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Questions and Answers
Given the binomial expansion, what is the coefficient of the term T5?
Given the binomial expansion, what is the coefficient of the term T5?
- 1120 (correct)
- 16
- 4
- 70
In the given expression for T5, what is the exponent of 'x' after simplification?
In the given expression for T5, what is the exponent of 'x' after simplification?
- 2
- 8
- 16
- 4 (correct)
Which statement about the sequence 2, 6, 18, 54, 160,... is correct?
Which statement about the sequence 2, 6, 18, 54, 160,... is correct?
- It is an arithmetic sequence.
- It is not a geometric sequence because the last term is incorrect. (correct)
- It is a geometric sequence with a common ratio of 4.
- It is a geometric sequence with a common ratio of 3.
What is the common difference in the sequence x, 2x + y, 3x + 2y, ...?
What is the common difference in the sequence x, 2x + y, 3x + 2y, ...?
Is the sequence x, 2x + y, 3x + 2y, ... an arithmetic progression?
Is the sequence x, 2x + y, 3x + 2y, ... an arithmetic progression?
In the arithmetic sequence 1, 5, 9, 13, 17, ..., what is the common difference?
In the arithmetic sequence 1, 5, 9, 13, 17, ..., what is the common difference?
The sum of the first 10 terms of the arithmetic sequence 1, 5, 9, 13, 17,... is:
The sum of the first 10 terms of the arithmetic sequence 1, 5, 9, 13, 17,... is:
Which of the given statements correctly identifies an arithmetic sequence?
Which of the given statements correctly identifies an arithmetic sequence?
Using the given values, what is the correct sum of the arithmetic sequence?
Using the given values, what is the correct sum of the arithmetic sequence?
If the formula for the sum of an arithmetic sequence is $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$, what does $a_1$ represent?
If the formula for the sum of an arithmetic sequence is $S_n = \frac{n}{2}[2a_1 + (n - 1)d]$, what does $a_1$ represent?
How many distinct arrangements are possible for the letters in the word 'PUPIAN'?
How many distinct arrangements are possible for the letters in the word 'PUPIAN'?
What is the key concept used to solve the arrangement problem of the word 'PUPIAN'?
What is the key concept used to solve the arrangement problem of the word 'PUPIAN'?
What is the correct formula for simple interest?
What is the correct formula for simple interest?
If an investment of $70,000 earns $15,000 in interest at a 3.8% annual rate, what is the time it took in years?
If an investment of $70,000 earns $15,000 in interest at a 3.8% annual rate, what is the time it took in years?
In the simple interest formula, if the interest (I) and the time (T) are constant, how does the principal (P) affect the interest rate (R)?
In the simple interest formula, if the interest (I) and the time (T) are constant, how does the principal (P) affect the interest rate (R)?
What is the decimal form of 3.8%?
What is the decimal form of 3.8%?
A right triangle has sides of length 9 and 40. What is the area of the triangle?
A right triangle has sides of length 9 and 40. What is the area of the triangle?
Jandrik travels 15 km west and then 36 km south. What is the straight-line distance in kilometers from his starting position?
Jandrik travels 15 km west and then 36 km south. What is the straight-line distance in kilometers from his starting position?
If $a$ and $b$ are real numbers such that $a + b = 15$ and $ab = 45$, what is the value of $a^2 + b^2$?
If $a$ and $b$ are real numbers such that $a + b = 15$ and $ab = 45$, what is the value of $a^2 + b^2$?
An isosceles right triangle has a leg length greater or equal to 13 cm. What is the minimum possible area of this triangle?
An isosceles right triangle has a leg length greater or equal to 13 cm. What is the minimum possible area of this triangle?
There are 4 distinct Model A cars and 4 distinct Model B cars. If they are arranged in a row such that no two cars of the same model are adjacent, how many possible arrangements are there?
There are 4 distinct Model A cars and 4 distinct Model B cars. If they are arranged in a row such that no two cars of the same model are adjacent, how many possible arrangements are there?
A line segment is drawn from the center of a polygon perpendicular to one of its sides. What is this line segment called?
