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Worksheets

MATHEMATICS MAJORSHIP

Total questions: 90

Worksheet time: 45mins

Name
Class
Date
1.

In the arithmetic sequence -2, 1, 4, 7, ..., which term is 100?

a)

34th

b)

35th

c)

36th

d)

40th

2.

The first term of an arithmetic sequence is 3 and the 20th term is 98. What is the 25th term?

a)
100
b)
110
c)
130
d)
123
3.

The 19th term of an arithmetic sequence is 85 and the 12th term is 43. Find the common difference.

a)
6
b)
4
c)
10
d)
8
4.

Insert one term between 18 and 32 to make a geometric sequence.

a)
20
b)
28
c)
30
d)
24
5.

Insert one term between 81 and 169 to make a geometric sequence.

a)
117
b)
100
c)
130
d)
150
6.

Find the general term An of the sequence 7, 16, 25, 34, 43, 52, 61, ...

a)

An = 7n + 5

b)

An = 10n - 3

c)

An = 8n + 1

d)

An = 9n - 2

7.

In n arithmetic sequence, the 23rd term is 157 and the common difference is -4. What is he 34th term?

a)
113
b)
121
c)
145
d)
99
8.

If the number x-1, x+2 and 2x+4 are consecutive terms of a geometric sequence, what is x?

a)

4

b)

8

c)

12

d)

16

9.

If a and b are integers and the sum of ab and b is odd, which of the following could be true?

I. a and b are both odd

II. a is even and b is odd

III. a is odd and b is even

a)
I only
b)
II and III
c)
I and III
d)

II only

10.

What day follows the day before yesterday if 2 days from now will be Sunday?

a)
Thursday
b)
Saturday
c)
Wednesday
d)
Monday
11.

A shareholder sells his shares for more than he paid for them. This is known as:

a)
Dividend income
b)
Capital gain
c)
Shareholder profit
d)
Market loss
12.

What is the ratio of 15\frac{1}{5} to 515\frac{5}{15} ?

a)
4:5
b)
3:5
c)
2:3
d)
1:5
13.

Thalia laid tiles on the floor. She began with 1 square tile at the corner of the room. She added three tiles to form 2x2 tile square and then 5 tiles to form 3x3 tiles square. She continues in this way until the whole floor is covered. Last, she adds 25 tiles. What is the size of the floor?

a)

166 square tiles

b)

169 square tiles

c)

266 square tiles

d)

269square tiles

14.

The surface on the earth between the tropic of cancer and the Arctic Circle is called ______.

a)

Cone

b)

Zone

c)

Plane

d)

Circle

15.

An 18th century Swiss Mathematician, he introduced the "Law of Large Number" in his (The Art of Conjecture). In statistics, this implies that the larger the sample, the more likely will the sample become representative of he population. Who was he?

a)
Jacob Bernoulli
b)
Bernhard Riemann
c)
Carl Friedrich Gauss
d)
Leonhard Euler
16.

He invented a method of determining the optical values of linear function subject to a certain constraints. This method is known as linear programming. Who is he?

a)
George Dantzig
b)
John von Neumann
c)
Alan Turing
d)
Norbert Wiener
17.

Who published a treatise on treatise on trigonometry which contains the earliest use of our abbreviations: sin, cos, sec, tan, for sine, tangent and secant?

a)

Gregorio de Saint

b)

Albert Gerald

c)

John Napier

d)

Johann Herdde

18.

He has been described as the greatest "might-have-been" in the history of mathematics.

a)

Gregorio De Saint

b)

Gaspard Monge

c)

Bonaventura Cavalier

d)

Blaise Pascal

19.

There are types of correlation between paired data perfect positive correlation, perfect negative correlation, same positive correlation, same negative correlation and no correlation.

a)
perfect correlation
b)
weak negative correlation
c)
no correlation
d)
strong positive correlation
20.

He was a 16th century mathematician, who was the first to define that the probability of an event to happen is the quotient of the number of the favorable outcomes and the number of all outcomes. Who is he?

a)
Gerolamo Cardano
b)
Johannes Kepler
c)
Isaac Newton
d)
Leonhard Euler
21.

A subset of the sample space is ____.

a)
a sample
b)
a parameter
c)
an event
d)
a variable
22.

The figure shows ______.

a)

No corralation

b)

Perfect positive correlation

c)

Same negative correlation

d)

Same positive correlation

23.

The figure shows_____.

a)

No correlation

b)

Perfect positive correlation

c)

Same negative

d)

Same positive correlation

24.

