Solution and Answer Guide For Discovering
Mathematics A Quantitative Reasoning
[- 52 - 5] + [-22 - 12] - ANSWERSD. 9
1 x² - 1 is undefined for values - ANSWERSC. ±1
The sum of (8x² - 7x - 2y), (5x² - 6x - 15y) and -4x² + 11x - 9y is - ANSWERSA. 9x² - 2x - 26y
Angel bought 63 4 meters of silk, 31 2 meters of satin and 82 5 meters of velvet. How many
meters of cloth did she buy? - ANSWERSB. 18 1/20
Mr. Tan has 13 2/5 liters of gasoline in his car. He wants to travel far so he added 16 1/2 liters
more. How many liters of gasoline is in the tank? - ANSWERSA. 29 9/10 liters
Agnes said, "I'm thinking of a number N. If I increased my number by 56.2, the sum is 14.62."
What was Agnes' number? - ANSWERSA. -41.58
How many thirds are there in six-fifths? - ANSWERSC. 33/5
What is the variance of the scores 5, 4, 3, 6, and 2? - ANSWERSA. 2
Maria was preparing the oven to bake brownies. The recipe's direction was to preheat the oven
to 350°F but her oven thermometer was in °C. What should be the thermometer reading? -
ANSWERSC. 176.67°C
The equation of the line that passes through (5,8) and with a slope 4 is - ANSWERSA. 4x - 12 = y
,Determine the value of n so the line that passes through (2,1) and (n,5) has a slope of 4/7 -
ANSWERSB. 10
Find the value of k such that x² + 5x + k = 0 has equal roots. - ANSWERSA. 25/4
A quadratic equation in x with roots 2 + √5 and 2 - √5 is - ANSWERSB. x² - 4x + 1 = 0
The product of two consecutive positive integers is larger than the sum of the two integers by
155. The integers are - ANSWERSB. 13 and 14
The measure of each exterior angle of a regular 20-gon is - ANSWERSA. 180
Three coins are tossed. How many outcomes are possible? - ANSWERSC. 8
A card is drawn from a well-shuffled deck. What is the probability of drawing a king? -
ANSWERSB. 1/13
What is the radius of the circle whose circumference is Aπ? - ANSWERSA. 2
What is the measure of each angle in a regular octagon? - ANSWERSA. 135°
Find the radius of a circle if the length of a 60° arc is 18π. - ANSWERSC. 44
Find the degree measure of the arc of the sector whose area is 8π in a circle with radius 6 cm. -
ANSWERSB. 80°
One leg of a triangle is 9.2 cm. If the tangent of the angle between the hypotenuse and the
other leg is 1.56, how long is the other leg? - ANSWERSB. 6.90 cm
, A teacher saves P5000 every 6 months in an account that pays 20% compounded monthly. How
much will her savings be after 10 years? - ANSWERSB. 111,197.06
Which of the following statements is a proposition? - ANSWERSA. Mindanao is an island in the
Philippines
∧ - ANSWERSA logical operator that means P and Q
Tautology - ANSWERSA proposition that is always true
Valid and Sound Statement - ANSWERSIf you study hard... then your job opportunities increase.
Circle Equation - ANSWERSThe equation with center at (3,0) and radius = 4 is x² + y² - 6x = 7
Line - ANSWERSIt has length, but no width and no thickness and extends indefinitely in both
directions.
Polygon - ANSWERSA union of three or more coplanar segments that intersect at endpoints,
each shared by only two non-collinear segments
Function - ANSWERSConsidered the main building block of Calculus
Plane - ANSWERSA flat surface that extends infinitely in all directions
Altitude - ANSWERSA segment of a triangle if it is perpendicular from a vertex to the opposite
side
Mathematics A Quantitative Reasoning
[- 52 - 5] + [-22 - 12] - ANSWERSD. 9
1 x² - 1 is undefined for values - ANSWERSC. ±1
The sum of (8x² - 7x - 2y), (5x² - 6x - 15y) and -4x² + 11x - 9y is - ANSWERSA. 9x² - 2x - 26y
Angel bought 63 4 meters of silk, 31 2 meters of satin and 82 5 meters of velvet. How many
meters of cloth did she buy? - ANSWERSB. 18 1/20
Mr. Tan has 13 2/5 liters of gasoline in his car. He wants to travel far so he added 16 1/2 liters
more. How many liters of gasoline is in the tank? - ANSWERSA. 29 9/10 liters
Agnes said, "I'm thinking of a number N. If I increased my number by 56.2, the sum is 14.62."
What was Agnes' number? - ANSWERSA. -41.58
How many thirds are there in six-fifths? - ANSWERSC. 33/5
What is the variance of the scores 5, 4, 3, 6, and 2? - ANSWERSA. 2
Maria was preparing the oven to bake brownies. The recipe's direction was to preheat the oven
to 350°F but her oven thermometer was in °C. What should be the thermometer reading? -
ANSWERSC. 176.67°C
The equation of the line that passes through (5,8) and with a slope 4 is - ANSWERSA. 4x - 12 = y
,Determine the value of n so the line that passes through (2,1) and (n,5) has a slope of 4/7 -
ANSWERSB. 10
Find the value of k such that x² + 5x + k = 0 has equal roots. - ANSWERSA. 25/4
A quadratic equation in x with roots 2 + √5 and 2 - √5 is - ANSWERSB. x² - 4x + 1 = 0
The product of two consecutive positive integers is larger than the sum of the two integers by
155. The integers are - ANSWERSB. 13 and 14
The measure of each exterior angle of a regular 20-gon is - ANSWERSA. 180
Three coins are tossed. How many outcomes are possible? - ANSWERSC. 8
A card is drawn from a well-shuffled deck. What is the probability of drawing a king? -
ANSWERSB. 1/13
What is the radius of the circle whose circumference is Aπ? - ANSWERSA. 2
What is the measure of each angle in a regular octagon? - ANSWERSA. 135°
Find the radius of a circle if the length of a 60° arc is 18π. - ANSWERSC. 44
Find the degree measure of the arc of the sector whose area is 8π in a circle with radius 6 cm. -
ANSWERSB. 80°
One leg of a triangle is 9.2 cm. If the tangent of the angle between the hypotenuse and the
other leg is 1.56, how long is the other leg? - ANSWERSB. 6.90 cm
, A teacher saves P5000 every 6 months in an account that pays 20% compounded monthly. How
much will her savings be after 10 years? - ANSWERSB. 111,197.06
Which of the following statements is a proposition? - ANSWERSA. Mindanao is an island in the
Philippines
∧ - ANSWERSA logical operator that means P and Q
Tautology - ANSWERSA proposition that is always true
Valid and Sound Statement - ANSWERSIf you study hard... then your job opportunities increase.
Circle Equation - ANSWERSThe equation with center at (3,0) and radius = 4 is x² + y² - 6x = 7
Line - ANSWERSIt has length, but no width and no thickness and extends indefinitely in both
directions.
Polygon - ANSWERSA union of three or more coplanar segments that intersect at endpoints,
each shared by only two non-collinear segments
Function - ANSWERSConsidered the main building block of Calculus
Plane - ANSWERSA flat surface that extends infinitely in all directions
Altitude - ANSWERSA segment of a triangle if it is perpendicular from a vertex to the opposite
side
