30215924 upcat reviewer practice test 2

8/6/2019 30215924 UPCAT Reviewer Practice Test 2

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PRACTICE

TEST 2With answer key, solution and UPCAT

review tips

MATHEMATICS






MATHEMATICS (30 ITEMS)

1. When

7521

52

5

1

3

13

vis simplified and written as decimal, what is the 10

thdigit after the

decimal point?

(A) 5 (B) 6 (C) 7 (D) 9

2. For what value of k is the sum of the roots of the equation 064 22 ! k xk x

equal to twice their product?

(A) k = 2 only (B) k= 2, 3 (C) k = 1, 2 (D) k = 3 only

3. Tatlong buklet ang maaaring i-print gamit ang tatlong printer sa loob ng

tatlong minuto. Gaano karaming mga buklet ang maaaring i-print gamit ang anim

na printer sa loob ng anim na minuto?

(A) 10 (B) 12 (C) 14 (D) 16

4. Ang isang basketball team ay may layunin na maipanalo ang 90% ng kanilang

mga laro. Ang kanilang rekord ay 10 panalo at 2 talo. Kung manalo sila sa

natitirang bahagi ng kanilang mga laro, gaano karaming mga laro ang

kinakailangan upang maabot ang kanilang layunin?

(A) 2 laro (B) 8 laro (C) 10 laro (D) 3 laro






5. The circle defined by the equation 93422

¡

¢ ¢

y x is moved

horizontally until its center is on the line 6! x . How far does the center of the

circle move?

(A) 2 (B) 9 (C) 10 (D) 15

6. If 11143

! x , what is the value of x?

(A)7

1(B)

7

12(C)

12

7(D)

7

1

7. The number 23a74b is divisible by 9 and 8, where a and b represent distinctdigits of the number. What is a-b?

(A) 3 (B) 5 (C) 6 (D) 8

8. What is the equation of the line which passes through the point 2,3 and is

parallel to the line whose equation is 523 ! x y .

(A) 032 ! y x (B) 1232 ! y x (C)

1232 ! y x (D) 032 ! y x

9. Ako ay n taong gulang sa taong2

n , " ang sabi ni Mang Berto noong 1971.

Anong taon siya ipinanganak?

(A) 1892 (B) 1812 (c) 1927 (d) 1956

10. What is the simplified improper fraction for 488.4 ?

(A)9

44(B)

33

148(C) 33

160(D)

125

606






11. A circular table is pushed into a corner of a rectangular room so that it touches

both walls. A point on the edge on the edge of the table between the two points of

contact is 2 inches from one wall and 9 inches from the other wall. What is the

radius of the table?

(A) 20 inches (B) 12 inches (C) 15 inches (D) 17 inches

12. Find the total surface area in square meters of a rectangular solid whose length

is 7 meters, width is 6 meters, and depth is 3 meters.

(A) 32 (B) 162 (C) 81 (D) 126

13. Evaluate the following sum:

1002...181512

(A) 139,659 (B) 156,744 (C) 167,817 (D) 189,463

14. Twelve consecutive integers are added together. What is the remainder when

the sum is divided by 4?

(A) 1 (B) 2 (C) 3 (D) no remainder

15. What is three times the sum of x and y given that°¯®

!

!

1515

230230

y x

y x

(A) 81 (B) 90 (C) 102 (D) 120






16. What is the slope of the line 123

!y x

?

(A)2

3 (B)

3

2 (C)

3

1(D)

3

2

17. The product of a positive number, its square , and its reciprocal is81

100. What

is the number?

(A)100

81(B)

81

100(C)

10

9(D)

9

10

18. The lines x y ! and 2

9!

x

y form a triangle in the first quadrant with the y-

axis. What is the area of this triangle?

