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01 Set, function, Polynomial function
1. Let ๎ be the set of letters in the
word VENN and ๎ be the set of
letters in the word DIAGRAM
(a) List the elements of ๎ and ๎
(b) Find
and
(c) Find ๎โฉ ๎
(d) Decide whether the statement is true
of false
โ
ฒ. ๎ฒ
At a conference, the 58 delegates speak
many different languages. 28 speak
Arabic, 27 speak Chinese, and 39 speak
English. 12 speak Arabic and Chinese,
16 speak both Chinese and English, and
17 speak Arabic and English.
2 speak all three languages. How many
delegates speak:
(a) Chinese only
(b) none of these languages
(c) neither Arabic nor Chinese?
- This Venn diagram consists of three
overlapping circles A, B, and C. List
the letters in set
(a)
(b) ๎
(c) ๎โฉ ๎
(d) ๎โฉ ๎โฉ ๎
A platform diving squad of 25 has 18
members who dive from 10 m, and 17
who dive from 4 m. How many dive
from both platforms?
In a factory, 56 people work on the
assembly line. 47 work day shifts and 29
work night shifts. How many work both
day shifts and night shifts?
There are 38 stalls in a marketplace. 21
stalls sell food, 14 stalls sell craft, and 7
stalls sell neither food nor craft. Find
the number of stalls which sell:
(a) both food and craft
(b) food or craft but not both.
From the selection of 86 movies on a
plane, Sandra has seen 13 and Robert
has seen 14. 69 of the movies have been
seen by neither. Find the number of
movies seen by:
(a) both Sandra and Robert
(b) Robert but not Sandra.
In a year group of 63 students, 22 study
Biology, 26 study Chemistry, and 25
study Physics. 18 study both Physics and
Chemistry, 4 study both Biology and
Chemistry, and 3 study both Physics and
Biology. 1 student studies all three
subjects. How many students study:
(e) Zero; -1, multiplicity 1
zero; 3, multiplicity 2; Degree 3
(f) Zero; -2, multiplicity 2
zero: 4, multiplicity 1, Degree 3
For each polynomial function;
(a) List each zero and its multiplicity
(b) Sketch the graph of ๎ช
, showing its
intercepts and behavior at the zeros.
๎ต
๎ต
๎ถ
๎ต
๎ถ
๎ต
๎ต
๎ต
๎ต
(19~24) Construct a polynomial function
that might have the given graph (more
than one answer may be possible)
- Which of the following is an
equation of the line A graphed in
the xy-plane that passes through the
point ๎๎ ๎ด๎ ๎ถ๎๎ธ๎
and is perpendicular
to the line B whose equation is
- Which of the following equations
represents a line in the xy-plane
with an x-intercept at ๎๎ ๎ต๎ ๎ฝ๎
and a
slope of 4?
- Which of the following equations
represents a line in the xy-plane
with an x-intercept at
and a
y-intercept at
- Two lines graphed in the xy-plane
have the equations ๎ต๎ผ
๎ต๎ฝ and
๎ถ, where ๎ฏ is a constant. For
what value of
will the two lines be
perpendicular?
- In the xy-plane, line k intersects the
y-axis at the point
and
passes through the point
, If
the point
lies on like k, what
is the value of ๎ป?
- Line p is defined by ๎ท๎ฝ
๎น, line r
is perpendicular to line p in
xy-plane. What is the slope of line
r?
- Line
is defined by
Line
is perpendicular of like
in
the xy-plane. What is the slope of
line ๎ฎ?
- The graph of the equation
is a line in the xy-plane, where a
and k are constant. If the line
contains the points
and
, what is the value of k?
- In the xy-plane, line ๎ฐ passes
through the point
and is
parallel to the line represented by
the equation
. If line
also
passes through the point ๎๎ถ๎ ๎จ๎
, what
is the value of ๎จ๎
