Mathematics Exam Questions
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Questions and Answers

What is the missing term in the series 5, 20, 80, ___, 1280?

  • 40 (correct)
  • 61
  • 35
  • 50
  • What are the prime factors of 273?

  • 3 x 6 x 9 x 11
  • 3 x 11 x 17 (correct)
  • 3 x 3 x 7 x 7
  • 3 x 7 x 13
  • What is the sum of the first 20 counting numbers?

  • 400
  • 210 (correct)
  • 420
  • 105
  • What is the largest prime number less than 100?

    <p>97 (A)</p> Signup and view all the answers

    What property is illustrated in the equation 5 + (2 + 6) = (5 + 2) + 6?

    <p>Associative Property (A)</p> Signup and view all the answers

    What is the result of the operation $70 ÷ 7 × 5 + 64 ÷ 4 × 2$?

    <p>34 (C)</p> Signup and view all the answers

    How much greater is the sum of the first 20 counting numbers than the sum of the first 10 counting numbers?

    <p>55 (D)</p> Signup and view all the answers

    Which of the following numbers is NOT divisible by 3?

    <p>22 (A)</p> Signup and view all the answers

    What is the value of the expression $3 + 4(5 - 2 × 6) + 12(2 + 4) + 1$?

    <p>83 (B)</p> Signup and view all the answers

    What is the next term in the sequence 1280, ___, 20, 480?

    <p>320 (A)</p> Signup and view all the answers

    Which of the following is the Greatest Common Factor (GCF) of 12 and 42?

    <p>6 (B)</p> Signup and view all the answers

    How many floors does the CBRC Headquarters have as indicated in the address?

    <p>2 (A)</p> Signup and view all the answers

    What mathematical operation comes first in the expression $1 + (3 × 6) - 13$?

    <p>Parentheses (D)</p> Signup and view all the answers

    Which of the following represents the content of the warning regarding the material?

    <p>Copyright protection is applicable. (C)</p> Signup and view all the answers

    What is the primary purpose of the document as indicated in the provided content?

    <p>Classified examination for analysis (D)</p> Signup and view all the answers

    Which of the following best describes the listing of numbers at the beginning of the document?

    <p>It indicates examination questions (B)</p> Signup and view all the answers

    How many eggs are required for 32 cups of flour in the custard recipe?

    <p>16 (A)</p> Signup and view all the answers

    What is the least common multiple of 24 and 80?

    <p>480 (D)</p> Signup and view all the answers

    If a tree that is 5 feet tall casts a shadow of 7 feet, how tall is a second tree that casts a 21 feet shadow?

    <p>15 feet (B)</p> Signup and view all the answers

    In dividing a stick of 96 cm in the ratio 3:4:5, how long is the longest part?

    <p>40 cm (B)</p> Signup and view all the answers

    Simplify the expression $\frac{a^2 - 1}{a^3 + 1}$.

    <p>$\frac{(a - 1)(a + 1)}{(a + 1)(a^2 - a + 1)}$ (C)</p> Signup and view all the answers

    What is the result of simplifying $2\sqrt{9x^4y^2}$?

    <p>$6x^2y^2$ (C)</p> Signup and view all the answers

    How much will Carol pay if the ice cream costs 30 pesos and she wants one additional scope for 15 pesos?

    <p>45 pesos (C)</p> Signup and view all the answers

    If a stick is divided in the ratio of 3:4:5, what is the combined length of the shorter parts?

    <p>36 cm (B)</p> Signup and view all the answers

    How much will Rozan Department Store pay for a double bed originally priced at P5,000 after a 20% discount?

    <p>Php 4,000.00 (A)</p> Signup and view all the answers

    What will be the total amount due at the end of 2 years for an investment of P10,000 at 8% annual simple interest?

    <p>Php 11,600 (D)</p> Signup and view all the answers

    If an employee currently earns Php 14,000 and will receive a 10% increase, what will the new salary be?