(A) 6.75 (B) 7.75 (C) 8.75 (D) 9.75

19. Simplify the expression x x x x

x

(A)2 x x x (B)

x x

x

x x (C) x x x x 2

(D)5

x

20. If 24441 ! x x , then the value of x x2 is

(A) 24 (B) 212 (C) 510 (D) 525

21. A cube has a volume of 3125 cm . What is the area of one face of a cube?

(A) 220 cm (B) 225 cm (C) 2

3

241 cm (D) 25 cm






22. The vertex of a parabola hbb x y !2 has coordinates 5,2 . What is the

value of h?

(A) 3 (B) 4 (C) 5 (d) 6

23. The diagonals of a rhombus measure 24 inches and 32 inches. The perimeter

of a rhombus

(A) cannot be determined uniquely from the given information

(B) must be 80 inches

(C) must be 280 inches

(D) must be 160 inches

24.Simplify:q p

pq

q

p

q

q p

x

x

x

x

¹¹ º

¸©©ª

¨

¹¹ º

¸©©ª

¨

(A)

22 p pq

x

(B)

22 q pq

x

(C) pq

x2

(D) pq

x

25. Determine the solution of the following equation.

? A 462143122 ! x x x x

(A) 0 (B) 32 (C) 2

1(D) 2

3






26. A car traveled 3 miles south, 9 miles east, and then another 9 miles south.

What is the straight-line distance (in miles) between the point where the car started

and where it stopped?

(A) 21 (B) 36 (C) 37 (D)15

27. Find the y-intercept of the perpendicular bisector of AB where A 8,5 and B 2,2 .

(A) 6.75 (B) 7.75 (C) 8.75 (D) 8.75

28. For what value of k will the graph of k x x y ! 23

2

be tangent to the x-axis?

(A)2

1(B)

3

2(C)

3

1(D)

4

3

29. The sum of the first five terms of a geometric sequence is 93. If its common

ratio is 2, what is the first term?

(A) 2 (B) 3 (C) 4 (D) 5

30. A certain number was to be added to2

1 but by mistake

2

1was divided by the

number. However, the correct result was obtained. Find the number.

(A) 1or 2 (B) 1or 2 (C) 1-or 2

1(D) 1or

4

1






SOLUTION:1. When

75

21

5

25

1

3

13

vis simplified and written as decimal, what is the 10

thdigit after the

decimal point?

(A) 5 (B) 6 (C) 7 (D) 9

Solution:

75

21305

1

3

10

75

21

5

25

1

3

13

v!

v

253

32

!

3

25

3

2v!

decimalrepeating55555.59

55

9

50-!!!

The 10th

digit after the decimal point is 5.






2. For what value of k is the sum of the roots of the equation 064 22 ! k xk x

equal to twice their product?

(A) k = 2 only (B) k= 2, 3 (C) k = 1, 2 (D) k = 3 only

Solution:

R ecall:

In the quadratic equation 02 ! cb xax , the sum of the roots is equal to

a

b and the

product of the roots isa

c .

Therefore in 064 22 ! k xk x

Sum of roots = 46 k

And Product of roots =2

k .

We now solve for the value of k using the following equation

2246 k k !

0232 ! k k

012 ! k k

2or 1 !! k k






3. Tatlong buklet ang maaaring i-print gamit ang tatlong printer sa loob ng

tatlong minuto. Gaano karaming mga buklet ang maaaring i-print gamit ang anim

na printer sa loob ng anim na minuto?(A) 10 (B) 12 (C) 14 (D) 16

Solution:

x

66

3

33 y!

y

12! x

4. Ang isang basketball team ay may layunin na maipanalo ang 90% ng kanilang

mga laro. Ang kanilang rekord ay 10 panalo at 2 talo. Kung manalo sila sa

natitirang bahagi ng kanilang mga laro, gaano karaming mga laro ang

kinakailangan upang maabot ang layunin?

(A) 2 laro (B) 8 laro (C) 10 laro (D) 3 laro

Solution:

10

9

12

10!

x

x, Cross-Multiply

x x 910810100 !