He invented a method of determining the optimal values of a linear function subject to certain constrains. This method is known as linear programming. Who is he?

a)
John von Neumann
b)
George Dantzig
c)
Leonhard Euler
d)
David Hilbert
25.

If the opposite sides of a quadrilateral are equal, the figure is a _______.

a)
rectangle
b)
trapezoid
c)
kite
d)
parallelogram
26.

The ULTRA football field is 100 meters from the goal line to goal line. If it is 360 meters around a football field, How wide is the field?

a)
80 meters
b)
75 meters
c)
90 meters
d)
70 meters
27.

The sum of he sides of a polygon is _____ of the polygon.

a)
the area
b)
the volume
c)
the perimeter
d)
the diameter
28.

Perform the operation given that A= {-4, -2, 0, 2, 4}, B= {-4, -2, 0, 3, 4}

A U B =

a)
{-4, -2, 0, 2, 3, 4}
b)
{-4, -2, 0, 3}
c)
{-2, 0, 2, 3, 4}
d)
{-4, -2, 0, 2, 4}
29.

Simplify the expression:

3x152x250×2x2+16x+306x+9\frac{3x-15}{2x^2-50}\times\frac{2x^2+16x+30}{6x+9}

a)

x+32x3\frac{x+3}{2x-3}

b)

x32x+3\frac{x-3}{2x+3}

c)

x32x3\frac{x-3}{2x-3}

d)

x+32x+3\frac{x+3}{2x+3}

30.

Ruka average 91 on 5 her exams. if she wants to have an average of 92, what score must she get on her 6th exam?

a)
95
b)
90
c)
97
d)
93
31.

Romar's first score in his Math exams were 90, 92, 93, and 95. What must his score be in his fifth exam in order for him to have an average score 92?

a)
90
b)
85
c)
94
d)
88
32.

Sphere of equal size are piled in he form of a complete pyramid with a rectangular base, find the total number of spheres in the pile if the number of spheres in the long side is 5 and that of the short side is 4 until the top layer consists of a single row of 2 spheres.

a)
45
b)
40
c)
30
d)
35
33.

all 500 boys in a school play basketball or volleyball or both. If 30% of the boys play volleyball and 90% play basketball, how many play both basketball and volleyball?

a)
100
b)
250
c)
200
d)
150
34.

Insert one term between 18 and 32 to make a geometric sequence.

a)
30
b)
28
c)
24
d)
20
35.

Perform the indicated operation and reduce result to simplest form.

a)

yxz\frac{y}{xz}

b)

z2y2z2\frac{z^2}{y^2z^2}

c)

x2xy2\frac{x^2}{xy^2}

d)

x2yz2\frac{x^2}{yz^2}

36.

Simplify this complex fraction: 11a21+1a\frac{1-\frac{1}{a^2}}{1+\frac{1}{a}}

a)

aa+1\frac{a}{a+1}

b)

a+1a\frac{a+1}{-a}

c)

aa1\frac{a}{a-1}

d)

a1a\frac{a-1}{a}

37.

The length of line AB is 15 units. Suppose the coordinates of A are (9, -7) and the coordinates of B are (x,2). What is/are the value/s of x?

I. 21

II. 17

III. 14

IV. -3

a)

I only

b)

I and II

c)

I and IV

d)

I, II, and III

38.

They used vigesimal number system of based twenty system using only three symbol namely shell-like, dot and line.

a)

Egyptian

b)

Babylonian

c)

Mesoamerican

d)

Native American

39.

He developed the Method of Indivisibles and published Geometria Indisibilis.

a)
Bonaventura Cavalieri
b)
René Descartes
c)
Isaac Newton
d)
Galileo Galilei
40.

What is/are the goal/s o mathematics education in the Philippines?

I. Problem solving

II. Critical thinking

III. Creativity

IV. Reasoning

a)

I only

b)

II only

c)

I and II

d)

I, II, III, IV

41.

One learns Math by building on Math lessons previous learned. This is ________.

a)

Humanist

b)

Psychological

c)

Learning by doing

d)

Constructivist

42.

Evaluate 25(x2+1x2)dx\int_2^5\left(x^2+\frac{1}{x^2}\right)dx

a)

2331023\frac{3}{10}

b)

331333\frac{1}{3}

c)

3931039\frac{3}{10}

d)

4031040\frac{3}{10}

43.

limx2x2x2x23x+2\lim_{x\rightarrow2}\frac{x^2-x-2}{x^2-3x+2}

a)
3
b)
1
c)
4
d)
2
44.

