This document appears to be a mathematics exam containing multiple choice questions testing concepts related to coordinate geometry and functions. Specifically, it contains 50 questions testing knowledge of coordinates, ordered pairs, quadrants, relations, functions, function notation and operations including composition, addition, subtraction, multiplication, and division of functions. It provides context for students to demonstrate their understanding of foundational concepts in coordinate geometry and functions.
Math 2318 - Test 3In this test we will try something differe.docxandreecapon
Math 2318 - Test 3
In this test we will try something different. The answers are provided, your job is to show the work in how to get that
solution. On problem 1 only A is a vector space. You will show why it is a vector space but you will also show why B
and C are not vector spaces. On question 2 only V is a vector space. You will show why it is a vector space and you
will also show why W and U are not vector spaces.
Solve the problem.
1) Determine which of the following sets is a subspace of Pn for an appropriate value of n.
A: All polynomials of the form p(t) = a + bt2, where a and b are in ℛ
B: All polynomials of degree exactly 4, with real coefficients
C: All polynomials of degree at most 4, with positive coefficients
A) A and B B) C only C) A only D) B only
1)
2) Determine which of the following sets is a vector space.
V is the line y = x in the xy-plane: V = x
y
: y = x
W is the union of the first and second quadrants in the xy-plane: W = x
y
: y ≥ 0
U is the line y = x + 1 in the xy-plane: U = x
y
: y = x + 1
A) U only B) V only C) W only D) U and V
2)
Find a matrix A such that W = Col A.
3) W =
3r - t
4r - s + 3t
s + 3t
r - 5s + t
: r, s, t in ℛ
A)
0 3 -1
4 -1 3
0 1 3
1 -5 1
B)
3 0 -1
4 -1 3
0 1 3
1 -5 1
C)
3 -1
4 3
1 3
1 -5
D)
3 4 0 1
0 -1 1 -5
-1 3 3 1
3)
Determine if the vector u is in the column space of matrix A and whether it is in the null space of A.
4) u =
5
-3
5
, A =
1 -3 4
-1 0 -5
3 -3 6
A) In Col A and in Nul A B) In Col A, not in Nul A
C) Not in Col A, in Nul A D) Not in Col A, not in Nul A
4)
Use coordinate vectors to determine whether the given polynomials are linearly dependent in P2. Let B be the standard
basis of the space P2 of polynomials, that is, let B = 1, t, t2 .
5) 1 + 2t, 3 + 6t2, 1 + 3t + 4t2
A) Linearly dependent B) Linearly independent
5)
Find the dimensions of the null space and the column space of the given matrix.
6) A = 1 -5 -4 3 0
-2 3 -1 -4 1
A) dim Nul A = 2, dim Col A = 3 B) dim Nul A = 4, dim Col A = 1
C) dim Nul A = 3, dim Col A = 2 D) dim Nul A = 3, dim Col A = 3
6)
1
Solve the problem.
7) Let H =
a + 3b + 4d
c + d
-3a - 9b + 4c - 8d
-c - d
: a, b, c, d in ℛ
Find the dimension of the subspace H.
A) dim H = 3 B) dim H = 1 C) dim H = 4 D) dim H = 2
7)
Assume that the matrix A is row equivalent to B. Find a basis for the row space of the matrix A.
8) A =
1 3 -4 0 1
2 4 -5 5 -2
1 -5 0 -3 2
-3 -1 8 3 -4
, B =
1 3 -4 0 1
0 -2 3 5 -4
0 0 -8 -23 17
0 0 0 0 0
A) {(1, 3, -4, 0, 1), (0, -2, 3, 5, -4), (0, 0, -8, -23, 17), (0, 0, 0, 0, 0)}
B) {(1, 3, -4, 0, 1), (0, -2, 3, 5, -4), (0, 0, -8, -23, 17)}
C) {(1, 3, -4, 0, 1), (2, 4, -5, 5), -2, (1, ...
enjoy the formulas and use it with convidence and make your PT3 AND SPM more easier..togrther we achieve the better:)
good luck guys and girls...simple and short ans also sweet formulas..
Lesson plan. Old curriculum.
