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Questions and Answers
Which of the following numbers has the largest value?
What grade should Ruben aim for in the 7th subject to achieve an average of 91?
How many liters does the tank contain when it is 50% full if it contains 18 liters at 20% full?
What is the volume in cubic inches of a rectangular solid with dimensions 1.5 feet by 1½ feet by 3 inches?
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What would Danny receive for his 10 hours of work at a rate of P50 per hour?
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If the ratios of hours worked by Cesar, Bert, and Danny are 3:4:5, respectively, how many hours did Cesar work?
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What is the total sum of Ruben's grades before calculating the required grade for the seventh subject?
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If the total work hours at the internet shop is 24 hours divided among three technicians, what does the ratio 3:4:5 imply about the total hours worked?
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What is the area of the triangle with vertices at (1,4), (2,3), and (3,0)?
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What is the altitude to the hypotenuse in a right triangle with legs measuring 10 cm and 24 cm?
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What is the tenth term in the sequence 3, 10, 17, 24, …?
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What is the inverse of the function y = x^2 + 10x?
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What is the remainder when x^4 – 5x^3 + 6x^2 + 2x + 1 is divided by (x – 2)?
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In the function y + 25 = (x + 5)^2, what is the value of y when x = 0?
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If Fe's age and Sita's age sum up to 60 and Fe was twice Sita's age twelve years ago, how old is Sita now?
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What is the value of the hypotenuse in a right triangle with legs measuring 10 cm and 24 cm?
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If x is the present age of Fe, and 12 years ago his age was represented as x - 12, what is the value of x?
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Victor's average dropped from 94 to 93 after a new test. What was his most recent grade?
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What will happen to the area of a rectangle if its length increases by 20% and width decreases by 10%?
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If X is 3 of Y and Y is 4 of Z, what part of Z is X?
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What equation is used to derive the new score after changing average scores?
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In the equation x - 12 = (2)(48 - x), what does x represent in the context?
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After performing the operation, what is the computed value of 60 - x when x equals 36?
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What property is applied in the equation 8x = 15z to derive x = z?
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What is the value of x in the equation $x^2 + 2x = 1443$?
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What is the limit of the function f(x) as x approaches 4, given that $f(x) = \begin{cases} 4 & x = 4, \ x - 7 & x > 4 \end{cases}$?
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What is the remainder when 534,214,557,989,215 is divided by 4?
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If today is Saturday, what day of the week will it be 125 days from today?
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What is the surface area of a sphere with a radius of 6 cm?
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How can dividing by 0.125 be expressed in terms of multiplication?
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If the sum of the supplement and complement of an angle is 124 degrees, what is the angle?
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What is the next integer after 39?
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What is the reference angle for 216 degrees?
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Which of the following angles is coterminal with 40 degrees?
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What is the coterminal angle of 216 degrees when it is reduced within one full rotation?
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Which equation represents a line passing through the origin and the point (3, 4)?
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What is the formula to find reference angles in the third quadrant?
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Which of the following correctly describes the equation given for a line through (0,0) and (3,4)?
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How do you determine the range of the function f(x) = -2x^2 + 4x?
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Which of the following expressions represents the standard form of coterminal angles?
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Study Notes
Mathematics Exam Questions Overview
- Identify the largest number among a given set: Options include 85, 39, 65, 94. The largest is 94.
- To achieve a 91 average score in six subjects, determine the required grade for the seventh subject. Current grades are 88, 90, 97, 90, 91, and 86.
- For a water tank, if 20% capacity is 18 liters, calculate the capacity at 50% full.
- Volume calculation for a rectangular solid with dimensions: 1.5 feet, 1.5 feet, and 3 inches. Convert dimensions to inches for volume measurement.
- Determine the area of a triangle with vertices at points (1,4), (2,3), and (3,0).
- Calculate the altitude to the hypotenuse in a right triangle with legs measuring 10 cm and 24 cm.
- Find the tenth term in the series 3, 10, 17, 24, … using the formula for arithmetic sequences.
- Solve for the inverse of the quadratic function y = x² + 10x.
- Find the remainder when dividing a polynomial x⁴ – 5x³ + 6x² + 2x + 1 by (x – 2).
- Age problem: Given sum of ages of Fe and Sita is 60 with a condition that Fe was twice as old as Sita 12 years ago.
- Average grade calculation of Victor after four tests with grades leading to an average drop after a subsequent test.
- Analyze the effects on area when the dimensions of a rectangle change by certain percentages.
- Relationship between proportions of X, Y, and Z in a given ratio.
- Find the day of the week 125 days from a Saturday.
- Calculate the limit of a piecewise function at a specific point.
- Determine the surface area of a sphere with a radius of 6 cm.
- Analyze angles in standard position and their coterminal equivalents.
- Find the equation of a line through specific coordinates and derive its slope.
- Establish the range of a quadratic function expressed as f(x) = -2x² + 4x.
Problem Solving Techniques
- Use a calculator for numerical comparison and polynomial divisions.
- Apply the arithmetic mean formula for average calculations.
- Ratio and proportion concepts for age-related questions.
- Understand the geometric properties necessary for area and volume calculations.
- Familiarize with quadratic functions for inverse solving and limits.
- Coterminal angles can be computed using the expression 360N + θ.
Key Formulas
- Average: ( \text{Average} = \frac{\text{Sum of all values}}{\text{Number of values}} )
- Volume of a rectangular prism: ( V = l \times w \times h )
- Area of triangle using coordinates: ( \text{Area} = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| )
- Surface area of a sphere: ( A = 4\pi r^2 )
- Slope formula for a line: ( m = \frac{y_2 - y_1}{x_2 - x_1} )
General Tips
- Ensure to convert all measurements to a consistent unit before calculations.
- Check for common numerical patterns in sequences and series for simpler solutions.
- For piecewise functions, evaluate limits from both sides to determine continuity.
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Description
Test your skills in comparing numbers and calculating averages with this math quiz. You'll encounter questions that require critical thinking and basic calculations, perfect for honing your mathematical abilities. Challenge yourself to find the largest value and compute necessary scores for achieving desired averages.
