This is 50 items Practice Examinations set 3 in Board Examination in Mathematics composed of previous Board Exams Questions. Read each questions and choices carefully! Choose the best answer. Familiarize each and every questions to increase the chance of passing the Engineering Board Examination.

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โ Mathematics Board Examination Mastery Test 2: Engineering Pre-Board

**Choose the letter of the best answer in each questions.**

1. A man is three times as old as his son. Five years ago. He was five times old as his son was at that time. How old is the son.

a. The son is 10 years old.

b. The son is 12 years old.

c. The son 9 years old.

d. The son is 15 years old.

Answer: **Option A**

Explanation:

2. Two years ago, a boy is 2/3 as old as his sister. In two years, the boy will be ยพ as old as she. How old are they?

a. The boy is 10 yrs. old and his sister is 14 years old.

b. The boy is 12 years old

c. The sister of the boy is older than him.

d. The boy is 13 yrs. old and his sister is 14 yrs. old.

Answer: **Option A**

Explanation:

3. Mary is twice as old as Ana was when Mary was as old as Ana is now. How old is Ana?

a. Ana is 16 yrs. old.

b. Ana is 15 years old.

c. Ana is 17 years old.

d. Ana is 13 years old.

Answer: **Option A**

Explanation:

4. The sum of the parentsโ ages is twice the sum of their childrenโs ages. Five years ago, the sum of the parentsโ ages is four times the sum their childrenโs ages. In 15 years, the sum of the parentsโ ages will be equal to the sum of their childrenโs ages. How many children are there?

a. There are 4 children

b. There are 6 children

c. There are 5 children

d. There are 2 children

Answer: **Option C**

Explanation:

5. A and B can do a piece of work in 20 days, B and C in 30 days, C & A in 40 days. How long can each worker do the work alone?

a. t_{A} = 1/A = 240/5 = 48 days; t_{B} = 1/B = 240/7 = 34.3 days; t_{C} = 1/C = 240/1 = 240 days

b. t_{A} = 1/A = 240/4 = 60 days; t_{B} = 1/B = 240/6 = 40 days; t_{C} = 1/C = 240/2 = 120 days

c. t_{A} = 1/A = 240/6 = 40 days; t_{B} = 1/B = 240/7 = 34.3 days; t_{C} = 1/C = 240/1 = 240 days

d. t_{A} = 1/A = 240/3 = 80 days; t_{B} = 1/B = 240/1 = 240 days; t_{C} = 1/C = 240/4 = 60 days

Answer: **Option A**

Explanation:

6. Ding can finish a job in 8 hours. Tito can do it in 5 hrs. If Ding worked ahead for 3 hours and then Tito was asked to help him finish it, how long will Tito have to work with Ding?

a. t = 1.90 hrs.

b. t = 1.00 hr.

c. t = 1.92 hrs.

d. t = 1.94 hrs.

Answer: **Option C**

Explanation:

7. A pipe can fill up the tank with the drain open in 3 hrs. If the pipe runs with the drain open for 1 hr. and then the drain is closed, it will take 45 more minutes for the pipe to fill up the tank. If the drain will be closed right at the start of filling, how long will the pipe be able to fill up the tank?

a. 1.30 hr.

b. 1.40 hr.

c. 1.25 hr.

d. 1.00 hr.

Answer: **Option C**

Explanation:

8. How much tin and how much lead can be added to 700 kg of an alloy containing 50% tin and 25% lead to make an alloy which is 60% tin and 20% lead?

a. Add 175 kg of lead and no lead.

b. Add 170 kg of tin with lead

c. Add 175 kg of lead and tin

d. Add 175 kg of tin and no lead

Answer: **Option D**

Explanation:

9. A man bought 20 pcs of assorted calculators for P20, 000. These calculators are three types, namely:

a) Programmable at P3000/pc.

b) Scientific at P1500/pc.

c) Household type at P500/pc.