    <p>Php 15,400.00 (B)</p> Signup and view all the answers

    How much is the total amount John paid for a motorcycle, if he initially paid Php 1,800 and has monthly payments of Php 800 for 3 years?

    <p>Php 28,800 (B)</p> Signup and view all the answers

    What is the interest earned after 3 months on an investment of Php 6,000 at an 8% annual interest rate?

    <p>Php 120 (D)</p> Signup and view all the answers

    Simplify the expression $(4x + 9y - 10z) - (3x + 5y + 11z)$.

    <p>7x + 3y - z (D)</p> Signup and view all the answers

    What is the measure of an angle if its measure is twice that of its complement?

    <p>60 degrees (B)</p> Signup and view all the answers

    What angle relationship exists between the two acute angles of a right triangle?

    <p>Complementary (B)</p> Signup and view all the answers

    If the measures of the angles of a triangle are in the ratio of 2:3:4, what is the measure of the middle angle?

    <p>60° (A)</p> Signup and view all the answers

    What is the perimeter of a rectangle with length 15 cm and width 10 cm?

    <p>50 (A)</p> Signup and view all the answers

    Which set of numbers does NOT represent the sides of a right triangle?

    <p>7, 8, 12 (D)</p> Signup and view all the answers

    In a right triangle, the ratio of adjacent to hypotenuse is known as what?

    <p>Cosine (B)</p> Signup and view all the answers

    Simplify the expression $(3x - 9) / (x^2 - 9)$.

    <p>3/(x-3) (D)</p> Signup and view all the answers

    What is the probability of rolling a number divisible by 2 on a standard die?

    <p>1/2 (C)</p> Signup and view all the answers

    What is the probability of drawing a jack from a standard deck of cards?

    <p>1/13 (D)</p> Signup and view all the answers

    What is the probability of randomly selecting a red ball from a box containing 6 red, 4 white, and 5 blue balls?

    <p>2/5 (C)</p> Signup and view all the answers

    If a graduated class has 500 boys representing 25% of the total, how many students are there in total?

    <p>2,000 (D)</p> Signup and view all the answers

    In a class of 20 boys and 15 girls, what percentage do the girls represent?

    <p>43% (C)</p> Signup and view all the answers

    What is 25% of 572?

    <p>137 (A)</p> Signup and view all the answers

    If Mark answered 70% of 60 items correctly on his exam, how many items did he answer incorrectly?

    <p>18 (D)</p> Signup and view all the answers

    What is the total number of items if 500 boys represent 25% of the graduating class?

    <p>2,000 (B)</p> Signup and view all the answers

    Flashcards

    70 ÷ 7 x 5 + 64 ÷ 4 x 2

    Perform the order of operations (PEMDAS/BODMAS) to solve the equation.

    3 + 4(5 − 2 × 6) + 12(2 + 4) + 1

    Evaluate the expression by following the order of operations.

    1 + (3 × 6) −

    An incomplete expression; requires additional information to solve.

    Greatest Common Factor (GCF) of 12 and 42

    The largest whole number that divides both 12 and 42 evenly without a remainder.

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    Order of Operations (PEMDAS/BODMAS)

    A set of rules to evaluate mathematical expressions in the correct order.

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    Mathematical Expression

    A combination of numbers, variables, and operators that represents a value.

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    Factors

    Numbers that divide another number evenly.

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    Evaluate

    To find the numerical value of an expression.

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    Prime Factors of 273

    The prime numbers that multiply together to equal 273.

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    Largest Prime < 100

    The prime number nearest to 100 that is less than 100.

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    Sum of First 20 Counting Numbers

    The total value when adding all whole numbers from 1 to 20

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    Associative Property

    The grouping of numbers in an addition or multiplication problem does not change the sum or product.

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    Sum of first 20 vs sum of first 10

    How much more are the first 20 numbers than the first 10 numbers when added together.

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    Missing term in sequence

    Find the missing term in the given series which follows a certain calculation, and find the next.

