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# General Mathematics

Aims to develop learners' understanding of concepts and techniques drawn from number and algebra, trigonometry, finance, networks and decision mathematics.

## finite probability

Two race car drivers Ryan and Philip were taking laps around the race track. It was noted that Ryan drove 52.5 miles in the same time that Philip drove 37.5 miles. If Ryan's average speed was 30 mph more than that of Philip, what was Ryan's average speed?

• a. 75 mph
• b. 85 mph
• c. 115 mph
• d. 105 mph

p=(5,125,000V2−449,000V+19307)/(125V2(1,000V−43))

• 0

Given the Function: {(10, 9), (11, 8), (12, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Range:

• 9 8 7

For the function g(x) = 3x, find g(0) =

• 1

f(x)=x+2 f(x)=x+2 | -x2 + x + 6

• f - g

The relation pairing an SSS member to his/her SSS number is a one-to-one function.

• True
• False

After taking a certain antibiotic, the concentration (C) of the drug in the patient's bloodstream is given by C(x)=(0.04t)/(t2−2)

• a. 4 hours
• b. 3 hours
• c. 5 hours
• d. 2 hours

Given f(x)=x−2 f(x)=x−2, find the following: f(3)=

• 1

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. -x + 3

• f - g

Given f(x)=x−2 f(x)=x−2, find the following: f(0)=

• -2

Given f(x)=x−2 f(x)=x−2, find the following: f(−1)=

• -3

If g(x) = -4a+7. Find g(2a).

• -8a+7

Let f(x) = 4x-5 and g(x) = 3x, find (fog)(x).

• 12x-5
• Solve for the logarithmic expression:
• log7 (73 • 78) = Answer
• 11

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=5−9x

• YES

f(x)=x+2 f(x)=x+2 | x - 2

• g/f

Maya has an internet service that currently has a monthly access fee of Php 999.00 pesos and a connection fee of Php 1.00 per hour. How much will she pay if she was able to use the service for 15 days?

• 1359

Find the value of the following logarithmic expressions (c) log5 5 =

• 1

Find the solution for each rational equation: 3/x+1 = 2/x-3

• 11

Evaluate ƒ(x) = /x +2/, given the ƒ(-9).

• a. -11
• b. 7
• c. -7
• d. 11

Given the equation (5^(-2x -10) = 25^(x + 1)), solve for the value of x that will make the equation true.

• -3

For the function g(x) = 3x, find g(4) =

• 81

The weekly sale S (in thousands of units) for the t^th week after the introduction of the product in the market is given by S=(120t)/(t2+100)

• a. Fourth
• b. Ninth
• c. Tenth
• d. Fifth

The graph of a function and its inverse are always reflections of each other in the line y = x

• True
• False

Let f(x) = 4x-5 and g(x) = 3x, find (fg)(x).

• 12x^2-15x

Solve for the following logarithmic functions: (a) log3 (2x-1) = 2 x =

• 5

Given ƒ(x) = x2 and g(x) = 2x – 3, compute (ƒ o g)(x); then find (ƒ +g)(2).

• a. 5
• b. 7
• c. 6
• d. 4

The total cost for playing paintball is Php 100 per gun for rent and Php 1000 per 2000 paintballs. Assuming only 2000 paintballs is allowed for team who will play, which of the following function notation matches the situation?

• a. P(x) = 100x + 2000
• b. P(x) = 100 + 2000x
• c. P(x) = 2000 - 100x
• d. P(x) = 2000x + 100x

Find g(7) in a function g(x) = x2 -3x – 2.

• a. -9
• b. 26
• c. 9
• d. -5

One hundred meters of fencing is available to enclose a rectangular area next to a river. Give a function A that can represent the area that can be enclosed in terms of x. x2 +

• 50

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=x

• YES

Admission price to Enhcanted Kingdom park is Php 600 per person. The average patron attending EK spends about Php 500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.