8! x

Number of

booklets

Number of

printers

Time in

minutes






5. The circle defined by the equation 93422 ! y x is moved horizontally until

its center is on the line 6! x . How far does the center of the circle move?

(A) 2 (B) 9 (C) 10 (D) 15

Solution:

The center of the circle 93422! y x is 3,4 .

The distance between the point 3,4 and the line 6! x is

.1046 !

6. If 11143

! x , what is the value of x?

(A)7

1(B)

7

12(C)

12

7(D)

7

1

Solution:

11143

! x

4

1

3

11!

x, Multiply both sides by x12 , we have

x x 3412 ! 127 ! x

7

12

! x






7. The number 23a74b is divisible by 9 and 8, where a and b represent distinct

digits of the number. What is a-b?

(A) 3 (B) 5 (C) 6 (D) 8

Solution:

If the last 3 digits are divisible by 8, so is the entire

number.

The last 3 digits of 23a74b are 74b, 74b is divisible by 8 when b=4.

23a744 is divisible by 9 if 2+3+a+7+4+4 is divisible by 9. Simplifying2+3+a+7+4+4 the result is

a+20, therefore a=7.

The value of a-b is 3.

A number is divisible by 9 if the sum of the digits is

divisible by 9






9. Ako ay n taong gulang sa taong2

n , " ang sabi ni Mang Berto noong 1971.

Anong taon siya ipinanganak?

(A) 1892 (B) 1812 (c) 1927 (d) 1956

Solution:

n square of n

difference between

the square of n and

n(this is the year of

birth).

39 1521 1482

40 1600 1560

41 1681 1640

42 1764 1722

43 1849 1806

44 1936 1892

45 2025 1980

The most realistic answer






10. What is the simplified improper fraction for 488.4 ?

(A)9

44(B)

33

148(C)

33

160(D)

125

606

Solution:

Let 488.4! x , Since two digits are repeating multiply both sides by 102, the result is

-8484.484100 ! x

Therefore, -- 8484.48484.484100 ! x x

48099 ! x

99

480! x

33

160! x






11. A circular table is pushed into a corner of a rectangular room so that it touches

both walls. A point on the edge on the edge of the table between the two points of

contact is 2 inches from one wall and 9 inches from the other wall. What is the

radius of the table?

(A) 20 inches (B) 12 inches (C) 15 inches (D) 17 inches

Solution:

Denote the walls as the x and y axes. The equation of the circle with radius r and

center r r , is 222r r yr x !

The point (2,9) is a point on the circle, we substitute this to the equation of the

circle and solve for r, we have,

22292 r r r !

222 188144 r r r r r !

085222 ! r r

0517 ! r r

17,5 !! r r

because 5!r is not feasible it has to be 17!r






12. Find the total surface area in square meters of a rectangular solid whose length

is 7 meters, width is 6 meters, and depth is 3 meters.(A) 32 (B) 162 (C) 81 (D) 126

Solution:

Surface Area = whl wlh 222

where l=length, w= width, h = height

Using the formula the Surface area of a rectangular solid in our problem is

162362672372!v

v

v

lw

h






13. Evaluate the following sum:

1002...181512

(A) 139,659 (B) 156,744 (C) 167,817 (D) 189,463

Solution:

An arit hmetic sequence is a sequence in which the difference between any two

consecutive terms is the same. In our problem the common difference is 3!d . The

sum of the members of a finite arithmetic progression is called an arit hmetic series

To find the sum of a finite arithmetic series, you need to know three things. The

first term ? A1a , the last term ? An

a and the number of terms ? An and use the formula .

¹ º

¸©ª

¨ !2

1 n

n

aanS

In 1002181512 - , 121 !a , 1002!n

a , to get the value of n use the formula for

the t hn term of arithmetic sequence which is d naa

n11 !

d naan

11 !

31121002 �! n

13990 ! n 1330 ! n

331! n

Therefore,

¹ º

¸©ª

¨ !

