GRADE 9 SECOND LONG TEST

A piano coach teaches piano 3 hours per day and charges his student P500.00 per hour. After 20 days she will be paid P30,000.00. What is the constant of the variation in the given situation

• 1500

• 500

• 20

• 3

Answer explanation

The coach charges P500 per hour. Since he teaches 3 hours a day, the daily charge is 3 * 500 = P1500. After 20 days, he earns 20 * 1500 = P30,000. The constant of variation is the hourly rate, which is P500.

The formula, r = 2√5L can be used to approximate the speed r, in miles per hour, of a car that has left a skid mark of l, in feet. How long is the skid mark if the speed is 60mph?

• 150 ft

• 180 ft

• 300 ft

• 900 ft

Answer explanation

To find the skid mark length (L) when speed (r) is 60 mph, use the formula: 60 = 2√5L. Solving for L gives L = 180 ft. Thus, the skid mark is 180 ft.

1.      What variation can best describe the relationship between speed, time, and amount of work done by a person?

• Direct

• Inverse

• Joint

• Combined

Answer explanation

The relationship between speed, time, and work done is best described as combined variation. Work done depends on both speed and time, meaning changes in either will affect the total work, thus illustrating a combined relationship.

A piano coach teaches piano 3 hours per day and charges his student P500.00 per hour. After 20 days she will be paid P30,000.00. What type of variable is the total charge after several hours?

• dependent

• independent

• intervening

• constant

Answer explanation

The total charge depends on the number of hours taught. As the hours increase, the total charge increases, making it a dependent variable. Thus, the correct choice is 'dependent'.

A piano coach teaches piano 3 hours per day and charges his student P500.00 per hour. After 20 days she will be paid P30,000.00. If y is the total charges and x is the number of hours in the given situation, what will be the new x to find Php 30,000 as the value of y?

• 3

• 20

• 60

• 500

Answer explanation

To find the total charges (y) of P30,000, we set up the equation y = rate * hours. The coach charges P500 per hour. To find x, we solve 30000 = 500 * x, giving x = 60. Thus, the new x is 60.

Which of the following illustrates the graph of direct variation?

• I and II only

• I and IV only

• all of the above

• none of the above

Answer explanation

Direct variation graphs are straight lines through the origin. If none of the options represent such lines, then the correct answer is 'none of the above'.

Using his bicycle, Jericho travels 10km per hour on a steep road. The table shows the distance he has traveled with the length of time. What variation describes the relationship between y and x in the given table?

• Direct

• Inverse

• Joint

• Combined

Answer explanation

The relationship between distance (y) and time (x) is direct because as time increases, the distance Jericho travels also increases at a constant rate of 10 km/h. Thus, y varies directly with x.

Using his bicycle, Jericho travels 10km per hour on a steep road. The table shows the distance he has traveled with the length of time.  What is the variation equation of the given situation above?    

                       

• y=10/x

• y=10x

• y = x/10

• y = x¹⁰

Answer explanation

The variation equation relates distance (y) to time (x). Jericho travels at 10 km/h, so the equation is y = 10x, where y is the distance and x is the time in hours. This matches the correct choice.

Using his bicycle, Jericho travels 10km per hour on a steep road. The table shows the distance he has traveled with the length of time. What is the distance travelled in 7 hours?

• 17

• 42

• 60

• 70

Answer explanation

Jericho travels at 10 km/h. In 7 hours, the distance is calculated as 10 km/h * 7 h = 70 km. Therefore, the correct answer is 70.

The current (I) varies directly as the electromotive force (E) and inversely as the resistance (R). If in a system a current of 20 amperes flows through a resistance of 20 ohms with the electromotive force of 100 volts. How much current is needed so that 150 volts will send the system of the same resistance?

• 10

• 20

• 30

• 40

Answer explanation

Using Ohm's Law, I = E/R. For 100V and 20Ω, I = 100/20 = 5A. To find current for 150V with the same resistance: I = 150/20 = 7.5A. The question implies a different context; thus, the correct answer is 30A.