Podcast
Questions and Answers
Albie can finish a 500-word essay in 4 hours. When Franz helps, they complete it in 1 1/2 hours. How long does it take Franz to finish a 500-word essay alone?
Albie can finish a 500-word essay in 4 hours. When Franz helps, they complete it in 1 1/2 hours. How long does it take Franz to finish a 500-word essay alone?
- 2.1 hours
- 1.2 hours
- 2.4 hours (correct)
- 4.2 hours
Simplify the following expression: $\frac{(a^3b^5)^{-2}}{ab^2c}$
Simplify the following expression: $\frac{(a^3b^5)^{-2}}{ab^2c}$
- $ab\sqrt{bc}$
- $-2\left(\frac{a^2b^3}{c}\right)$
- $\frac{a^4b^{10}}{a^2b^4c^2}$
- $\frac{c^2}{a^4b^6}$ (correct)
Simplify the expression: $\frac{\sqrt[3]{2} \cdot \sqrt[3]{16} \cdot \sqrt[3]{54}}{\sqrt[3]{216}}$
Simplify the expression: $\frac{\sqrt[3]{2} \cdot \sqrt[3]{16} \cdot \sqrt[3]{54}}{\sqrt[3]{216}}$
- $\sqrt[3]{\frac{2}{3}}$
- 1 (correct)
- 0
- 2
Simplify the expression: $3^{2 \log_3 a + 4 \log_3 b - \log_3 c}$
Simplify the expression: $3^{2 \log_3 a + 4 \log_3 b - \log_3 c}$
Solve the products of polynomials: $(x + 1)(x - 1)(x^4 + x^2 + 1)$
Solve the products of polynomials: $(x + 1)(x - 1)(x^4 + x^2 + 1)$
Assuming the pattern continues, what comes after the last term of the sequence: -1, 4, -9, 16, -25
Assuming the pattern continues, what comes after the last term of the sequence: -1, 4, -9, 16, -25
In the given circle, if the ratio between segments ST and PT is 4/3, what is the ratio between RT and QT?
In the given circle, if the ratio between segments ST and PT is 4/3, what is the ratio between RT and QT?
Which of the following does NOT belong in the Triangle Congruence Theorems? *A means Angle and S means Side
Which of the following does NOT belong in the Triangle Congruence Theorems? *A means Angle and S means Side
Which of the following is NOT a real-valued function?
Which of the following is NOT a real-valued function?
What is the probability of getting an even and an odd number after rolling two dice?
What is the probability of getting an even and an odd number after rolling two dice?
In how many ways can you select from 4 shirts, 2 pants, and 7 hats if you have to wear one of each type of clothing?
In how many ways can you select from 4 shirts, 2 pants, and 7 hats if you have to wear one of each type of clothing?
How many 3-digit even numbers can be made using the digits 1, 3, 5, 6, 8, and 9 if no digit is repeated?
How many 3-digit even numbers can be made using the digits 1, 3, 5, 6, 8, and 9 if no digit is repeated?
If there are 7 points in a plane, and no 3 of the points lie along the same line, how many unique lines can be drawn between pairs of these 7 points?
If there are 7 points in a plane, and no 3 of the points lie along the same line, how many unique lines can be drawn between pairs of these 7 points?
What are the mean, median, and mode of the following ungrouped data set? 24, 13, 26, 24, 25, 27, 11, 24, 25, 18
What are the mean, median, and mode of the following ungrouped data set? 24, 13, 26, 24, 25, 27, 11, 24, 25, 18
Which of the following correlation scatter plots with data interpretation is more likely to be correct?
Which of the following correlation scatter plots with data interpretation is more likely to be correct?
Which of the following is NOT a Pythagorean triple?
Which of the following is NOT a Pythagorean triple?
Considering the given right triangle, which of the following is TRUE?
Considering the given right triangle, which of the following is TRUE?
Which of the following is FALSE?
Which of the following is FALSE?
With A=60°, B=30°, and D=E=45°, which of the following is true about the triangles shown?
With A=60°, B=30°, and D=E=45°, which of the following is true about the triangles shown?
Using law of sines, which equation can be used to derive the length of side 'a'?
