Mathematics 2019 Board Exam

Mathematics 2019 Board Exam

1.      What angle (degree) does the line  make with the reference line ?

·       -48.64

·       32.47

·       -24.28

·       38.64

2.       You deposit your money in a bank at 12 percent simple interest. How much will your money be at the end of 2 years if you deposited P25,000.00?

·       P30,000

·       P28,000

·       P31,000

·       P29,000

3.       On a scale drawing A is 5 mm and B is drawn 11 mm. If the actual size of B is 5 meters, then the size (in meters) of A is

·       5

·       2 and 3/11

·       10

·       4 and 6/11

4.       Find the groundspeed (mph) for the specified airspeed, heading and wind: airspeed = 180 mph, heading 290°, wind 30 mph from 80°.

·       120

·       207

·       462

·       389

5.       A guy wire 78 ft long runs from the top of a telegraph pole 56 ft high to the ground and pulls on the pole with a force of 290 lb. What is the horizontal pull (lb) of the wire on the top of the pole?

·       452

·       567

·       378

·       202

6.       Between 12:00 noon and 2:00 PM, the population of a certain bacteria triples. When will the population be 27 times what it was at 12:00 noon?

·       6:00 PM

·       8:00 PM

·       4:00 PM

·       3:00 PM

7.       If a man can run P km in X hours, how long (hours) will it take to run Q km at the same rate?

·       PX/Q

·       QX/P

·       Q/PX

·       PQ/X

8.       An artillery observer in a captive balloon 2700 ft above his guns observes that the angle of depression of an enemy fort is 27°56′. Find the distance (ft) from the guns to the fort, if they lie at the same elevation.

·       3287

·       5092

·       6392

·       4591

9.       Lucas can plow the field in 5 days while his father can do it in 2 days. How many days will they require working together?

·       3 and 2/7

·       1 and 3/7

·       2 and 1/7

·       4 and 4/7

10.    Compute for the coordinates of the point P that is 1/3 of the way from  to .

·       P(87/3,32/2)

·       P(84/3,34/3)

·       P(85/4,35/3)

·       P(86/4,35/2)

11.    A man wishes to raise a 300‑lb weight to the top of a wall 15 ft high by dragging the weight up an incline. What is the length (ft) of the shortest inclined plane he can use if his pulling strength is 135 lb?

·       33.3

·       13.7

·       22.5

·       49.1

12.    The fourth root of 100 is

·       square root of 10

·       square root of 5

·       cube root of 5

·       cube root of 10

13.    The volume of a sphere varies directly as the cube of its radius. The volume of a sphere with 4‑inch radius is 100 cu in. What is the ratio of proportionality?

·       1.56

·       2.31

·       4.63

·       3.47

14.   What is the general solution to this differential equation: ?

·       A[e^{4x}] + B[e^{-3x}]

·       A cos 4x + B sin 3x

·       A cos 3x + B sin 4x

·       A[e^{-4x}] + B[e^{3x}]

15.   If x and y are integers, for which ordered pair (x,y) is  an odd integer?

·       (2, −5)

·       (−1, 3)

·       (4, 1)

·       (6, 3)

16.   The equations  and  are plotted on the same graph. All of the following points lie on both graphs EXCEPT

·       (12,1)

·       (6,1)

·       (0,3)

·       (9,0)

17.    The number of children in a town is 46% of the population or 3,610 people. How many people are living in the town?

·       7,848

·       6,054

·       8,941

·       9,625

18.   If  and x and y are functions of t alone, then  is

·       (6x cos y) dx/dt − [3x² sin y] dy/dt

·       (6x cos y) dy/dt + [3x² sin y] dx/dt

·       (6x cos y) dy/dt − [3x² sin y] dx/dt

·       (6x cos y) dx/dt − [3x² sin y] dy/dt

19.    If segment MS is parallel to the y‑axis and its midpoint is on the x‑axis, find the coordinate of S if M is at (a,b).

·       (−a,−b)

·       (−a,b)

·       (a,−b)

·       (0,0)

20.    A ship or airplane goes from A to B; then the navigator changes heading to point straight at C. Find distance (miles) of C from B when AB = 250 miles on course S 57°40′ W, and C is 350 miles west and 30 miles north of A.

·       300

·       200

·       215

·       325

21.    It refers to a conic section whose set of points are equidistant from a fixed point and a fixed line.

·       Hyperbola

·       Parabola

·       Line

·       Circle

22.    If a two‑digit number has x as its unit digit and y as its ten’s digit, represent the number.

·       x + y

·       x − y

·       10y + x

·       10x − y

23.    Two cities are 800 km apart. At 4:00 PM Train A leaves one city toward the other at 600 km/h. At 5:00 PM Train B leaves the first city in the same direction at 800 km/h. Which statement is correct?

