Challenging Questions Mathematics – Compulsory Part Learning Unit: Exponential and logarithmic functions Question M0-03-01 Simplify the following expression and express your answer with positive indices: $$ \sqrt[4]{a^{-3}\sqrt[3]{a^{-2}\sqrt{a^{-1}}}} $$ # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-10 A person takes out a loan of $100,000 from a bank and agrees to repay it in 24 equal monthly installments. The bank charges an annual interest rate of 6%, which is applied monthly on the remaining balance... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-09 Consider three sequences \(f(n)\), \(g(n)\) and \(h(n)\), # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-08 Consider a sequence with the first term \(a\) and the final term \(b\), # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-07 Consider a geometric sequence \(T_n=ar^{n-1}\) and the series of \(n\) terms \(S_n=\frac{a(r^n-1)}{r-1}\) where \(r \neq 1\), # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-06 # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-05 Find the minimum number of terms of a geometric sequence \(1, \frac{3}{2}, \frac{9}{4} \,……\,\) such that the sum is greater than \(1000\). # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-04 The first, third, and 13th terms of an arithmetic sequence form a geometric sequence. Find the common ratio of the geometric sequence. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-03 In an arithmetic sequence, the sum of the first \(n\) terms is equal to the sum of the next \(n+1\) terms, where \(n \geq 1\). Which term in this sequence is equal to \(0\)? # More challenging questions... » read more
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-02 If \(a^2\), \(b^2\) and \(c^2\) form an arithmetic sequence where \(a\), \(b\) and \(c\) are real numbers, show that \(\frac{1}{b+c}\), \(\frac{1}{c+a}\) and \(\frac{1}{a+b}\) also form an arithmetic sequence. # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: Arithmetic and geometric sequences and their summations Question M0-07-01 Consider a sequence \(a, b, c, \ldots \ldots\) # More challenging questions will be updated # Answer
Challenging Questions Mathematics – Compulsory Part Learning Unit: More about polynomials Question M0-04-10 \( (x – a) \) is a common factor of \( f(x) \) and \( g(x) \). # More challenging questions will be updated # Answer