MSTE - NOVEMBER 2024 (PAST BOARD)

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NOVEMBER 2024 (PAST BOARD)

1. An interior angle of 8.4° is specified for a 2° arch bases horizontal curve. The forward PI Station is (64 + 27.46). Locate the P.C. and P.T. station.

• a. (62 + 17.08) and (66 + 37.08)
• b. (62 + 37.08) and (66 + 17.08)
• c. (63 + 17.08) and (67 + 37.08)
• d. (63 + 37.08) and (67 + 17.08)

2. During an indoor rock concert in Philippine Arena, sound intensities of 0.15 W/m² are poduced. Density of air is 1.29 kg/m³ and speed of sound is 340 m/s. Determine the intensity levels of these sounds in decibels. Assume threshold of hearing is 1.0x10¯¹² watt/m²

• a. 112
• b. 121
• c. 211
• d. 131

3. The Arroyos are planning to build a brick patio that approximates the shape of a trapezoid. The shorter base of the trapezoid needs to start with a row of 5 bricks and each row must increase by 2 bricks on each side until there are 25 rows. How many bricks do the Arroyos need to buy?

• a. 1325
• b. 1235
• c. 1532
• d. 1352

4. Specifications for a construction job state that wall forms can be removed once the concrete reaches compressive strength of 3400psi. The maturity curve (Nurse - Saul) for the concrete is shown in the figure below. The cement hydration is assumed to cease below a temperature of 30° F. The average temperature of the concrete during the curing process is 70° F. Determine the number of hours that the contractor has to wait before removing forms.
Hint Δt = TTF/(T-T₀)

Here is the maturity curve diagram:

• a. 40
• b. 50
• c. 55
• d. 45

5. The contractor can remove the wall forms once the concrete has achieved a compressive strength of 3400 psi. Using the Nurse-Saul maturity curve for the concrete, assume that hydration stops if the temperature falls below 30°F. The concrete's average curing temperature is 70°F. How many hours must the contractor wait before the forms can be safely removed?

Here is the maturity curve diagram:

• a. 80.6
• b. 97.5
• c. 57.9
• d. 98.3

6. The Ferris wheel first appeared at the 1893 Chicago Exposition. Its axle was 45ft. long. Spokes radiated from it that supported 36 wooden cars, which could hold 60 people each. The diameter of the wheel itself was 250 ft. Suppose the axle was located at the origin, find the coordinates of the location of the car at 90° counterclockwise.

• a. (0,150)
• b. (150,0)
• c. (125,0)
• d. (0,125)

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Published: By: YANGINEER - May 05, 2025

MSTE - SEQUENCES AND SERIES

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• The number on the right represents the next page or the next number, except for the last number.
• Last Page will be the Answer Key of all the items
• A solution is provided for each question if you need assistance.
• Answer as many questions as you can.
• Wishing you the best of luck on your exam!

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1. Find the 𝑛-th term of the arithmetic progression: 3, 7, 11, 15, ...

• a. 4n+1
• b. 4n - 1
• c. n + 4
• d. n - 4

2. What is the sum of the first 13 terms of the arithmetic sequence: 3, 7, 11, 15, ...?

• a. 351
• b. 321
• c. 375
• d. 362

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Published: By: YANGINEER - May 03, 2025

MSTE-1 (SET THEORY)

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• The number on the right represents the next page or the next number, except for the last number.
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• Answer as many questions as you can.
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Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

1. Determine A ∪ B.

• a. {1, 2, 3, 4, 5, 6, 7, 8, 9}
• b. {1, 4, 5, 8, 9}
• c. {1, 2, 3, 5, 6, 7, 8, 9}
• d. {1, 2, 3, 4, 5, 6, 8, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

2. Determine A ∩ B.

• a. {5, 8}
• b. {7}
• c. {3, 4, 5}
• d. {5, 8, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

3. Determine A'.

• a. {2, 3, 5, 6, 8}
• b. {1, 4, 5, 8, 9}
• c. {2, 3, 6, 7}
• d. {2, 3, 6, 7, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

4. Determine (A ∪ B)'.

• a. {5}
• b. {4}
• c. {3}
• d. {7}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

