WorksheetsSET #9 - RECENT MELE QUESTIONS
Total questions: 100
Worksheet time: 50mins
Solve the system: xy = 24, y – 2x + 2 = 0
{(3, 4)}
{(4, -8), (-3, 6)}
{(4, 6), (-3, -8)}
{(3, 4), (-8, 6)}
Solve the equation: √x² – √3x = 2x – 6
12
4
3
5
Solve: √8 + 3√18 – 7√2 =
3√2
5 – 3√2
4√2
2√2
If −9 < x < 4 and −12 < y < −6, then
108 < xy < 24
108 > xy > 24
108 < xy < 120
−21 < xy < −10
What is the value of E in the following equation? 2x⁴ + 3x³ + 7x² + 10x + 10 / (x − 1)(x² + 3)² = A/(x − 1) + (Bx + C)/(x² + 3) + (Dx + E)/(x² + 3)²
2
3
0
-1
If 3ˣ = 54, then 3ˣ⁻² is equal to:
6
5
8
9
Which of the following is the value of x² + 1/x² when x + 1/x = 5?
28
24
23
25
Evaluate the following logarithm: log₂(√2/8)
2.5
5.2
-2.5
-5.2
Given log₁₀ 2 = 0.3010, find log₁₀ 32.
1.863
0.256
1.365
1.505
Given: log(2x – 3) = 1/2. What is the value of x if the base of the logarithm is 9?
1
2
3
4
If log₃ N = 2/3, then N is equal to:
4
2
3
5
What is the value of x if log(base x) 1296 = 4?
5
4
3
6
Solve for x if 2log x – log(30 – 2x) = –1.
12
10
-30
15
If log₂ 2 = 0.69 and log₉ 3 = 1.10, find log₉ 6.
1.7836
1.5698
1.1236
2.1475
If log₇ 6 = 1.2925, what is the value of log₇ 11?
1.65
1.73
1.42
1.51
What is the product (AB) of the following complex numbers? Express your answer in polar form.
50∠90°
50∠30°
50∠45°
50∠60°
Add the following complex numbers: 3 + 4i and 2 – 5i.
12 + 2i
24 – 5i
6 – i
5 – i
The function is defined as f(x) = 1/(1+x). For what value of x is f(f(x)) undefined?
{-1, -1/2}
{-1, -2}
{1, 0}
{0}
If f(x) = 2x2+2 , find the value of f(x + 4).
2x2+16x+24
2x2+16x
2x2+6x+4
2x2+16x+34
If f(x) = (3x−4)2 , then how much does f(x) increase as x goes from 2 to 3?
1.372
1.732
1.273
1.723
If f(x) = x3−x−1 , what is the set of all c if f(c) = f(–c)?
all real numbers
{–1, 0, 1}
{0}
{0, 1}
If f(x) = 3x−1 , then f^{–1}(x) is equal to:
x – 1/3
3x + 1
(x + 1)/3
(x – 1)/3
If f(x) = x – 2x2 + 2, what is f(a – 2)?
9a – 2a^2 – 8
9a – 2a^2 + 8
2a – 9a^2 – 8
2a + 9a^2 – 8
If f(x) = 3x + 2 and g(f(x)) = x, then g(x) is equal to:
x – 2/3
4x + 9
1/3(x – 2)
3x – 2
Solve for x in the following equation: x + 4x + 7x + 10x + ... + 64x = 1430
3
4
5
2
Four positive integers form an arithmetic progression. If the product of the first and the last term is 70 and the product of the second and third term is 88, what is the first term?
3
14
5
8
What is the value of x if 1, 1/4, 1/x, 1/10 form a harmonic progression?
3
7
8
5
Find the sum of the infinite progression: 2, 1, 2/3, 2/5, ...
3/4
1/2
2/3
1/3
The sides of a right triangle are in arithmetic progression whose common difference is 6. Find the hypotenuse.
6
30
18
24
If 3, 5, 8.333, and 13.889 are the first four terms of a sequence, then which of the following could define the sequence?