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    Divisibility of 99,132.

    Identify any number that 99,132 is NOT divisible by.

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    Missing term in sequence (2nd question).

    Fill the blank spot in the given series that matches a certain sequence calculation and identify the next.

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    Complementary Angles

    Two angles are complementary if their sum is 90 degrees.

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    Angle Relationship in Right Triangle

    The two acute angles in a right triangle are complementary.

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    Ratio of Angles

    The ratio of the measures of the angles of a triangle is a way to represent their relative sizes.

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    Perimeter of a Rectangle

    The perimeter of a rectangle is the total distance around its sides.

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    Perimeter of a Square

    The perimeter of a square is the total distance around its sides. Since all sides of a square are equal, you can multiply the length of one side by 4.

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    Sides of a Right Triangle

    The lengths of the sides of a right triangle follow the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse (longest side) and a and b are the other two sides.

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    Cosine

    In a right triangle, the cosine of an acute angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

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    Pythagorean Theorem

    In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

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    Least Common Multiple (LCM) of 24 and 80

    The smallest positive integer that is a multiple of both 24 and 80.

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    Ratio for Eggs and Flour (Custard Recipe)

    A recipe calls for 4 eggs for every 8 cups of flour.

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    Eggs Needed for 32 Cups of Flour

    To make a custard dish with 32 cups of flour using the recipe from problem 24 , you would require 16 eggs.

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    Height of a Second Tree (Proportional Shadows)

    If a 5-foot tree casts a 7-foot shadow and another tree casts a 21-foot shadow, the height of the second tree is 15 feet.

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    Longest Part (Ratio of division of a stick)

    A 96 cm stick divided in a 3:4:5 ratio, the longest part/segment has length 48cm.

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    Simplify (𝑎^2 − 1) / (𝑎^3 +1)

    Simplifying the expression (𝑎^2 − 1) divided by (𝑎^3 +1) gives the result of (𝑎-1)/(𝑎^2).

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    Simplify 2(9x^4y^2)^1/2

    The expression 2√9x^4y^2, simplified, equals 6x^2y.

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    Ice Cream Cost Calculation

    The cost of ice cream is calculated by basic addition of base price and scope cost. For example if the basic price is 30 peso and extra scope is 15, then the additional cost will be 15 pesos per scope.

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    Discount Calculation

    Finding the amount of money saved when a price is reduced by a certain percentage.

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    Simple Interest

    Interest calculated only on the principal amount, not on accumulated interest.

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    Total Amount Paid

    The sum of the initial price and all subsequent payments.

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    Percentage Increase

    Calculating the amount of increase in a quantity as a proportion of the original quantity.

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    Monthly Installment

    A fixed amount paid regularly over a specified period to repay a loan or purchase.

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    Probability of an Event

    The likelihood of a specific outcome occurring in a random experiment. It is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

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    Probability of Getting a Number Divisible by 2

    In a standard six-sided die, there are three numbers divisible by 2 (2, 4, 6). Therefore, the probability is 3/6, which simplifies to 1/2.

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    Probability of Getting a Jack (Standard Deck)

    There are four Jacks in a standard deck of 52 cards. So the probability is 4/52, which simplifies to 1/13.

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    Probability of Drawing a Red Ball

    Out of 15 balls (6 red, 4 white, 5 blue), the probability of drawing a red ball is 6/15, which simplifies to 2/5.

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    Percentage Calculation

    To find a percentage of a number, divide the percentage by 100 and multiply by the number. For example, 25% of 572 is (25/100) * 572 = 143.

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    Percent of Students

    To find the percentage of girls in a class, divide the number of girls by the total number of students and multiply by 100. In this case, there are 15 girls out of 35 students, which is (15/35) * 100 = 42.86% which rounds to 43%.

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    Whole from a Percentage

    If we know a percentage (25%) and a part (500 boys) of the whole, to find the whole (total graduating class), divide the part by the percentage and multiply by 100. So, 500 / 25 * 100 = 2000.