5. Determine (A ∩ B)'.

• a. {1, 2, 3, 5, 6, 8}
• b. {1, 2, 3, 4, 6, 7, 9}
• c. {1, 2, 3, 6, 7, 8, 9}
• d. {1, 2, 3, 6, 7, 9}

Let U={1, 2, 3, 4, 5, 6, 7, 8, 9} A={1, 4, 5, 8, 9} B={2, 3, 5, 6, 8}

6. Determine (A\B)'.

• a. {1, 5, 9}
• b. {1, 6, 9}
• c. {1, 2, 9}
• d. {1, 4, 9}

7. Which of the following represents the set equivalent to A′ ∪ B′.

• a. A ∪ B
• b. A ∩ B
• c. (A ∪ B)'
• d. (A ∩ B)'

8. Which of the following represents the set equivalent to (A ∪ B ∪ C) ∩ B.

• a. B
• b. A
• c. A ∩ B
• d. A ∪ B

9. Which of the following represents the set equivalent to (A ∪ B) ∩ (A ∩ B).

• a. A + B
• b. A - B
• c. A ∩ B
• d. A ∪ B

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

10. How many people like only pizza?

• a. 25
• b. 15
• c. 60
• d. 20

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

11. How many people like only pasta?

• a. 25
• b. 15
• c. 55
• d. 20

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

12. How many people like only burgers?

• a. 25
• b. 15
• c. 50
• d. 20

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

13. How many people like exactly two of the three foods?

• a. 25
• b. 20
• c. 15
• d. 30

In a survey of 100 people:
• 60 people like pizza.
• 55 people like pasta.
• 50 people like burgers.
• 30 people like both pizza and pasta.
• 25 people like both pasta and burgers.
• 20 people like both pizza and burgers.
• 15 people like all three items.

14. How many people like all three foods?

• a. 25
• b. 20
• c. 15
• d. 30

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

15. How many students like only basketball?

• a. 13
• b. 14
• c. 15
• d. 16

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

16. How many students like only football?

• a. 3
• b. 4
• c. 5
• d. 6

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

17. How many students like neither basketball nor football?

• a. 6
• b. 8
• c. 9
• d. 7

In a class of 40 students:
• 25 students like basketball.
• 18 students like football.
• 12 students like both basketball and football.

18. How many students like either basketball or football?

• a. 21
• b. 41
• c. 31
• d. 11

At a beverage counter, four types of drinks are available: Mocha, Chocolate, Coffee, and Vanilla. The shop recorded the following orders:

30 customers ordered Mocha
29 ordered Chocolate
23 ordered Coffee
26 ordered Vanilla

Some customers ordered more than one drink:
18 ordered both Mocha and Chocolate
9 ordered both Mocha and Coffee
15 ordered both Mocha and Vanilla
15 ordered both Chocolate and Coffee
14 ordered both Chocolate and Vanilla
14 ordered both Coffee and Vanilla

In addition:
6 customers ordered Mocha, Chocolate, and Coffee
9 ordered Mocha, Chocolate, and Vanilla
7 ordered Mocha, Coffee, and Vanilla
9 ordered Chocolate, Coffee, and Vanilla
4 customers ordered all four drinks

19. Assuming each customer placed at least one order, how many unique customers visited the shop?

• a. A + B
• b. A - B
• c. A ∩ B
• d. A ∪ B

At a beverage counter, four types of drinks are available: Mocha, Chocolate, Coffee, and Vanilla. The shop recorded the following orders:

30 customers ordered Mocha
29 ordered Chocolate
23 ordered Coffee
26 ordered Vanilla

Some customers ordered more than one drink:
18 ordered both Mocha and Chocolate
9 ordered both Mocha and Coffee
15 ordered both Mocha and Vanilla
15 ordered both Chocolate and Coffee
14 ordered both Chocolate and Vanilla
14 ordered both Coffee and Vanilla

In addition:
6 customers ordered Mocha, Chocolate, and Coffee
9 ordered Mocha, Chocolate, and Vanilla
7 ordered Mocha, Coffee, and Vanilla
9 ordered Chocolate, Coffee, and Vanilla
4 customers ordered all four drinks

20. How many customers ordered exactly one type of drink?

• a. 35
• b. 10
• c. 25
• d. 15

ANSWER KEY:

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Published: By: YANGINEER - May 02, 2025