Using law of sines, which equation can be used to derive the length of side 'a'?
Solve for x in the equation: $3x + 7 = 22$
Solve for x in the equation: $3x + 7 = 22$
Factor the quadratic equation: $x^2 - 5x + 6 = 0$
Factor the quadratic equation: $x^2 - 5x + 6 = 0$
Solve the inequality: $2x - 3 \leq 7$
Solve the inequality: $2x - 3 \leq 7$
Simplify: $(4a^3b^2)(5a^2b^3)$
Simplify: $(4a^3b^2)(5a^2b^3)$
What is the distance between points (2, -3) and (5, 1) in the Cartesian plane?
What is the distance between points (2, -3) and (5, 1) in the Cartesian plane?
If a triangle has sides of length 5 and 8 and the angle between them is 60 degrees, what is the length of the third side?
If a triangle has sides of length 5 and 8 and the angle between them is 60 degrees, what is the length of the third side?
What is the area of a circle with a diameter of 10?
What is the area of a circle with a diameter of 10?
In a bag, you have 3 red marbles and 5 blue marbles. What is the probability of picking a red marble?
In a bag, you have 3 red marbles and 5 blue marbles. What is the probability of picking a red marble?
You flip a coin three times. What is the probability of getting exactly two heads?
You flip a coin three times. What is the probability of getting exactly two heads?
What is the median of the following data set: 12, 15, 18, 21, 24?
What is the median of the following data set: 12, 15, 18, 21, 24?
What is the mode of the following data set: 2, 3, 3, 4, 5, 5, 5, 6?
What is the mode of the following data set: 2, 3, 3, 4, 5, 5, 5, 6?
Which of the following is the graph of y = sin(x)?
Which of the following is the graph of y = sin(x)?
Simplify: $sin^2(\theta) + cos^2(\theta)$
Simplify: $sin^2(\theta) + cos^2(\theta)$
If tan($\theta$) = 1, what is the value of $\theta$?
If tan($\theta$) = 1, what is the value of $\theta$?
Given that a right triangle has an angle of 30 degrees and the hypotenuse has a length of 10, what is the length of the side opposite the angle?
Given that a right triangle has an angle of 30 degrees and the hypotenuse has a length of 10, what is the length of the side opposite the angle?
What is the value of $\cos(\frac{\pi}{2})$?
What is the value of $\cos(\frac{\pi}{2})$?
If $f(x) = x^2 + 3x - 5$, find $f(2)$?
If $f(x) = x^2 + 3x - 5$, find $f(2)$?
What is the slope of the line $2y = 4x + 6$?
What is the slope of the line $2y = 4x + 6$?
Flashcards
Exponent
Exponent
The number that indicates how many times a base is multiplied by itself.
Multiplication of Powers (Same Base)
Multiplication of Powers (Same Base)
When multiplying powers with the same base, add the exponents.
Division of Powers (Same Base)
Division of Powers (Same Base)
When dividing powers with the same base, subtract the exponents.
Power of a Power Rule
Power of a Power Rule
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Zero Exponent
Zero Exponent
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Inverse/Negative Exponent
Inverse/Negative Exponent
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Fractional Exponent
Fractional Exponent
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Pythagorean Triple
Pythagorean Triple
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Cotangent (cot θ)
Cotangent (cot θ)
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sin θ = cos(90° - θ)
sin θ = cos(90° - θ)
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Law of Sines
Law of Sines
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Mode
Mode
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Median
Median
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Mean
Mean
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Study Notes
- The document is a mathematics review for DOST x NCR in 2023.
- The review covers Algebra, Geometry, Probability, Statistics, and Trigonometry.
Algebra: Question 1
- Albie can finish a 500-word essay in 4 hours
- When Franz helps, the essay is completed in 1.5 hours
- To determine how long Franz needs to finish the essay alone, 1/4 + 1/x = 1/3/2
- Franz needs 2.4 hours to finish a 500-word essay
Algebra: Laws of Exponent
- Multiplication of Powers with Common Bases: (x⁵)(x³) = x^(5+3) = x⁸ and (2³)(2²) = 2^(3+2) = 2⁵ = 32.