• a. E(x) = (600 + 500)x
• b. E(x) = 600 + 500x
• c. E(x) = 600x + 500
• d. E(x) = (600x + 500)x

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 2x2 + 9x + 12

• f∙g

One hundred meters of fencing is available to enclose a rectangular area next to a river. Give a function A that can represent the area that can be enclosed in terms of x. Function : A =

• -0.5

Find the value of the following logarithmic expressions (a) log2 32 =

• 5

The cost of joining a gym membership includes a one time sign-up fee of Php 2000 plus Php 1000 for each month of membership. Which of the following function notations matches this situation?

• a. G(m) = (1000 + 2000)m
• b. G(m) = 2000 + 1000m
• c. None of the given
• d. G(m) = 1000 + 2000m

y−intercept

• 1

If g(x) = (x+2)/3. Find g(-8).

• -2

(log3 2)(log3 4) = log3 6

• True
• False

Given the Function: {(10, 9), (11, 8), (12, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Domain:

• 10 11 12

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). Are the two functions inverse of each other? (Note: "Yes" or "No")

• yes

What is the zero of the logarithmic function: f(x) = log3 (x-1)? Zero:

• 0

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). What is the equivalent conversion of 0°C to Fahrenheit?

• 32.00

3(log9 x)2 = 6 log9 x

• True
• False

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. x+4 / 2x+1

• f/g

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). What is the equivalent conversion of 68°F to Celsius?

• 20.00

The relation pairing a real number to its square is a one-to-one function.

• True
• False

Find the solution for the rational equation: ((2/(x+1)+5/2x)=2).

• 0 and -1/5

The vertical line test is used to determine whether a function is one-to-one when its graph is given.

• True
• False

All functions have inverse functions.

• True
• False

Let f(x) = 4x-5 and g(x) = 3x, find (f/g)(x).

• (4x-5)/3x

f(x)=squarerootof(x−3)

• 5

For the function g(x) = 3x, find g(-4) =

• 1/81

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 2x + 5

• f of g

Bananas are sold at Php 50.00 per kilo. Write a function notation that describes this situation.

• a. B(x) = x - 50
• b. B(x) = x / 50
• c. B(x) = 50x
• d. B(x) = x + 50

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=squarerootof(2−5x8)

• NO

Solve for the value of x: 7x+4 = 492x-1 x =

• 2

If g(x) = 3x^2+2x-1. Find g(-1).

• 0

Which of the following is the inverse of f(x) = ½(3x + 4)?

• a. f-1(y) = ½ (3y-4)
• b. f-1(y) = 2/3 (y-2)
• c. f-1(y) = 2/3 (y-4)
• d. f-1(y) = 1/3 (2y+4)

Admission price to Universal Studios park is Php 2600 per person. The average patron attending spends about Php 1500 on food, drinks, games, and souvenirs. Find the function notation that accurately describes this situation.

• a. E(x) = (2600x + 1500)x
• b. E(x) = 2600 + 1500x
• c. E(x) = (2600 + 1500)x
• d. E(x) = 2600x + 1500

If g(x) = 4|x-3|+2. Find g(1).

• 10

f(x)=x+2 f(x)=x+2 | x3 + 2x2 - 4x - 8

• f - g

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 3x + 5

• f + g

f(x)=x+2 f(x)=x+2 | x2 - 2

• f ∘ g

log 22 = (log 2)2

• True
• False

Find the value of the following logarithmic expressions (b) log9 729 =

• 3

Given the Function: {(1, 2), (2, 5), (3, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Domain:

• 1 2 3

Tell whether the following is a characteristic of stocks or bonds: (a) A form of debt financing, or raising money by borrowing from investors.

• Bond

Simplify the given expressions and find the value of x.

• 64

Solve for the following logarithmic functions: (b) logx 16 = 2 x =

• -4

Solve for the following logarithmic functions: and

• 4

What is the zero of the logarithmic function: f(x) = log3 (x-1)? What is the vertical asymptote of the function? x =

• 0

Temperatures are normally expressed in degree Celsius in the Philippines and in Fahrenheit in some western countries. If the function for fahrenheit to celsius conversion is (T(°C) = (T(°F) - 32) × 5/9), the celsius to fahrenheit conversion is (T(°F) = (T(°C) × 9/5) + 32). What is the equivalent conversion of 70°F to Celsius?