The surface of two spheres are 12π cm2 and 108π cm2. What is the ratio of their volumes?

a)

1:27

b)

2:3

c)
3:4
d)
1:9
45.

The sum of two numbers is 45 and their product is 499. Find the sum of their squares.

a)
900
b)
1027
c)
850
d)
1100
46.

It is a correspondence between two sets x and y such that to each element x of the set y, there correspondence exactly one element y of the set Y, is called a.

a)
Association
b)
Mapping
c)
Relation
d)
Function
47.

One factor of a32a2a+2a^3-2a^2-a+2 is a1a-1 find the other factors.

a)
(a - 1)(a + 3)
b)
(a - 3)(a + 2)
c)
(a + 2)(a - 1)
d)
(a - 2)(a + 1)
48.

What is e complete simplified equivalent of 25+i\frac{2}{5+i}

a)

5 - i / 13

b)

2 + 5i / 29

c)

5 + i/12

d)

3 - 2i/10

49.

Evaluate the limit as r approaches -1 of r3+3r2+3r+1r+1\frac{r^3+3r^2+3r+1}{r+1}

a)
-1
b)
0
c)
1
d)
3
50.

What is the sum of the first 20 counting number, the first 20 even counting number and the first 20 odd counting numbers?

a)

1020

b)

1030

c)

1015

d)

1025

51.

Evaluate the determinant of Matrix A.

2 3 4

A=-1 -1 -2

5 4 3

a)
-7
b)
-10
c)
0
d)
-5
52.

The trace of the square matrix A, to (A) is the sum of its diagonal elements of

3 5 2

A= 2 4 5

6 7 2

2 6 3

B= 2 3 8

7 1 9

Find the tr (A) + tr (B)

a)

19

b)

20

c)

21

d)

23

53.

simplify x - 3y(x - 8y) - (-6x + 7y)

a)

7x - 3xy + 24y2 - 7y

b)

7x - 3xy - 24y2 + 7y

c)

-7x - 3xy - 24y2 - 7y

d)

-7x - 3xy - 24y2 + 7y

54.

What conic section represent 4x2 - y2 +8x +4y = 15

a)
Hyperbola
b)
Parabola
c)
Circle
d)
Ellipse
55.

How many different arrangements of the word PARRAMATTA are possible?

a)
28800
b)
25600
c)

37800

d)
27720
56.

A lot of technology application is utilized in which branch of algebra?

a)
Commutative Algebra
b)
Linear Algebra
c)
Boolean Algebra
d)
Abstract Algebra
57.

Quantity is to Number theory, as space is to ______

a)
Geometry
b)
Algebra
c)
Calculus
d)
Statistics
58.

What is the primary Mathematical tool used in Artificial Intelligence?

a)

Linear Algebra

b)

Trigonometry

c)

Business Math

d)

Abstract Geometry

59.

two adjacent angles whose distinct sides lie on the same line are called what?

a)
adjacent angles
b)
linear pairs
c)
complementary angles
d)
vertical angles
60.

There are 24 mangoes in a basket, of which 7 are rotten. What is the probability that when randomly getting two mangoes at the same time both are rotten?

a)
7/92
b)
3/92
c)
5/92
d)
9/92
61.

Mr. Park is 20 years older than his son now. Five years from now, the Mr. Park age will be 5 less than twice his son's age. Find the son's present age.

a)
20
b)
30
c)
15
d)
25
62.

If the sum of the supplement and the complement of an angle is 100 degrees, what is the angle?

a)
80 degrees
b)
85 degrees
c)
90 degrees
d)
75 degrees
63.

Find the equation of variation if m varies directly as the square of n, and m is 150 when n=5.

a)
m = 30n^2
b)
m = 12n^2
c)
m = 4n^2
d)
m = 6n^2
64.

A math teacher asks students to create their own word problems from a given equation. This promotes:

a)
Basic arithmetic skills in problem-solving.
b)
Rote learning of mathematical concepts.
c)
Critical thinking and creativity in mathematics.
d)
Memorization of formulas in math.
65.

Which is a characteristic of a learner centered math classroom?

a)

Teacher dictates solutions step by step

b)

Students are passive listeners

c)

Students ask questions and explore solutions

d)

Emphasis is on written exams only

66.

Spiral progression in the K-12 curriculum means

a)
a method of focusing solely on advanced concepts without review
b)
a method of revisiting key concepts at increasing levels of complexity throughout the curriculum
c)
a technique for teaching in a linear and fixed manner
d)
a strategy for introducing new topics without prior knowledge
67.