·       Train A arrives first by an hour or more

·       Two trains arrive at exactly the same time

·       Train A arrives after Train B, by less than an hour

·       Train A arrives first, by less than an hour

24.    Given two lines L1 and L2 with slopes 1/8 and 5/9, respectively. Find the tangent of the angle from L1 to L2.

·       36/79

·       33/76

·       39/78

·       31/77

25.   The integral of  is

·       (x⁴/3) − (x²/2) + 1 + c

·       (x³/3) − (x²/2) + x

·       x⁴/4 − x²/2 + x + c

·       x²/3 − 1 + c

26.    Add 70 mm + 3 meters + 2 cm and express in meters.

·       3.09

·       3.0009

·       3.9

·       3.009

27.    Robert has 12 coins totaling P1.45. None of his coins is larger than a 25‑centavo coin. Which of the following cannot be the number of 25‑centavo coins that he has? (Coins are 25‑, 10‑, and 5‑centavos.)

·       5

·       1

·       2

·       3

28.    The surface area of a sphere, initially zero, increases uniformly at the rate of 4 cm²/s. Find the rate (cm/s) at which the radius is increasing at the end of 2 s.

·       0.40

·       0.10

·       0.30

·       0.20

29.   What is the value of x if ?

·       5.75

·       2.26

·       3.5

·       0.17

30.    A piece of artillery at G is firing at T from a range of 15,000 yards. An airplane observer telephones that a shot fell at S, 500 yards to the right and 400 yards beyond T. What correction in range (yards) should be applied for future shots?

·       Reduce by 410

·       Reduce by 553

·       Reduce by 778

·       Reduce by 672

31.   Solve for x given:  and .

·       −4/35

·       4/35

·       2/33

·       −2/33

32.    Taxi no. 1 started 2.5 h before taxi no. 2 which has a speed of 83 kph. After traveling for 3.6 h, taxi no. 2 overtook taxi no. 1. What was the speed of taxi no. 1 (kph)?

·       55

·       63

·       78

·       49

33.   An ellipse has equation . Determine the distance from the center to a vertex.

·       13

·       15

·       10

·       17

34.   If the perimeter of rhombus ABCD is 64 and BD is , find AC.

·       14

·       21

·       16

·       28

35.   The simultaneous equations , ,  have the solution

·       x = −5, y = −6, z = −35

·       x = 5, y = 7, z = 8

·       x = −5, y = −6, z = −39

·       x = 6, y = 6, z = 10

36.    A ship, 600 miles away from A with bearing 72° from A, sails on course 190° at 25 knots. If planes are dispatched from A to intercept the ship, how far (miles) from A will interception occur?

·       457

·       326

·       273

·       579

37.    A wire 100 cm long is cut into two pieces, each bent to make a square. The area of one square is 225 cm² greater than the other. What is the sum of the areas (cm²) of the two squares?

·       289

·       256

·       392

·       353

38.    Solve for y in .

·       ±2.48

·       ±2.12

·       ±2.57

·       ±2.39

39.    The sides of a triangle are 12, 8, and 15 in. In a similar triangle, the longest side is 40 in. Of the other two sides, what is the length of the shorter side (in)?

·       27.8

·       21.3

·       15.4

·       18.6

40.    The area bounded by  and the x‑axis from x = 0 to x = 3 is

·       7

·       11

·       9

·       4

41.    A rectangle is w units long. The other side measures 15 units less than 4 times as long. What is the perimeter?

·       5(w − 15)

·       10(5)

·       5(w + 10)

·       10(w − 3)

42.    A body falls s ft from rest in a vacuum; the vertical velocity v in ft/s is given by , . What is the velocity of a parachutist who has fallen 4000 ft before opening the parachute?

·       679.14

·       507.22

·       369.19

·       402.11

43.   What is the focal distance of the parabola ?

·       4

·       5

·       7

·       6

44.    Find the length (ft) of the arc subtended by a central angle of 35° in a circle whose radius is 20 ft.

·       12.2

·       15.1

·       10.7

·       13.9

45.    The volume of a fixed mass of a perfect gas at constant temperature is inversely proportional to the pressure. If the volume is 8 L at 3 atm, find the volume (L) at 5 atm.

·       6.7

·       4.8

·       5.2

·       5.6

46.    What is the length (cm) of the shortest side of a right triangle if its hypotenuse is 30 cm and its perimeter is 72 cm?

·       18

·       19

·       16

·       17

47.    An airplane heading is 60° with airspeed 250 mph, and a wind of 40 mph blows from 200°. Find the drift angle.

·       12°37′

·       3°10′

·       17°43′

·       5°14′

48.    A regular polygon has 54 diagonals. How many sides does it have?

·       10

·       12

·       9

·       8

49.    Artillery at G fires at invisible target T. An observer at B sees both G and T and measures: BG = 2080 yd, azimuth 38°20′; BT = 5380 yd, azimuth 284°50′. Find azimuth of T from G.

·       190°23′

·       187°54′

·       200°12′

·       267°42′

50.    Divide 50 into two parts with ratio 1:4. What is the larger part?

·       40

·       20

·       25

·       30