• 21.11

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=3−8x2

• NO

Simplify (x2 + 2x – 3) – (x2 – 2x -3).

• a. 4x – 6
• b. 0
• c. 4x
• d. -2x2 -4x – 6

Which of the following does not represent an exponential function?

• a. The conversion of fahrenheit to celsius
• b. half life of nuclear matter
• c. compound interest of loans acquired
• d. population growth of microorganisms

(log3 2)(log3 4) = log3 8

• True
• False

Are the following functions one-to-one? (Answer by typing "Yes" or "No" - without the quotation marks) f(x)=10

• NO

log3 2x2 = 2 log3 2x

• True
• False

For the function g(x) = 3x, find g(-2) =

• 1/9

Solve for the value of x: 4x+2 = 82x x =

• 1

Tell whether the following is a characteristic of stocks or bonds: (a) A form of equity financing or raising money by allowing investors to be part owners of the company.

• Stock

Given the Function: {(1, 2), (2, 5), (3, 7)}, give the domain and the range. (Note: give the values separated by a space. example: Range: 1 2 3) Range:

• 2 5 7

The average cost per unit C(x), in dollars, to produce x units of toy cars is given by C(x)=(8000)/(x−50)

• a. \$43.60
• b. \$56.40
• c. \$6.15
• d. \$6.67

3/(x+1)=2/(x−3)

• 11

Given ƒ(x) = x2 and g(x) = 2x – 3, find (ƒ o g)(x).

• a. 4x2 – 12x + 9
• b. 4x2 - 9
• c. 4x2 + 9
• d. 4x2 + 12x - 9

If h (x) = (x + 2)/3, find h(-8).

• a. ½
• b. -½
• c. -2
• d. 2

Let f(x) = -10x-18 and g(x) = -3x, find (f-g)(x).

• -7x-18

Which of the following function notation describes the ordered number pair P(x) = {(1,11), (2,22), (3,33), (4,44)}?

• f(x) = x - 11
• f(x) = 11/x
• f(x) = x + 11
• f(x) = 11x

Consider the rational expression f(x)=5x−1−x+2, What is its vertical asymptote? x =

• 2

3 log9 x2 = 6 log9 x

• True
• False

Simplify (4q2r2s3 )3 .

• a. 64q6r6s9
• b. 43q6r6s9
• c. 12q6r6s9
• d. 43q5r5s6

The absolute value function for the domain of all positive real numbers has an inverse function.

• True
• False

From the table of values, identify which value of x are the zeroes of the function.

• -3 and 2

f(x)=x+2 f(x)=x+2 | x2 + x - 2

• f + g

Without using a calculator, find the value of the following logarithmic expression.

• 5

Find the value of each logarithmic expression. (Note: There's only one answer for the pair of logarithmic expressions indicated below.)

• 5

Simplify the expression (-4a2b-1c-2) (2a3b2c-1).

• a. -8a5c3/b
• b. -8a5bc-3
• c. -8a2b
• d. -8a5b/c3

For the function g(x) = 3x, find g(2) =

• 9

f(x)=x+2 f(x)=x+2 | 1/x-2

• f/g

Which of the is the inverse of (f(x) = 4x+12)?

• (f(x) = 12x-4)
• (f(x) = 12x+4)
• (f(x) = (x/4)+3)
• (f(x) = (x/4)-3)

Consider the rational expression f(x)=5x−1−x+2, What is its horizontal asymptote? y =

• -5

log3 2x2 = log3 2 + 2 log3 x

• True
• False

Which of the following function notation describes the ordered number pair P(x) = {(1,6), (2,11), (3,16), (4,21)}?

• a. f(x) = 5x + 1
• b. f(x) = 5x - 1
• c. f(x) = 11/5x
• d. f(x) = x + 6

(Matching Type) Given f(x) = x + 4 and g(x) = 2x + 1 match the expression to its simplification operation. 2x+1 / x+4

• g/f

Let f(x) = 4x-5 and g(x) = 3x, find (f+g)(x).

• 7x-5
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