Practice Math
1.
The nth term of an arithmetic sequence is given by un = 5 + 2n. (a) Write down the common difference.
(1)
(b)
(i) (ii)
Given that the nth term of this sequence is 115, find the value of n. For this value of n, find the sum of the sequence.
(5) (Total 6 marks)
2.
A sum of $ 5000 is invested at a compound interest rate of 6.3 % per annum. (a) Write down an expression for the value of the investment after n full years.
(1)
(b)
What will be the value of the investment at the end of five years?
(1)
(c)
The value of the investment will exceed $ 10 000 after n full years. (i) (ii) Write down an inequality to represent this information. Calculate the minimum value of n.
(4) (Total 6 marks)
3.
(a)
Consider the geometric sequence −3, 6, −12, 24, …. (i) (ii) Write down the common ratio. Find the 15th term.
(3)
Consider the sequence x − 3, x +1, 2x + 8, ….
IB Questionbank Maths SL
1
(b)
When x = 5, the sequence is geometric. (i) (ii) Write down the first three terms. Find the common ratio.
(2)
(c)
Find the other value of x for which the sequence is geometric.
(4)
(d)
For this value of x, find (i) (ii) the common ratio; the sum of the infinite sequence.
(3) (Total 12 marks)
4.
Clara organizes cans in triangular piles, where each row has one less can than the row below. For example, the pile of 15 cans shown has 5 cans in the bottom row and 4 cans in the row above it.
(a)
A pile has 20 cans in the bottom row. Show that the pile contains 210 cans.
(4)
(b)
There are 3240 cans in a pile. How many cans are in the bottom row?
(4)
IB Questionbank Maths SL
2
(c)
(i)
There are S cans and they are organized in a triangular pile with n cans in the bottom row. Show that n2 + n − 2S = 0. Clara has 2100 cans. Explain why she cannot organize them in a triangular pile.
(6) (Total 14 marks)
(ii)
5.
Ashley and Billie are swimmers training for a competition. (a) Ashley
The nth term of an arithmetic sequence is given by un = 5 + 2n. (a) Write down the common difference.
(1)
(b)
(i) (ii)
Given that the nth term of this sequence is 115, find the value of n. For this value of n, find the sum of the sequence.
(5) (Total 6 marks)
2.
A sum of $ 5000 is invested at a compound interest rate of 6.3 % per annum. (a) Write down an expression for the value of the investment after n full years.
(1)
(b)
What will be the value of the investment at the end of five years?
(1)
(c)
The value of the investment will exceed $ 10 000 after n full years. (i) (ii) Write down an inequality to represent this information. Calculate the minimum value of n.
(4) (Total 6 marks)
3.
(a)
Consider the geometric sequence −3, 6, −12, 24, …. (i) (ii) Write down the common ratio. Find the 15th term.
(3)
Consider the sequence x − 3, x +1, 2x + 8, ….
IB Questionbank Maths SL
1
(b)
When x = 5, the sequence is geometric. (i) (ii) Write down the first three terms. Find the common ratio.
(2)
(c)
Find the other value of x for which the sequence is geometric.
(4)
(d)
For this value of x, find (i) (ii) the common ratio; the sum of the infinite sequence.
(3) (Total 12 marks)
4.
Clara organizes cans in triangular piles, where each row has one less can than the row below. For example, the pile of 15 cans shown has 5 cans in the bottom row and 4 cans in the row above it.
(a)
A pile has 20 cans in the bottom row. Show that the pile contains 210 cans.
(4)
(b)
There are 3240 cans in a pile. How many cans are in the bottom row?
(4)
IB Questionbank Maths SL
2
(c)
(i)
There are S cans and they are organized in a triangular pile with n cans in the bottom row. Show that n2 + n − 2S = 0. Clara has 2100 cans. Explain why she cannot organize them in a triangular pile.
(6) (Total 14 marks)
(ii)
5.
Ashley and Billie are swimmers training for a competition. (a) Ashley