How many of each type did he buy?

a. 3 pcs programmable type; 4 pcs scientific type; 10 pcs household type

b. 2 pcs programmable; 5 pcs scientific; 13 pcs household

c. 5 pcs scientific; 2 pcs programmable; 12 pcs household

d. 2 pcs programmable; 4 pcs scientific; 13 households

Answer: **Option B**

Explanation:

10. Find the smallest number which when: you divide by 2, the remainder is 1; you divide by 3, the remainder is 2; you divide by 4, the remainder is 3; you divide by 5, the remainder is 4; and when you divide by 6, the remainder is 5.

a. x = 59

b. x = 49

c. x = 35

d. x = 65

Answer: **Option A**

Explanation:

11. The sum of the digits of a 3 โ digit number is 17. The hundredโs digit is twice the unitโs digit. If 396 were subtracted from the number, the order of the digits will be reversed. Find the number.

a. 845

b. 584

c. 854

d. 458

Answer: **Option C**

Explanation:

12. The sum of the digit of a 3 โ digit number is 17. The hundredโs digit is twice the unitโs digit. Find the number.

a. 683 and 584

b. 386 and 854

c. 683 and 854

d. 863 and 854

Answer: **Option C**

Explanation:

13. At what time after 3โoclock will the hands of the clock be together?

a. 3:16.36

b. 3:10.00

c. 3:20.30

d. 3:60.36

Answer: **Option A**

Explanation:

14. Expand (x^{2}-2y)^{6}

a. Q = x^{12} โ 12x^{10}y + 60x^{8}y^{2} โ 160x^{6}y^{3} + 240x^{4}y^{4} โ 192x^{2}y^{5} โ 64y^{5}

b. Q = x^{14} โ 12x^{12}y + 60x^{10}y^{2} โ 160x^{8}y^{3} + 240x^{6}y^{4} โ 192x^{2}y^{5} โ 64y^{5}

c. Q = x^{12} โ 12x^{10}y^{2} + 60x^{8}y^{3} โ 160x^{6}y^{4} + 240x^{4}y^{5} โ 192x^{2}y^{6} โ 64y^{7}

d. Q = y โ 12x^{10}y^{2} + 60x^{8}y^{4} โ 160x^{6}y^{6} + 240x^{4}y^{8} โ 192x^{2}y^{10} โ 64y^{12}

Answer: **Option A**

Explanation:

15. Find the middle term in the expansion of (x^{2}-2y)^{10}

a. 8064x^{10}y^{5}

b. โ8064x^{10}y^{5}

c. 6084x^{10}y^{5}

d. โ6084x^{10}y^{5}

Answer: **Option B**

Explanation:

16. In the expansion of (x^{2}-2y)^{10}, find the term involving, a) y^{3} ; b) x^{12}

a. 5th term, 5th term

b. 2th term, 5th term

c. 3th term, 5th term

d. 4th term, 5th term

Answer: **Option D**

Explanation:

17. In the expansion of (x^{2}– 1/x^{3})^{30}, find the term (or term free of x).

a. 13th term

b. 14th term

c. 15th term

d. 16th term

Answer: **Option A**

Explanation:

18. The midpoint of the sides of a 2 m x 2 m square are interconnected to form a smaller square. The midpoints of the sides of the square formed are again interconnected to form another smaller square. If the process will be repeated indefinitely, find the sum of the areas of all the squares formed including that of the original square.

a. S_{โ} = 6 sq. m.

b. S_{โ} = 7 sq. m

c. S_{โ} = 8 sq. m

d. S_{โ} = 5 sq. m

Answer: **Option C**

Explanation:

19. At what time after 3โoclock will the hands of the clock be bisected by the second hand?

a. 3:00:07.57

b. 3:59:02.50

c. 3:00.07.57

d. 3:45.57

Answer: **Option C**

Explanation:

20. A and B can do a piece of work in 20 days, B and C in 30 days, C & A in 40 days. If the three work together, how long will they be able to finish the job?

a. t = 240/12 days

b. t = 240/13 days

c. t = 240/14 days

d. t = 240/10 days

Answer: **Option B**

Explanation:

21. Solve for x, y & z in the following simultaneous equation:

x^{y} x^{z} = 100 000 โ equation 1;

x^{y}/x^{z} = 10 โ equation 2;

(x^{y})^{z} =1 000 000 โequation 3.

a. x = 10, y = 3, z = 1

b. x = 10, y = 3, z = 2

c. x = 10, y = 4, z = 2

d. x = 10, y = 2, z = 3

Answer: **Option B**

Explanation:

22. Solve for x in: log _{2} log _{3} log _{x} 2 = 1

a. x = ^{6}โ2

b. x = ^{4}โ2

c. x = ^{8}โ2

d. x = ^{9}โ2

Answer: **Option D**

Explanation:

23. Solve for x, log x^{2} โ log 5x = log 20

a. 200

b. 250

c. 100

d. 75

Answer: **Option C**

Explanation:

24. When you divide (x^{4} – ax^{3} – 2x^{2} – 3+ b) by (x – 1), the remainder is +2. When you divide it by x + 2, the remainder is โ1. Find a & b.

a. a = โ 7/3, b = 11/3

b. a = 7/3, b = -11/3

c. a = -7/3, b = -11/3

d. a = 7/3, b = 11/3

Answer: **Option A**

Explanation:

25. Derive the Pythagorean Theorem

a. a^{2} + b^{2} = c^{2}

b. a^{3} + b^{3} = c^{3}

c. a + b = c

d. a^{4} + b^{4} = c^{4}

Answer: **Option A**

Explanation:

26. At what time after 3โoclock will the hands of the clock be opposite each other?

a. 3:49.09

b. 3:30.02

c. 3:00.00

d. 3.45.60

Answer: **Option D**

Explanation:

27. Solve for the interior angles of the pentagram.

a. 60ยฐ

b. 180ยฐ

c. 90ยฐ

d. 360ยฐ

Answer: **Option B**

Explanation:

28. Find the area of hex decagon of trimester 32 units.

a. 80.44 sq. units

b. 90.44 sq. units

c. 50.55 sq. units

d. 50.44 sq. units

Answer: **Option A**

Explanation:

29. At a certain instance, the captain of a ship observed that the angle of elevation of the top of a lighthouse 50 meters above the water level is 60ยฐ. After traveling directly away from the lighthouse for 5 minutes, the same captain noticed that the angle of elevation is now just 30ยฐ. If the telescope is 6 meters above the water line, find the velocity of the ship.

a. 11.16m/min

b. 10.16m/min

c. 15.16m/min

d. 16.10m/min

Answer: **Option B**

Explanation:

30. Find the diameter of the circumscribing semi-circle.

a. 7.056 units

b. 6.056 units

c. 5.056 units

d. 8.056 units

Answer: **Option D**

Explanation:

31. Find the radius of the small circle

a. 23

b. 24

c. 25

d. 30

Answer: **Option C**

Explanation:

32. Find the area of the shaded region.

a. 25ฯ sq. units

b. 23ฯ sq. units

c. 22ฯ sq. units

d. 20ฯ sq. units

Answer: **Option A**

Explanation:

33. Find the area of the shaded region.

a. 2ฯ sq. units

b. 3ฯ sq. units

c. 4ฯ sq. units

d. 5ฯ sq. units

Answer: **Option A**

Explanation:

34. Find the area of the shaded region.

a. 3.97 sq. units

b. 3.87 sq. units

c. 3.67 sq. units

d. 3.57 sq. units

Answer: **Option B**

Explanation:

35. An equilateral triangle with inscribed circle is drawn inside a circle whose radius is 2 m. Another equilateral triangle with inscribed circle is drawn inside the smaller circle, and so on and so forth. Find the sum of perimeters of all triangles drawn.

a. S = 12โ1 m.

b. S = 15โ3 m.

c. S = 13โ 3 m.

d. S = 12โ3 m.

Answer: **Option D**

Explanation:

36. Four grapefruits (considered spheres) 6 cm in diameter were placed in a square box whose inside base dimensions are 12cm by 12 cm. In the space between the first four grapefruit, a fifth of the same diameter was then placed on top of them. How deep must the box be so that the top will just touch the fifth grapefruit?

a. h = 10.24 cm

b. h = 15.24 cm

c. h = 11.24 cm

d. h = 12.24 cm

Answer: **Option A**

Explanation:

37. A spherical ball of radius 3 cm was drooped into a conical vessel of depth 8 cm and radius of base 6 cm. what is the area of the portion of the sphere which lies above the circle of contact with the cone?

a. A = 90.48

b. A = 80.48

c. A = 90.38

d. A = 80.38

Answer: **Option A**

Explanation:

38. Find the volume of the solid common to two cylinders intersecting at 90ยฐ angle if radius of cylinders are both 3 m.

a. 133 cm^{3}

b. 122 cm^{3}

c. 144 cm^{3}

d. 111 cm^{3}

Answer: **Option C**

Explanation:

39. Find the volume of a right conoid whose radius of base is 1m and every cross section is an isosceles of altitude 2 m.

a. ฯ sq. unit

b. ฯ cu. sq. unit

c. ฯ km unit

d. ฯ cu. Unit

Answer: **Option D**

Explanation:

40. Find the location of the center of the circle defined by the equation, X^{2} + y^{2} + 4x โ 6y โ 12 = 0

a. center at (2, 3)

b. center at (-2, 3)

c. center at (3, 2)

d. center at (-3, 2)

Answer: **Option B**

Explanation:

41. Find the equation of a parabola whose latus rectum is joined by points (2, 1) & (-4, 1).

a. (x + 1)^{4} = 6 (y – 5/2)

b. (x +1)^{2} = 6 (y +5/2)

c. (x โ 1)^{2} = -6(y โ5/2)

d. (x + 1)^{2} = -6(y – 5/2)

Answer: **Option D**

Explanation:

42. A car headlight reflector is cut by a plane along its axis. The section is a parabola having the light center at the focus. If the distance of focus from vertex is ยพ cm, and if the diameter of reflector is 10cm, find its depth.

a. 25/3 cm

b. 24/2 cm

c. 25/2 cm

d. 24/3 cm

Answer: **Option A**

Explanation:

43. Find the equation of an ellipse with axis parallel to X-axis, center at (0, 0), eccentricity is 1/3, and distance between foci is 2.

a. x^{2}/9 + y^{2}/8 = 1

b. x/9 + y/8 = 1

c. x^{3}/9 + y^{3}/8 = 1

d. x/8 + y/9 = 1

Answer: **Option A**

Explanation:

44. Find the equation of the locus of a point that moves so that difference of its distance form points (-4, 0) and (4, 0) is 6.

a. (xโ2)^{2}/9 โ (yโk)^{2} = 1

b. ((x+0)^{2}/9 โ (y-k)^{2} = 1

c. (x-0)^{2}/9 โ (y-k)^{2} = 1

d. (x-0)^{2}/9 + (y- k)^{2}

Answer: **Option C**

Explanation:

45. The altitude and radius of a cone were measured and found to be 2 m and 1 m respectively. If the maximum possible errors in measurement are 3 cm and 2 cm respectively, find the maximum possible error in calculating the volume.

a. 0.109 cu. meter

b. 0.115 cu. meter

c. 0.125 cu. meter

d. 0.151 cu. Meter

Answer: **Option B**

Explanation:

46. A 6 ft. tall man walks away from a 20 ft. high lamppost at the rate of 3 ft/sec. Find:

a) How fast is the tip of his shadow moving?

b) How fast is the length of his shadow changing?

a. 6/14 ft/sec

b. 3/7 ft/sec

c. 6/7 ft/sec

d. 9/7 ft/sec

Answer: **Option D**

Explanation:

47. A dive-bomber is losing altitude at the rate of 600 km/hr. How fast is the visible surface of the earth decreasing when the bomber is 1km high? Assume that the radius of the earth is equal to 6400 km.

a. The visible area is decreasing at 20.12 x 10^{6} km^{2}/hr

b. The visible area is decreasing at 23.12 x 10^{6} km^{2}/hr

c. The visible area is decreasing at 20.12 x 10^{6 }km^{2}/hr

d. The visible area is decreasing at 24.12 x 10^{6} km^{2}/hr

Answer: **Option D**

Explanation:

48. Find the angle that the parabola x^{2} = y + 2 makes with the x โ axis.

a. ฮธ = 71.53ยฐ

b. ฮธ = 70.53ยฐ

c. ฮธ = 69.53ยฐ

d. ฮธ = 72.53ยฐ

Answer: **Option B**

Explanation:

49. Divide 90 into 3 parts so that their product is in its maximum.

a. the numbers are 30, 40 and 20

b. the numbers are 30, 30 and 30

c. the numbers are 30, 35, and 25

d. the numbers are 40, 25 and 25

Answer: **Option B**

Explanation:

50. Find the minimum possible sum for three positive numbers whose product is 27.

a. 9

b. 8

c. 5

d. 4

Answer: **Option A**

Explanation:

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