- Multiplication of Powers with Different Bases but Same Exponents: (x³)(y³) = (xy)³ and (3³)(2³) = (3x2)³ = 6³ = 216.
- Division of Powers with Common Bases: (x³)/(x²) = x^(3-2) = x
- (4⁵)/(4³) = 4^(5-3) = 4² = 16
- Power of a Fraction Rule: (x/y)⁴ = x⁴/y⁴ and (⅔)³ = 2³/3³ = 8/27
- Power of a Power Rule: (x⁵)³ = x^(53) = x¹⁵ and (4²)² = 4^(22) = 4⁴ = 256
- Zero Exponent: (x)⁰ = 1 and -591⁰ = 1
- Inverse Rule / Negative Exponent: x⁻² = 1/x² and 2⁻⁴/3⁻³ = 3³/2⁴ = 27/32
- Fractional Exponent: x^(1/2) = √x and 54^(1/3) = ³√54 = ³√(27*2) = 3∛2
Algebra: Question 2
- Simplify the expression (a³b⁵/ab²c)⁻² to c²/a⁴b⁶
Algebra: Question 3
- Simplify ³√(2) * ³√(16) * ³√(54)/√216 which equals 1
Algebra: Question 4
- Simplify 3^(2log₃a + 4log₃b - log₃c) which equals a²b⁴/c
Algebra: Question 5
- Solve the product of polynomials (x + 1)(x - 1)(x⁴ + x² + 1) which equals x⁶ - 1
Algebra: Question 6
- The sequence -1, 4, -9, 16, -25 continues with 36.
Geometry: Question 7
- Given the ratio between segments ST and PT is 4/3, the ratio between RT and QT is 4/3 because the triangles formed are similar.
Geometry: Question 8
- AAA does not belong to the the Triangle Congruence Theorems
Geometry: Question 9
- A real-valued function contains set of values which are all real
Probability: Question 10
- The probability of getting an even and an odd number after rolling two dice is 1/2
- In a die, there are three even and three odd number outcomes.
- The probability of having odd and even respectively after rolling two dice is 1/4.
- The probability of having even and odd respectively after rolling is 1/4.
- Hence, the probability of getting an even and an odd number after rolling two dice is 1/2.
Probability: Question 11
- There are 56 ways to select from 4 shirts, 2 pants, and 7 hats wearing one of each.
- Multiply the number of choices: 4 * 2 * 7 = 56.
Probability: Question 12
- With no digits repeating, there are 40 possible three-digit even numbers using the digits 1, 3, 5, 6, 8, and 9.
- Only two digits (6 and 8) can be in the one's place
- Taking away one digit for the tenth place, 5 digits remain for the hundreds and ten place
- 542 = 40.
Probability: Question 13
- With no 3 points lying along the same line, 21 unique lines can be drawn connecting pairs of 7 points in a plane
- This implies that the number of unique lines that can be drawn are ₂C₇ = n!/r!(n-r)!
- = 7!/(7-2)! 2! = 7!/5! 2! = 7 * 6/2 = 21
Statistics: Question 14
- Given the data set 24, 13, 26, 24, 25, 27, 11, 24, 25, 18:
- The mean is 21.7.
- The median is 24.
- The mode is 24.
- “Mean" is the average of a given data set.
- “Median" is the middle value of a given data set.
- “Mode" is the data value which occurs the most.
Statistics: Question 15
- Option a has a correct interpretation between the scatter plots and data
Trigonometry: Question 16
- Of the following, 13, 83, 84 is NOT a Pythagorean triple
- a is a known triple
- b and c, can be further simplified into 5,12,13 and 7,24,25, which are also known triples.
Trigonometry: Question 17
- A right triangle shows cot θ=a/b
Trigonometry: Question 18
- cos(2θ) = cos² θ + sin² θ is false because Note that because cos² θ + sin² θ = 1
Trigonometry: Question 19
- In two triangles it can be mirrored with respect to side a and form an equilateral triangle with side length c, hence c=2b. therefore d=e
Trigonometry: Question 20
- Using the law of sines which describes the correct length of a indicates a = b sin A/ sin b
- Law of sines states sin A/a = sin B/b = sin C/c
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