A line segment is drawn from the center of a polygon perpendicular to one of its sides. What is this line segment called?
What is the result of 1/2 * 9 * 40?
What is the result of 1/2 * 9 * 40?
Given that $\sqrt{15^2+36^2}= x$, what is value of $x$?
Given that $\sqrt{15^2+36^2}= x$, what is value of $x$?
Seph invests a total of Php 500,000 in two businesses, a computer shop and a coffee shop. If the computer shop yields 5% monthly interest and the coffee shop yields 3%, how much should be invested in each to earn Php 18,000 monthly?
Seph invests a total of Php 500,000 in two businesses, a computer shop and a coffee shop. If the computer shop yields 5% monthly interest and the coffee shop yields 3%, how much should be invested in each to earn Php 18,000 monthly?
In the given problem, if 'x' represents the amount invested in the computer shop and 'y' represents the amount invested in the coffee shop, which equation represents the total monthly interest earned?
In the given problem, if 'x' represents the amount invested in the computer shop and 'y' represents the amount invested in the coffee shop, which equation represents the total monthly interest earned?
Based on the problem, what is the first step in solving for the amount invested in each business using the system of linear equations?
Based on the problem, what is the first step in solving for the amount invested in each business using the system of linear equations?
After substituting the value of 'y' in the second equation, how is the value of 'x' determined?
After substituting the value of 'y' in the second equation, how is the value of 'x' determined?
What does the equation x + y = 500,000 represent in the context of Seph's investments?
What does the equation x + y = 500,000 represent in the context of Seph's investments?
If Seph had invested Php 100,000 more in the computer shop, what would be the new value of x, given that the total investment remains at Php 500,000?
If Seph had invested Php 100,000 more in the computer shop, what would be the new value of x, given that the total investment remains at Php 500,000?
In the step 0.05x + 15,000 - 0.03 = 18,000, how is the value 15,000 derived?
In the step 0.05x + 15,000 - 0.03 = 18,000, how is the value 15,000 derived?
What is the purpose of using the subtraction property of equality in the solution?
What is the purpose of using the subtraction property of equality in the solution?
Which of the following sets of numbers does NOT represent a Pythagorean triple?
Which of the following sets of numbers does NOT represent a Pythagorean triple?
Given a right triangle in the second quadrant where sin θ = $\frac{7}{25}$, what is the value of sec θ?
Given a right triangle in the second quadrant where sin θ = $\frac{7}{25}$, what is the value of sec θ?
A piggy bank contains 35 coins in total, consisting of 10-centavo and 25-centavo coins. If the total value of the coins is P5.90, how many 10-centavo coins are in the piggy bank?
A piggy bank contains 35 coins in total, consisting of 10-centavo and 25-centavo coins. If the total value of the coins is P5.90, how many 10-centavo coins are in the piggy bank?
If a right triangle has a sine value of $\frac{7}{25}$ and is located in the second quadrant, what is the value of tan θ?
If a right triangle has a sine value of $\frac{7}{25}$ and is located in the second quadrant, what is the value of tan θ?
Given a right triangle with sin θ = $\frac{7}{25}$, what is the length of the side adjacent to angle θ?
Given a right triangle with sin θ = $\frac{7}{25}$, what is the length of the side adjacent to angle θ?
If a piggy bank has P5.90 consisting of 10 and 25-centavo coins, and the total number of coins is 35, what is the total value of the 25-centavo coins?
If a piggy bank has P5.90 consisting of 10 and 25-centavo coins, and the total number of coins is 35, what is the total value of the 25-centavo coins?
What is the value of cos θ if sin θ = $\frac{7}{25}$ and the triangle is in the second quadrant?
What is the value of cos θ if sin θ = $\frac{7}{25}$ and the triangle is in the second quadrant?
In the context of Pythagorean triples, if 'a' is an odd number, how are 'b' and 'c' typically related?
In the context of Pythagorean triples, if 'a' is an odd number, how are 'b' and 'c' typically related?
What is the area of a triangle with side lengths 13, 14, and 15?
What is the area of a triangle with side lengths 13, 14, and 15?
