MTS 101 PRE-EXAM

Front

What value of k will make the equation x²-(4+k)x +9=0 to have real roots?

Back

K > 2 or k < -10

Front

Which of the following is not one of the properties of real numbers?

Back

It satisfies the principle of mathematical Induction

Front

The range of the function f(x) = 3x-2 is?

Back

R = (negative infinity, infinity)

Front

Let A = {a, b, c, d, e, f}. Which of the following is true? (i) d ∈ A (ii) y ∈ A (iii) m ∉ A (iv) a ∈ A (v) e ∉ A

Back

i, iii, iv

Front

The fifth term of an arithmetic series is 43.35 and the fourteenth term is 72.6. What is the thirty-first term in the series?

Back

127.85

Front

Define the term 'real numbers'.

Back

Real numbers include all the rational and irrational numbers, encompassing integers, fractions, and decimals.

Front

What is the principle of mathematical induction?

Back

A method of mathematical proof used to prove statements for all natural numbers.

Front

What is an arithmetic series?

Back

An arithmetic series is the sum of the terms of an arithmetic sequence, where each term differs from the previous one by a constant.

Front

What is the formula for the nth term of an arithmetic sequence?

Back

a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What does it mean for a function to have a range of (negative infinity, infinity)?

Back

It means the function can take any real number as its output.