REVIEW SHEET PAPER-1 GRADE 11 FIRST TERM EXAMINATION
1.
Consider the functions given below.
f(x) = 2x + 3
1
g(x) = , x ≠ 0
x
(a)
(b)
2.
(i)
Find (g ○ f)(x) and write down the domain of the function.
(ii)
Find (f ○ g)(x) and write down the domain of the function.
Find the coordinates of the point where the graph of y = f(x) and the graph of
y = (g–1 ○ f ○ g)(x) intersect.
The cumulative frequency graph below represents the weight in grams of 80 apples picked
from a particular tree.
(a)
Estimate the
(i)
median weight of the apples;
(ii)
30th percentile of the weight of the apples.
(b)
3.
Estimate the number of apples that weigh more than 110 grams.
Shown below are the graphs of y = f(x) and y = g(x).
If (f  g)(x) = 3, find all possible values of x.
4.
Let f (x) =
4
, x   2 and g (x) = x − 1.
x2
If h = g ◦ f, find
(a)
h (x);
(b)
5.
6.
h−1 (x), where h−1 is the inverse of h.
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.
A geometric sequence u1, u2, u3, ... has u1 = 27 and a sum to infinity of
(a)
81
.
2
Find the common ratio of the geometric sequence.
An arithmetic sequence v1, v2, v3, ... is such that v2 = u2 and v4 = u4.
N
(b)
Find the greatest value of N such that
v
n
0.
n 1
7.
(a)
(b)
Consider the set of numbers a, 2a, 3a, ..., na where a and n are positive integers.
a(n  1)
.
2
(i)
Show that the expression for the mean of this set is
(ii)
Let a = 4. Find the minimum value of n for which the sum of these numbers
exceeds its mean by more than 100.
Consider now the set of numbers x1, ... , xm, y1, ... , y1, ... , yn where xi = 0 for i = 1, ... ,
m and yi = 1 for i = 1, ... , n.
(i)
Show that the mean M of this set is given by
S by
(ii)
n
and the standard deviation
mn
mn
.
mn
Given that M = S, find the value of the median.
8.
The mean of the first ten terms of an arithmetic sequence is 6. The mean of the first twenty
terms of the arithmetic sequence is 16. Find the value of the 15th term of the sequence.
9.
An arithmetic sequence has first term a and common difference d, d ≠ 0.
The 3rd, 4th and 7th terms of the arithmetic sequence are the first three terms of a geometric
sequence.
(a)
3
Show that a =  d .
2
(b)
10.
11.
12.
13.
14.
15.
Show that the 4th term of the geometric sequence is the 16th term of the arithmetic
sequence.
16.
17.
18.
19.
20.