IB MATH STUDIES SL 1: IB-Style Review Questions for Test
Arithmetic and Geometric Sequences and Series, Compound Interest, Exponential Equations
1.
The graph below shows the temperature of a liquid as it is cooling.
y
100
90
80
Temperature (°C)
70
60
50
40
30
20
10
0
5
10
15
20
25
30
35
40
Time in minutes
(a)
Write down the temperature after 5 minutes.
(b)
After how many minutes is the temperature 50°C?
45
50
55
60 x
The equation of the graph for all positive x can be written in the form y = 100(5–0.02x).
(c)
Calculate the temperature after 80 minutes.
(d)
Write down the equation of the asymptote to the curve.
(Total 8 marks)
2.
Given the arithmetic sequence: u1 = 124, u2 = 117, u = 110, u4 = 103, …
(a)
Write down the common difference of the sequence.
(b)
Calculate the sum of the first 50 terms of the sequence.
uk is the first term in the sequence that is negative.
(c)
Find the value of k.
(Total 6 marks)
3.
The first term of an arithmetic sequence is 7 and the sixth term is 22. Find
(a)
the common difference;
(b)
the twelfth term;
(c)
the sum of the first 100 terms.
(Total 6 marks)
4.
Consider the geometric sequence 16, 8, a, 2, b, …
(a)
Write down the common ratio.
(b)
Write down the value of
(c)
(i)
a;
(ii)
b.
The sum of the first n terms is 31.9375. Find the value of n.
(Total 6 marks)
5.
Consider the geometric sequence 8, a, 2,… for which the common ratio is
(a)
Find the value of a.
(b)
Find the value of the eighth term.
(c)
Find the sum of the first twelve terms.
1
.
2
(Total 6 marks)
6.
Eva invests USD2000 at a nominal annual interest rate of 8 % compounded half-yearly.
(a)
Calculate the value of her investment after 5 years, correct to the nearest dollar.
Toni invests USD1500 at an annual interest rate of 7.8 % compounded yearly.
(b)
Find the number of complete years it will take for his investment to double in value.
(Total 6 marks)
7.
A basketball is dropped vertically. It reaches a height of 2 m on the first bounce. The height of
each subsequent bounce is 90% of the previous bounce.
(a)
What height does it reach on the 8th bounce?
(b)
What is the total vertical distance travelled by the ball between the first and sixth time the
ball hits the ground?
(Total 6 marks)