A. A₀ = 3; Aₙ = Aₙ₋₁ + 40/9 Aₙ₋₁
B. A₀ = 3; Aₙ₋₁ = Aₙ₊₂
C. A₀ = 3; Aₙ = 5/3 Aₙ₋₁
D. A₀ = 3; Aₙ₊₁ = 2Aₙ₊₂
Two numbers differ by 40 and their arithmetic mean exceeds their geometric mean by 2. What is the smaller number?
81
96
64
45
If kx² – (k + 3)x² + 13 is divided by x – 4, the remainder is 157. What is the value of k?
5
4
3
7
The average rate of production of PCB is one (1) unit for every 2 hours worked by two workers. How many PCBs can be produced in one month by 80 workers working 200 hours during the month?
2000
5000
3000
4000
A can do a job 50% faster than B and 20% faster than C. Working altogether, they can finish the job in 4 days. How many days will it take A to finish the job if he worked alone?
16
18
10
12
If John can paint a room in 30 minutes and Tom can paint it in 1 hour, how many minutes will it take them to paint the room if they work together?
15
20
12
10
A salesman started walking from office A at 9:30 a.m. at the rate of 2.5 kph. He arrived at office B 12 seconds late. Had he started at 9:00 a.m. and walked at 1.5 kph, he would have arrived at B one minute before the required time. At what time was he supposed to be at B?
10:13 a.m.
10:16 a.m.
10:22 a.m.
10:18 a.m.
A man walks a certain distance at the rate of 5 kph and returns at a rate of 4 kph. If the total time that it takes him is 3 hours and 36 minutes, what is the total distance that he walked?
8
9
18
16
John can shovel a driveway in 50 minutes. If Mary can shovel the driveway in 20 minutes, how long will it take them, to the nearest minute, to shovel the driveway if they work together?
12
13
14
16
Carpenter Pedro can make a bookshelf in 5 working days alone. Carpenter Juan can do the same bookshelf in 10 days working alone. How long will it take them to finish the same bookshelf if they work together?
4 – 1/3 days
3 – 2/3 days
3 – 1/3 days
2 – 2/3 days
At exactly what time after 2 o’clock will the hour hand and the minute hand of a continuously driven clock extend in the opposite direction for the first time?
2:43:6.8
2:43:58.1
2:43:12.2
2:43:38.2
A speed boat can make a trip of 100 km in one hour and 30 minutes if it travels upstream. If it travels downstream, it will take one hour and 15 minutes to travel the same distance. What is the speed of the boat in calm water?
80 kph
123.33 kph
66.67 kph
73.33 kph
A train can pass an average of 3 stations every 10 minutes. At this rate, how many stations will it pass in one hour?
30
26
18
15
Going against the wind, a domestic plane can travel 5/8 of the distance it can travel in one hour if it is going with the wind. If the plane can fly 300 kilometers an hour in calm air, what is the velocity of the wind?
69.23 kph
62.93 kph
63.92 kph
96.23 kph
John is four times as old as Harry. In six years, John will be twice as old as Harry. What is the age of Harry now?
2
3
4
5
What is the value of the following determinant?
1
3
4
0
Find the number of ways two balls, four dolls, and six toy guns can be given to 12 children, if each child gets a toy.
12,606
10,620
13,860
11,640
If three coins are tossed, how many possible ways are there for at least one coin showing tails?
5
6
8
7
What is the indicated root ³√–125?
–25
5
–5
25
Given that w varies as directly as the product of x and y and inversely as the square of z and that w = 4 when x = 2, y = 6, and z = 3, What is the value of w when x = 1, y = 4, and z = 2?
3
4
5
2
If 16 is four more than 3x, then x² + 5 is equal to:
18
21
8
10
A professional organization is composed of x ECEs and 2x CEs. If 6 ECEs are replaced by 6 CEs, 1/6 of the members will be ECEs. What is the value of x?
24
36
12
18
An hour-long test has 60 problems. If a student completes 30 problems in 20 minutes, how many seconds does he have on average for completing each of the remaining problems?
