Math HL – Year 1
Chapter 1 Test - Practice
1.
2.
Name: __________________________________
Period: _____
An arithmetic sequence has 5 and 13 as its first two terms respectively.
(a)
Write down, in terms of n, an expression for the nth term, an.
(b)
Find the sum of all the terms of the sequence which are less than 400.
The common ratio of the terms in a geometric series is 2x.
(a)
State the set of values of x for which the sum to infinity of the series exists.
(b)
If the first term of the series is 35, find the value of x for which the sum to infinity is 40.
3.
(a)
The sum of the first six terms of an arithmetic series is 81. The sum of its first eleven terms is
231. Find the first term and the common difference.
(b)
The sum of the first two terms of a geometric series is 1 and the sum of its first four terms is
5. If all of its terms are positive, find the first term and the common ratio.
(c)
Using mathematical induction, prove that
n
 (r  1)2
r 1
 n2 n , n 
+
.
r 1
2
4.
5.
Use mathematical induction to prove n7  n is a multiple of 7. (Hint: You will need the binomial
theorem!)
Find the x12 and constant terms of the expression
1
3
  2x 
x

8
3
6.
There are six boys and five girls in a school tennis club. A team of two boys and two girls will be
selected to represent the school in a tennis competition. In how many different ways can the team
be selected?
7.
A committee of five people is to be selected from a class of 12 boys and 9 girls. How many such
committees include at least 1 girl?
8.
How many 3-digit numbers contain no zeros?
4
Formulas and Equations
General Term of an Arithmetic Sequence
an  a1  d (n  1)
Sum of Arithmetic Series
n
sn  (a1  an )
2
General Term of a Geometric Sequence
an  a1 r n1
Sum of a Finite Geometric Series
a1(1  r n )
sn 
1 r
Sum of an Infinite Converging Geometric Series
a1
sn 
,0  r  1
1 r
Permutations
n Pr 
n!
(n  r )!
Combinations
n
n!
C


n r
 r  (n  r )!r !
 
Binomial Theorem
 n  nr r
( a  b)     a b
r 0  r 
n
n
5