A triangle has an area of 84, with a semi-perimeter of 21. What is the radius of the inscribed circle?
A triangle has an area of 84, with a semi-perimeter of 21. What is the radius of the inscribed circle?
If $z = 2 + 3i$, what is the magnitude of $z^2$, denoted as $|z^2|$?
If $z = 2 + 3i$, what is the magnitude of $z^2$, denoted as $|z^2|$?
How many diagonals does a regular icosagon have?
How many diagonals does a regular icosagon have?
Given a random variable X following a uniform distribution on the interval [0,10], what is the probability that $3 < X < 7$?
Given a random variable X following a uniform distribution on the interval [0,10], what is the probability that $3 < X < 7$?
What is the semi-perimeter of a triangle with sides of length 13, 14, and 15?
What is the semi-perimeter of a triangle with sides of length 13, 14, and 15?
What is the value of $i^2$?
What is the value of $i^2$?
Which of the following formulas is used to calculate the number of diagonals in a polygon?
Which of the following formulas is used to calculate the number of diagonals in a polygon?
Flashcards
Linear Equation
Linear Equation
A mathematical statement that represents a relationship between two or more variables, where each variable is raised to the power of one.
System of Linear Equations
System of Linear Equations
A set of two or more linear equations that share a common solution.
Solving for a Variable
Solving for a Variable
The process of finding the value of a variable in an equation by using the properties of equality to isolate the variable.
Substitution Method
Substitution Method
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Monthly Interest
Monthly Interest
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Principal Amount
Principal Amount
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Interest Earned
Interest Earned
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High-Yield Investment
High-Yield Investment
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Geometric Sequence
Geometric Sequence
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Arithmetic Sequence
Arithmetic Sequence
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Arithmetic Series
Arithmetic Series
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Sum of Arithmetic Series
Sum of Arithmetic Series
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Arithmetic Series Formula
Arithmetic Series Formula
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Common Ratio
Common Ratio
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Common Difference
Common Difference
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nth Term Formula (Arithmetic)
nth Term Formula (Arithmetic)
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Permutation
Permutation
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Simple Interest
Simple Interest
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Sn = [2a1 + (n-1)d]/2
Sn = [2a1 + (n-1)d]/2
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n! / (n1!n2!n3!...
n! / (n1!n2!n3!...
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a1
a1
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d
d
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n
n
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Area of a Right Triangle
Area of a Right Triangle
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Distance Formula
Distance Formula
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Squaring the Sum
Squaring the Sum
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Area of Isosceles Right-Angled Triangle
Area of Isosceles Right-Angled Triangle
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Arrangements of Two Sets
Arrangements of Two Sets
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Apothem
Apothem
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Incircle Radius Formula
Incircle Radius Formula
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Magnitude of a Complex Number
Magnitude of a Complex Number
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Icosagon
Icosagon
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Number of Diagonals in a Polygon
Number of Diagonals in a Polygon
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Uniform Distribution
Uniform Distribution
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Squaring a Complex Number
Squaring a Complex Number
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Absolute Value of a Complex Number
Absolute Value of a Complex Number
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Heron's Formula
Heron's Formula
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Pythagorean Triple
Pythagorean Triple
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Secant (sec θ)
Secant (sec θ)
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Sine (sin θ)
Sine (sin θ)
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Pythagorean Theorem
Pythagorean Theorem
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Study Notes
PUPCET 2025 Mock Exam - Mathematics
- Mathematics exam for PUP (Philippine University of the Philippines) students
- Prepared by the Public Information and Affairs Committee, Academic and Research Committee, and Volunteers
- Exam questions cover Systems of Linear Equations (Grade 8) and Arithmetic Sequences.