60
90
120
80
The sum of two numbers is 10 and the sum of the squares of the numbers is 52. Find the product of the two numbers.
24
16
32
12
After 8:00 p.m., a ride in a cab costs ₱25.00 plus ₱3.00 for every fifth of a kilometer traveled. If a passenger travels x kilometers, what is the cost of the trip in pesos, as a function of x?
28x
25 + 3x
25 + 15x
25 + 0.6x
On a scaled map, a distance of 10 cm represents 5 km. If a street is 750 meters long, what is the length on the map, in centimeters?
15
1.5
150
0.15
Between 1950 and 1960, the population of Singapore increased by 3.5 million. If the amount of increase between 1960 and 1970 was 1.75 million more than the increase from 1950 to 1960, compute for the total amount of increase in the population of Singapore between 1950 to 1970.
5.75 million
4.25 million
5.25 million
8.75 million
In a typical month, 1/2 of the UFO sightings in the California State are attributable to airplanes and 1/3 of the remaining sightings are attributable to weather balloons. If there were 108 sightings during one typical month, how many would be attributable to weather balloons?
36
54
24
18
If x is an integer, which of the following must be an odd integer?
4(x – 1)
4x – 1
3x² – 2
x² – 3
Ernie’s average in 6 subjects is 83. If his lowest grade is disregarded, the average of his remaining subjects is 84. What is his lowest grade?
76
77
79
78
A product has a current selling price of ₱325. If its selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?
₱302.75
₱202.75
₱213.23
₱156.00
Instead of multiplying the number by 17, Karla divided it by 17. If the answer she obtained is 1, what should have been the correct answer?
285
276
289
295
Kim was sent to the store to get 11 boxes of sardines. Kim could carry only two boxes at a time. How many trips would Kim have to make?
4
6
7
5
Simplify cos(30° – A) – cos(30° + A) as a function of angle A only.
sin A
tan A
cos A
sec A
In triangle ABC, (sin A)/(sin B) = 7/10 and (sin B)/(sin C) = 5/2. If angle A, B, and C are opposite sides a, b, and c, respectively, and the triangle had a perimeter of 16, what is the value of a?
12.33
8
4.67
5.33
At one side of a road is a pole 25 ft high fixed on top of a wall 5 ft high. On the other side of the road, at a point on the ground directly opposite, the flagstaff and the wall subtend equal angles. Find the width of the road.
30 feet
20 feet
45 feet
50 feet
If sec 2A = 1 / sin 13A, determine the value of A.
3°
6°
7°
5°
The sides of a triangle are 8, 15, and 17 units. If each side is doubled, by how many square units will the area of the triangle be increased?
120
60
180
240
Find the area of the spherical triangle ABC having the following parts: Angle A = 140°, Angle B = 75°, Angle C = 86°, Radius of sphere = 4 m
32.78 m²
41.41 m²
33.79 m²
34.56 m²
What is the area of a rhombus whose diagonals are 12 and 24?
144
164
108
132
A wire with length of 52 cm is cut into two unequal lengths. Each part is bent to form a square. If the sum of the area of the two squares is 97 sq. cm., what is the area of the smaller square?
16
81
64
49
The perimeter of a circular sector, whose central angle is 60°, is 14 feet. Find the radius of the circle.
3.68 feet
4.59 feet
6.32 feet
8.74 feet
An equilateral triangle has an altitude of 5√3 cm long. Find the area of the triangle.
25√3
3√5
15√3
10√3
A circle with radius r has a circumference equal to the perimeter of a square whose side is S. Which of the following is correct?
r = S/2π
r = S
r = 2S/π
r = Sπ
How long is each side of a regular hexagon with perimeter 108 centimeters?
18
24
32
12
How many sides have a polygon if the sum of the measures of the angles is 900°?
9
24
8
7
A rectangular room is to contain 125 square meters of flooring. If its length is to be five times its width, what should its dimensions be?
5 m × 75 m
25 m × 125 m
3 m × 15 m
5 m × 25 m
If the total number of diagonals of an N-gon is 77, then what is the value of N?