In planning for spiral progression, which of the following best reflects how a teacher should handle quadratic equations?

a)

Teach only one method

b)

Introduce multiple solution strategies in one grade

c)

Introduce simple factoring in grade 8, completing the squares in grade 9, and the quadratic formula in grade 10

d)

Focus on procedural fluency grade 7 to

68.

Which statement best reflects constructivist theory in teaching mathematical concepts?

a)

Knowledge is passed from teacher to student through examples

b)

Students learn best by listening and copying the process

c)

Students actively build understanding through guided inquiry and problem-solving

d)

learning occurs when errors are immediately corrected by the teacher

69.

A teacher gives praise every time a student simplifies a rational expression correctly. Over time the student become confident in doing math. This reflect which concept?

a)

Cognitive dissonance

b)

Operant conditioning

c)

Self-determination theory

d)

Insight learning

70.

Which technology best suited for teaching mathematical proofs interactively?

a)

Programming Software

b)

Dynamic Geometry Software

c)

Word Processing Software

d)

Database Software

71.

What is a key features of software like Desmos in mathematics education?

a)

It allows for word processing

b)

It focuses on database management

c)

It provides real-time graphing of equations

d)

It is primarily for creating presentation

72.

Which online platform is specially designed for collaborative mathematics problem-solving?

a)
Algebra Helper
b)
GeoGebra Online
c)
CalcBuddy
d)
Mathway
73.

In what way can 3D printing be utilized in mathematics education?

a)

To create traditional textbooks

b)

To produce physical models of geometric shapes

c)

To print worksheets

d)

To make visual presentations

74.

Which of the following technologies is most effective for engaging students in learning calculus?

a)

Graphing Calculators

b)

Word Processing Software

c)

Video Games

d)

Simple Calculator

75.

What advantage does using online math tutorials provide for students?

a)

They replace classroom instruction entirely

b)

They allow students to learn at their own pace

c)

They limit student interaction with peers

d)

They complicate the learning process

76.

Which of the following software tools allows for the simulation of statistical experiments?

a)

SPSS

b)

Excel

c)

Adobe Illustrator

d)

Notepad

77.

What is the main benefit of using formative assessment tools un mathematics classroom?

a)

They solely focus on final exams

b)

They provide insights into student understanding throughout the learning process

c)

They reduce the need for classroom participation

d)

They complicate assessment methos

78.

How can teachers effectively use online simulations in teaching probability?

a)

By showing students on theoretical concepts

b)

By allowing students to conduct virtual experiments and analyze results

c)

By limiting access to simulations

d)

by avoiding technology altogether

79.

What technology can enhance students' understanding of complex algebraic functions?

a)
Graphing calculators or software like Desmos
b)
Physical textbooks on algebra
c)
Online algebra tutorials
d)
Basic arithmetic worksheets
80.

Which ancients civilization in known for using a base-10 number system in their calculation?

a)

Indian

b)

Egyptians

c)

Greeks

d)

Indians

81.

What is he number 2/3 of whose square root is 10

a)

67

b)

100

c)

105

d)

205

82.

Given that x3+4=49\frac{x}{3}+4=49

a)
135
b)
150
c)
120
d)
100
83.

What is the total length of fabric materials if there are 72/10 meters and 15 4/5 meters available?

a)
20 meters
b)
25 meters
c)
23 meters
d)
18 meters
84.

Use absoltute value notation to describe the given situation: The distance between x and 3.

a)
|x + 3|
b)
|x - 5|
c)
|3 - x|
d)
|x - 3|
85.

Use absolute value notation to describe the given situation: The distance between x and -2 is 4

a)

|x + 2| = -4

b)

|x - 2| = -4

c)
|x - 2| = 4
d)
|x + 2| = 4
86.

The given multiplication table represents a cyclic group. Find d2.

a)

a

b)

b

c)

c

d)

d

87.

Solve the area bounded by the curve x= y>> + 2y and the line x= 3

a)

10 sq. u

b)

10.67 sq. u

c)

45.12 sq. u

d)

55sq. u

88.

Find the radius of x2 + y2 +12x - 14y = 36

a)

5

b)

9

c)

11

d)

13

89.

If the sum and product of the roots of the roots of a quadratic equation are 1/2 and -3 respectively, then the equation is.

a)
x^2 + 3x - 2 = 0
b)
4x^2 - 2x + 1 = 0
c)
3x^2 + x - 9 = 0
d)
2x^2 - x - 6 = 0
90.

Determine the area of a triangle with vertices. A(2,5), B(-3, 1), C(5, -2)

a)
10.5
b)
15.2
c)
23.5
d)
18.7