Question 1 - Investment Decisions
- Seph invests Php 500,000 in a computer shop (5% monthly interest) and a coffee shop (3% monthly interest)
- He wants a total monthly interest of Php 18,000
- Correct answer: Computer shop: Php 150,000, Coffee shop: Php 350,000
Question 2 - Arithmetic Sequence
- Fourth term of an arithmetic sequence is 2
- Seventeenth term is 7
- Determine the general term of the sequence
- Correct answer: an = 5n+6 / 13
Question 3 - Binomial Expansion
- Find the fifth term in the expansion of (2x + y)8
- Correct answer: 1120x4y4
Question 4 - True/False Statements
- Statement 1: 2, 6, 18, 54, 160 is a geometric sequence => False
- Statement 2: x, 2x + y, 3x + 2y... is an arithmetic sequence => True
- Statement 3: 1, 5, 9, 13, 17... The sum of the first 10 terms is 175 => False
Question 5 - Letter Arrangement
- Determine the number of ways to arrange the letters in the word PUPIAN
- Correct answer: 360 ways
Question 6 - Simple Interest
- Mx. Cruz wants to earn Php 15,000 in interest on a PHP 70,000 investment at 3.8% annual interest
- Determine the time length needed to reach the goal
- Correct answer: 5.64 years
Question 7 - Equation of a Line
- Determine the slope-intercept form of a line passing through (5, 4) and (6, 9)
- Correct answer: y=5x-21
Question 8 - Compound Interest
- Joshua invests Php 14,300 at a 6% interest rate compounded monthly for 4 years
- How much money will Joshua have?
- Correct answer: Php 18,167.99
Question 9 - Consecutive Odd Integers
- Find three consecutive odd integers.
- Sum of the smallest and largest: 62. Sum of all three: 93
- Correct answer: 29, 31, and 33
Question 10 - Normal Distribution
- In normal distribution, the mean, median, and mode are all equal and located at the center of the spread.
Question 11 - Number Pattern
- Determine the missing number in the sequence 1, 2, 7, 34, 203, 1420, …
- Correct answer: 11359
Question 12 - Divisible Polynomials
- Given the polynomial 2x4 - 9x3 + mn2 + nx + 54 = 0 is divisible by x2 + 4x + 3
- Find m+n
- Correct answer: -23
Question 13 - Factorization
- Factorize 4x² - 4y² + 40x - 28y + 51
- Correct answer: (2x+2y + 17)(2x -2y+3)
Question 14 - Positive Factors
- Find the sum of all positive factors of 756
- Correct answer : 2240
Question 15 - Intersection of Lines
- Find the point of intersection of line A: y = 4x + 8 and line B: y = 7x + 5
- Correct answer: (1,12)
Question 16 - Area
- Find the area of a triangle with side lengths 9, 40, and 41
- Correct answer: 180
Question 17 - Positional Change
- Determine the distance between an original position after going 15 km west then 36 km south
- Correct answer : 39
Question 18 - Algebraic Calculation
- Given 'a' + 'b' = 15 and ab = 45, find a² + b²
- Correct answer: 135
Question 19 - Right Angled Triangle
- Given ∆ABC, find the minimum value of its area , where dist(B,C) >= 13cm and ∠ACB= 90°
- Correct answer: 84.5 cm2
Question 20 - Arrangement and Models (Permutation)
- Determine the arrangements of 4 models of type A and 4 models of type B when they cannot be placed next to each other, lining up in a row.
- Correct answer: 1152
Question 21 - Line Segment
- Identify the geometric term for a line segment drawn from the center of a polygon perpendicular to a side.
- Correct answer: Apothem
Question 22 - Pythagorean Triples
- Which is not a Pythagorean Triple?
- Correct answer: 7-21-22
Question 23 - Trigonometry in Second Quadrant
- Given sin θ = 7/25 in the second quadrant, determine sec θ
- Correct answer: -25/24
Question 24 - Coin Values
- Determine the number of 10-centavo and 25-centavo coins in a piggy bank.
- There are 35 coins with a total value of P5.90
- Correct answer: Nineteen 10-centavo coins and sixteen 25-centavo coins
Question 25 - Reciprocal Difference
- Find the two positive numbers given their reciprocal difference and one is 3 times the other.
- Correct answer: 4 and 12
Question 26 - Age Problem
- Heather's age. One-half of her age in two years plus one-third of her age three years ago is 20.