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    Incorrect Answers

    To find the number of incorrect answers, calculate the percentage of incorrect answers (100% - 70% = 30%) and multiply it by the total number of items. So, 30% of 60 items is (30/100) * 60 = 18 incorrect answers.

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    Study Notes

    Mathematics Exam Questions

    • Basic Operations: Solve expressions like 707x5+644x2
    • Mathematical Expressions: Evaluate complex expressions involving addition, subtraction, multiplication, division, parentheses, and brackets.
    • Word Problems (Water Bill): Calculate water bills given meter readings, basic charges, and per-kiloliter costs, example provided with 417.8kl and 430.4kl meter readings.
    • Products of Integers: Identify integer products, example provided with 13 and an integer as the element
    • Prime Numbers: Recognize prime numbers and differentiate them from composite numbers; example provided with numbers
    • Prime Factorization: Determine the prime factors of a given number, example provided with 273.
    • Largest Prime Number: Identify the greatest prime number less than 100, example provided with a number range less than 100.
    • Mathematical Properties: Recognize and apply mathematical properties such as associative, distributive, and others.
    • Greatest Common Factor (GCF): Calculate the GCF of given numbers and expressions, example provided with 12 and 42.
    • Least Common Multiple (LCM): Calculate the LCM of numbers and expressions, example provided.
    • Series and Patterns: Identify missing terms in numerical series/patterns/sequences; example 5, 20, 80, ...
    • Counting Numbers (Sums): Calculate sums of counting numbers within a specific range, example provided with first 20 counting numbers.
    • Divisibility Rules: Apply divisibility rules/tests for different numbers; example provided with 99, 132 and a range of numbers up to 100.
    • Fractions (Operations): Solve problems involving fractions; example provided involving fraction 11/23 and operations.
    • Measurements (Conversions): Perform conversions between units of measurement, such as centimeters to kilometers; example 1km to cm
    • Proportions: Solve problems involving proportions (ratios), example provided with ratio m/12 = 30/24
    • Roots and Radicals: Simplify radical expressions, example provided with √9x⁴y²
    • Algebraic Expressions: Simplify algebraic expressions of different types. Examples are provided with complex expressions with addition, subtraction, brackets.
    • Solving Equations: Solve simple algebraic equations; examples provided including solving for x.
    • Functions: Evaluate functions for given values, example provided with a function and value for x.
    • Quadratic Equations: Solve quadratic equations, example provided with quadratic equation.
    • Geometry (Perimeter): Calculate the perimeter of shapes like rectangles, squares; examples provided with rectangle and square
    • Geometry (Area): Calculate areas of shapes like triangles, trapezoids, example provided with trapezoid
    • Geometry (Volume): Calculate volumes, example provided with a cube
    • Geometry (Right Triangles): Calculate sides of/work with/ identify sides of right triangles, example provided with two sides of a right triangle
    • Geometry (Similar Triangles): Solve ratio problems related to similar triangles, example provided with similar triangles involving heights/shadows
    • Word Problems (Ratio): Solve problems involving ratios, example provided with a problem involving the division of a stick
    • Ratio Problems (Work/Labor): Solve problems involving rates of work and labor; example provided with laborers harvesting coffee.
    • Average and Mean: Calculate averages/means; examples provided with test scores/quantities
    • Measures of Central Tendency/Statistical Distributions: Identify measures like mode, median, and range from data sets, example provided with a set of scores for a test
    • Probability: Calculate probabilities, examples provided with getting particular cards from a deck, or specific occurrences in experiments
    • Word Problems (Compound Shapes): Solve problems involving compound shapes, example provided with a shape
    • Angles: Calculate measures of angles, example provided with angles and their relationships

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    Description

    Test your understanding of various mathematical concepts including basic operations, word problems, and prime numbers. This quiz covers evaluating expressions, calculating water bills, and identifying prime factors. Challenge yourself with a range of questions to reinforce your math skills.

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