14
13
12
15
A circle has a circumference that is numerically equal to its area. If a certain square has the same area as the circle, what would be the length of the side?
√3π
√2π
√π
2√3
A rectangular solid has dimensions and . What is its diagonal?
7.071
7.253
6.325
9.125
Find the volume of the pyramid formed in the first octant by the plane 6x+10y+5z–30=0.
15
13
12
14
The upper and lower bases of the frustum of a rectangular pyramid are 3 m by 4 m and 6 m by 8 m, respectively. If the volume of the solid is 140 m³, how far apart are the bases?
6.5 m
4.5 m
5 m
3.5 m
By how many percent will the volume of the cube increase if its edge is increased by 20%?
44
72.8
1.728
7.28
A closed conical vessel with base radius of 1 m and altitude 2.5 m has its axis vertical. In upright position (vertex uppermost), the depth of water in it is 50 cm. If the vessel was inverted (vertex lowermost), how deep is the water in it?
196.8 cm
187.5 cm
204.6 cm
174.8 cm
When an irregular-shaped object is placed in a cylindrical vessel of radius 8 cm, containing water, the water surface rises 6 cm. What is the volume of the object if it is completely submerged in water?
384π cc
525π cc
632π cc
245π cc
A right prism has a base in the shape of regular octagon inscribed in a square 10 cm by 10 cm. If its altitude of 15 cm, find its volume in cc.
1,359.7
1,242.6
1,163.4
1,421.6
If two points in the number line have coordinates 1 and 7, find the coordinate of a point on the line which is twice as far from 1 as from 7.
3
4
6
5
Find the equation of the line with slope 2/3 and which passes through point of intersection of the lines 4x - 2y + 1 = 0 and x - 2y + 4 = 0.
4x - 6y + 9 = 0
6x - 4y + 11 = 0
6x - 4y + 9 = 0
4x - 6y + 11 = 0
Find x if the point (x, 2) is equidistant from (3,2) and (7,2).
5
8
6
6
A rectangle with sides parallel to the axes has vertices at (-3, 2), (2, 5), and (-3, 5). What is the coordinate of the fourth vertex?
(-5, 2)
(5, -2)
(5, 2)
(-3, -2)
The triangle defined by the points A(6, 1), B(2, 4), and C(-2, 1) is what?
right
obtuse
isosceles
scalene
Given the curve 36x2+9y2=36 , what is the length of its latus rectum?
0.6
0.75
1.5
1
Which of the following points (1,0), (−1,0), (4,4), (9,7) belong to the graph of the equation y=x2−x ?
(−1,0)
(9,7)
(4,4) and (1,0)
(1,0)
A circle is described by the equation x^2 + y^2 − 16x = 0. What is the length of the chord that is 4 units from the center of the circle?
12.563
13.856
8.523
9.632
What is the equation of the line that passes through (-3, 5) and is parallel to the line 4x − 2y + 2 = 0?
4y − 2x + 2 = 0
x + y + 10 = 0
4x − 2y + 11 = 0
2x + y + 11 = 0
A circle with its center in the first quadrant is tangent to both x- and y-axes. If the radius is 4, what is the equation of the circle?
(x–4)2+(y–4)2=16
(x+4)2+(y–4)2=16
(x–2)2+(y–2)2=16
(x+2)2+(y–2)2=16
What is the distance between the line x + 2y + 8 = 0 and the point (5, –2)?
4.025
4.205
4.502
4.052
Find the area enclosed by the following curve: x2+y2–10x–10y+25=0
85.47 square units
95.61 square units
78.55 square units
68.53 square units
What is the diameter of a circle with the following equation: x2+y2–6x+4y–12=0 ?
10
5
16
25
What conic section is described by the equation x2+y2–4x+2y–20=0 ?
circle
parabola
hyperbola
ellipse
The directrix of the parabola is y = 5 – 0 and its focus is at (4, –3). Find the length of its latus rectum.
16
12
2
4
