Maths Quiz

Which of the following is a rational number?

• √2

• √3

• 1.414213...

• 16/5

Which of the following expressions is correctly rationalized?

• (1)/(√3) → ((1 ⋅ √3))/(√3 ⋅ √3) =√3/3

• (1)/(√3) → √3/1

• (1)/(√3) → (1/3)

• (1)/(√3) → (1 ⋅ √(3^2 ))/√(3^2 )

If a real number’s decimal expansion is non-terminating but repeating, then the number is:

• A rational number

• An irrational number

• Always an integer

• Cannot be determined

The Fundamental Theorem of Arithmetic states that:

• Every prime is of the form 2n ± 1

• Every integer has an irrational factor

• Every composite number can be expressed as a product of primes in only one way (up to rearrangement)

• Every integer can be written as a fraction

Which of these is an irrational number?

• 0.75

• 22/7

• 3.14159... (π)

• 2/3

According to the Remainder Theorem, if a polynomial f(x) is divided by (x − a), the remainder is:

• f(a)

• x + a

• 0

• (x − a)

The Factor Theorem is a special case of the Remainder Theorem which says:

• If f(a) = 1, then (x − a) is a factor of f(x)

• If f(a) = 0, then (x − a) is a factor of f(x)

• If f(x) has no remainder, it is not divisible by (x − a)

• (x − a) always divides f(x) regardless of f(a)

If α and β are the zeros of the quadratic polynomial x² − 5x + 6, what is the value of α + β?

• 5

• −5

• 6

• −6

If α and β are zeros of x² + px + q = 0, the product of the zeros (α × β) is:

• p

• q

• −q

• q/(−p)

What is the remainder when f(x) = x³ − 3x² + 4x − 2 is divided by (x − 1)?

• 0

• −2

• x − 1

• −1