DepEd Lesson Plan is an exceptional example of a teacher's “roadmap” for a lesson. It contains a detailed description of the steps a teacher will take to teach a particular topic. It contains the following parts: Objectives, Content, Learning Resources, Procedures, Remarks, and Reflection
A lesson plan is a teacher's daily guide for what students need to learn, how it will be taught, and how learning will be measured.
finding related literature and studies
Literature that is informed and tested by research, these books, articles and reference sources will attempt to explain, describe, define and provide a background or theoretical framework for a field of inquiry
This literature review is focused on the rallying cry in the transition to post-pandemic education in the Philippines. The country experienced a series of lockdowns that catapulted prolonged closures of school premises for more than eighteen months and was considered the last country to reopen. As steps to conduct and resume limited in-person classes, selected schools have led the priming for the gradual transition, but the implications of readapting educational landscapes remain an emerging challenge to be dealt with. To delimit the discussion of educational reviews, subtopics were articulated, these are: 1) Integration of Health in Education; 2) Hybrid Learning; 3) Online Learning Space; 4) Assessment and Evaluation Methods; and 5) Enhancing Data Security. This paper reiterates the recalibration of curriculum from the basic and the higher institutions, the campaign for proactive thinking of curriculum planners as well as the underscore of insights that the online and hybrid learning will be mainstay imperative as the country adjusts and awaits the ebbing of the COVID-19.
declamation piece for high school, english TRAGEDY
advanced algebra exam (1st monthly test)
1. Gaudete Study Center Inc.
First Monthly Examination S.Y. 2013-2014
Mathematics IV
(Teacher Rose and Justine)
Name: Date:
I. Write the letter of the correct answer
on the blank before each number.
1. It is a set of two well ordered real numbers called
coordinates.
a. abscissa c. coordinate
b. ordinate d. ordered pair
2. These are the numerical descriptive reference of
a point from the two axes.
a. abscissa c. coordinate
b. ordinate d. ordered pair
3. It is the first coordinate which corresponds to a
real numbers on the x- axis.
a. abscissa c. coordinate
b. ordinate d. ordered pair
4. He is the one who have an idea of describing a
point on a lane.
a. Leibniz c. Newton
b. Descartes d. Euclid
5. The vertical number line is called
a. x-axis c. origin
b. y-axis d. coordinate
6. Where is the point (-5, 6) located?
a. QIV c. QII
b. QIII d. QI
7. Under what quadrant did non negative abscissa
and positive ordinate located?
a. QIV c. QII
b. QIII d. QI
8. Zero abscissa and non negative ordinate is
located?
a. upper x-axis c. lower x-axis
b. upper y-axis d. lower y-axis
9. What are the coordinates of a point that is
located 4 units to the left of the y-axis and 3 units
above the x-axis?
a. (-3, 4) c. (-4, 3)
b. (4, -3) d. (3, -4)
10. He is the one who introduce the words function,
coordinate, abscissa and ordinate.
a. Leibniz c. Newton
b. Descartes d. Euclid
11. Without plotting name the location of the point
(-42.11, -26.7).
a. QIV c. QII
b. QIII d. QI
For numbers 12-16 refer to the graph.
12. What is the coordinate of point B?
a. (3, 4 c. (4,3)
b. (-3,4 d. (4,-3)
13. What is the name of the point with (4,-3)
coordinate?
a. B c. E
b. H d. C
14. Under what quadrant did C located?
a. QIV c. QII
b. QIII d. QI
15. (-4 3) is the coordinate of point.
a. B c. E
b. H d. C
16. Quadrant three is consist of points
a. A B F c. D C l
b. G E D d. F H
17. It is a set of one or more ordered pairs
a. Function c. Coordinates
b. Relation d. Ordinates
18. The set of all abscissa in a relation is called the
a. Domain c. x-coordinate
b. Range d. y-coordinate
19. The set of all coordinates in a relation is called
the
a. Domain c. x-coordinate
b. Range d. y-coordinate
2. 20. It is a special type of relation wherein no two
ordered pairs have the same abscissa.