- Correct answer : 24
Question 27 - Mixture of Rice
- Find the kg of rice that sells for P10 per kilo to mix with rice that sells for P7.50 to make a 100-kilo mixture that sells for P8.50.
- Correct answer: 40
Question 28 - Travel Time and Displacement
- Ji leaves home for PUP Exam at 12 mph. 20 minutes later her mother brings his test permit. Mother drives at 36 mph.
- Correct answer: 6 miles
Question 29 - Probability of Fire Occurrence
- Given the probability of dangerous fires and the probability of fires producing smoke.
- Calculate the probability that a fire occurs when there is smoke
- Correct answer: 0.09
Question 30 - Meal Option Combination
- Calculate the possible number of meals offered with specified choices for side item, juice, and pasta.
- Correct answer: 32
Question 31 - Polynomial Roots
- Find the roots of the polynomial
- x³ — 6x² — 11x + 6 = 0
- Correct Answer: x = 1, 2, 3.
Question 32 - Logarithmic Equations
- Solve for
xin the logarithmic equationlog₃(x − 1) + log₃(x + 1) = 2 - Correct answer: √10
Question 33 - Radius of Inscribed Circle
- Find the radius of the circle inscribed in a triangle with sides 13, 14, and 15.
- Correct answer: 6
Question 34 - Complex Number
- Find the magnitude of z^2 if z = 2 + 3i
- Correct answer: 13
Question 35 - Diagonals in a Regular Polygon
- Find the number of diagonals in an icosagon
- Correct answer: 170
Question 36 - Uniform Distribution
- Given a uniform distribution
Xon [0,10], findP(3 < X < 7) - Correct answer: 0.4
Question 37 - Poisson Distribution
- Given
X ~ Poisson(λ = 4), find the variance - Correct answer: 4
Question 38 - Standard Deviation Scaling
- If the standard deviation of a dataset is 10, and every value is multiplied by 5, what is the new standard deviation?
- Correct answer: 50
Question 39 - Probability of Union
- Find
P(A∪B)givenP(A) = 0.4,P(B) = 0.6,P(A∩B) = 0.2 - Correct answer: 0.8
Question 40 - Geometric Distribution
- In a geometric distribution with
p = 0.25, find the probability of the first success occurring on the 4th trial. - Correct answer: 0.140625
Question 41 - Project Completion Time
- Sarah completes a project in 20 days and David completes the same project in 15 days. If they work together, how many days will it take to complete the project?
- Correct answer: 60/7 days
Question 42 - Rocket Distance
- What distance does a rocket traveling at 3 miles per second cover in 1 hour?
- Correct answer: 10,800 miles
Question 43 - Irrational Numbers
- Which of the following is NOT an irrational number?
- Correct answer: 7/3
Question 44- Two-Digit Numbers
- If 't' is the tens digit and 'u' is the units digit of a two-digit number, which expression represents the number?
- Correct answer: 10t + u
Question 45 - Age Calculation
- Jack is four years older than Jill. Three years ago, Jack's age was two years less than twice Jill's age. What is the equation to find Jill's current age?
- Correct answer: 2(x - 3) - 2 = x + 1
Question 46 - Approximation
- Estimate the value of 0.889 × 55 / 9.97
- Correct answer: 4.9
Question 47 - Sphere in Cube
- Find the volume of the largest sphere that can fit inside a cube with a volume of 216 cm³.
- Correct answer: 36π cm³
Question 48 - Lines Intersection
- Determine the point of intersection of Line A (y = 4x + 8) and Line B (y = 7x + 5)
- Correct answer: (1,12)
Question 49 - Algebraic Simplification
- Simplify the expression √256/(x² - 4) if x = 4
- Correct answer: 2
Question 50 - Fraction of Money Spent
- Kelly spent half her money on a DVD and 1/6 on popcorn. What fraction of her money did she spend in total?
- Correct answer: 2/3
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Description
Test your understanding of binomial expansion, sequences, and arithmetic progressions with this comprehensive quiz. Questions cover topics such as finding coefficients, common differences, and the sum of terms. Perfect for students in algebra class!
