3 10
• 4 24

The cross product i × j is equal to:

• 1 1
• 2 k
• 3 0
• 4 −k

The modulus of the complex number 5 − 12i is:

• 1 7
• 2 13
• 3 119
• 4 17

The determinant of the 3 × 3 identity matrix is:

• 1 1
• 2 3
• 3 −1
• 4 0

If 2ˣ⁺¹ = 16, then x is:

• 1 3
• 2 2
• 3 7
• 4 4

The domain of the function ln x is:

• 1 x > 0
• 2 All real numbers
• 3 x < 0
• 4 x ≥ 0

The derivative of ln (x² + 1) is:

• 1 1 ÷ (x² + 1)
• 2 2x ÷ (x² + 1)
• 3 2x
• 4 (x² + 1) ÷ 2x

The value of the integral of sin x from 0 to π is:

• 1 2
• 2 1
• 3 0
• 4 π

The inverse of the function f(x) = 2x + 3 is:

• 1 2x − 3
• 2 x ÷ 2 − 3
• 3 (x + 3) ÷ 2
• 4 (x − 3) ÷ 2

The sum of the squares of the roots of x² − 5x + 6 = 0 is:

• 1 5
• 2 13
• 3 11
• 4 25

The remainder when x³ − 2x + 1 is divided by x − 1 is:

• 1 1
• 2 0
• 3 2
• 4 −1

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

• 1 4
• 2 12
• 3 6
• 4 24

A card is drawn from a standard deck of 52 cards. The probability that it is a king is:

• 1 4/13
• 2 1/4
• 3 1/52
• 4 1/13

The slope of a line perpendicular to a line of slope 2 is:

• 1 −2
• 2 −1/2
• 3 2
• 4 1/2

The integral of 1 ÷ (1 + x²) with respect to x is:

• 1 sin⁻¹ x + c
• 2 1 ÷ x + c
• 3 tan⁻¹ x + c
• 4 ln (1 + x²) + c