a. relation c. abscissa
b. function d. coordinate
21. What is the domain of the set of ordered pairs
{(-2,5), (-1,7),(0,9),(1,11),(2,13)}
a.{0,1,2 } c. {-2,-1,0}
b. {5,7,9,11,13} d. {-2,-1,0,1,2}
22. {(5,2),(0,2),(1,3),(2,2)} is an example of
a. Mere relation b. Function
c. Domain d. Range
23. {(3,0),(3,1),(3,2),(3,4),(3,3)} the relation between
the elements of D and R is said to be
a. Many is to many
b. Many is to one
c. One is to many
d. One is to one
24. What is the set range of the set of ordered pairs
{(-3,2),(5,2),(7,1),(3,8),(-1,4)}
a. {-3,5,7} c. {2,1,8}
b. {-3,5,7,3,-1} d. {2,1,3,4}
25. {(2,5),(2,4),(2,3),(2,1)} is an example of
a. Mere relation b. Function
c. Domain d. Range
26. Which is not true about the relation?
a. It involves the association of an individual
or objects with another individual or objects.
b. Mother and child, husband and wife,
teacher and students.
c. No two ordered pairs have the same
abscissa.
d. It involves pairing and the manner or
action by which the elements in a pair are
associated.
27. Which of the following is a function?
a. {(x,2),(y,4),(2,6),(a,8)}
b. {(2,3),(2,-3),(2,4),(2,-4)}
c. {(1,2),(2,3),(1,3),(2,1)}
d. {(-1,6),(6,-1),(-1,3),(3,-2)}
For numbers 28-30 refer to the table.
cost P50 P60 P70 P80 P90
tax P1 P2 P2 P3 P3
28. The elements in the table is an example of
a. Function c. Coordinates
b. Relation d. Ordinates
29. What is the range of the ordered pairs in the
table?
a. {(50,60,70,80,90)} c. {(1,2,3)}
b. {(1,2,2,3,3)} d. {(50,60,70)}
30. What is the domain of the set of ordered pairs
in the table?
a. {(50,60,70,80,90)} c. {(1,2,3)}
b. {(1,2,2,3,3)} d. {(50,60,70)}
31. If f(x) = 2x2-3 what is f(-2)?
a. -23 c. 6
b. 5 d. 17
32. If g(x) = 3x/2-x what is g (6)?
a. 3.5 c. 6
b. 4 d. 6.5
For numbers 33-35 refer to the function
f (x)=3x+1/x-3
33. What is f (0)?
a. -1/3 c. 1/3
b. 1/4 d. -1/4
34. What is f (h+1)
a. 2h/h-2 c. 2h+1/2
b. 3h+1/h-2 d. 2h
35. What is f (2g)?
a. 3g+1 c. 1/2g-3
b. 6g+1/2g-3 d. -2g/2
for numbers 36-42refer to the function
f(x)=3x-2, g(x)=x2+2x+1 h(x)=3x2+x-2
36. What is (f + g ) (x)?
a. x+5 c.-x2
+5x-3
b. x2
+x+5 d. x2
+5x-1
37. What is ( f + g-h)(x)?
a. -2x2
+4x+1 c. 2x2
-4x+1
b. 2x2
+4x-1 d. -2x2
-4x-1
38. What is (g/h) (x)?
a. 2x+2/4x-1 c. 1/2x-1
b. x+1/3x-2 d. x-2/4x+1
39. What is (f*g) (x)?
a. 5x3
+10x2
+3x-2
b. 5x3
-10x2-3x+2
c. -3x3
+4x2
+x+2
d. 3x3
+4x2
-x-2
for numbers 40-48 refer to the function
f(x)=x-1, g(x)=x2
+1 and h(x)=4x2
+3.
Show your solution at the back of your
paper.
40-41. What is (fοg)(x)?
a. √x+1 c. x2
b. x √2 d. x
42-43. What is (fοh)(x)?
a. x+1 c. 2x+1
b. 2(x+1) d. x-1
44-45. What is (gοg)(x)?
a. x4
+2x3
+3
b. x4
-2x3
+2
c. x4
+2x2
+2
d. x4
-2x2
+2
46-48.What is [f (g+h)](x)?
a. 5x2
+4 c. x+8
b. 5x2
+3 d. x- 8
49-50. What is (g*h) (x)?
a. 4x2
+7x-3
b. 4x2-7x+3
c. 4x4
+7x2
+3
d. 4x4+7x2
-3