2

1 n

n

aanS

¹

º

¸©

ª

¨ !

2

100212331

817,167!






14. Twelve consecutive integers are added together. What is the remainder when

the sum is divided by 4?

(A) 1 (B) 2 (C) 3 (D) no remainder

Solution:

Let x be the first integer. The integers are

x

1 x

2 x

3 x

4 x

5 x 6 x

7 x

8 x

9 x

10 x

11 x

Sum = 6612 x = 21634 x

15. What is three times the sum of x and y given that°¯

£

!

!

1515

230230

y x

y x

(A) 81 (B) 90 (C) 102 (D) 120

Solution:

3030

6022

1515

230230!

°̄

¤

!

!

°̄

¤

!

! y x

y x

y x

y x

y x

Therefore three times the sum of x and y is 903033 !! y x .

Remainder when the sum

of 12 consecutive integers

is divided by 4






16. What is the slope of the line 123

!y x

?

(A)2

3 (B)

3

2 (C)

3

1(D)

3

2

Solution:

In bm x y ! , m is the slope and b is the y-intercept of the line.

Express 123

!y x

in the form bmx y ! .

123!

y x,Multiply both sides by 6

632 ! y x

623 ! x y

23

2! x y

32!m






17. The product of a positive number, its square , and its reciprocal is81

100. What

is the number?

(A) 100

81

(B) 81

100

(C)10

9

(D) 9

10

Solution:

Let x be a positive number.

81

10012 !¹ º

¸©ª

¨

x x x

81

1002 ! x

9

10! x






18. The lines x y ! and

2

9!

x y form a triangle in the first quadrant with the y-

axis. What is the area of this triangle?

(A) 6.75 (B) 7.75 (C) 8.75 (D) 9.75

Solution:

We sketch the graph of the two lines the result is:

4.5 units

3 units

We solve for the point of intersection of the lines x y ! and

2

9!

x y by

substitution method we have, 2

9! x x

92 ! x x

93 ! x

3! x , 3! y

The distance from the point of intersection to the base of the triangle formed is 3

units. Therefore, the height of the triangle is 3 units.






The difference between the y-intercepts of the lines x y ! and

2

9!

x y is equal

to the height of the triangle which is equal to 4.5 units.

The area of the triangle is half the product of the height and base

units.square75.62

5.43!

v!

19. Simplify the expression x x x x

x

(A)

2 x x

x (B)

x x x

x x (C)

x x x

x2

(D)5

x






Solution:

x

x x x

x

, it becomes

x x

x x

2

It becomes

x x x

xy2

It becomes

2 x x

x

Use the Law of exponent for power

mnnm

aa !

Use again the Law of Exponent for power

Use the Law of Exponent for product

nmnmaaa

!y






20. If 2444 1 ! x x , then the value of x x2 is

(A) 24 (B) 212 (C) 510 (D) 525

Solution:

24441 ! x x

244

44 !

x

x

, Multiply both sides by 4 we have,

96444 ! x x

9643 ! x

324 ! x

52 22 ! x

52 ! x

25! x

Therefore, 2

5

2

522 ¹

º

¸©ª

¨y!

x

x

2

12

5!

21

2 55 y!

525!






21. A cube has a volume of 3125 cm . What is the area of one face of a cube?

(A) 220 cm (B) 225 cm (C) 2

3

241 cm (D) 25 cm

Solution:

The volume of the cube is equal to3

s .

1253 ! s

5! s

The area of one face of a cube which is a square is

252! s

22. The vertex of a parabola hbb x y !2 has coordinates 5,2 . What is the

value of h?

(A) 3 (B) 4 (C) 5 (d) 6

R ecall: The vertex of the parabola k h xa y ! 2 is .,k h

2!b and 5! hb

52 ! h

3! h






23. The diagonals of a rhombus measure 24 inches and 32 inches. The perimeter

of a rhombus

(A) cannot be determined uniquely from the given information

(B) must be 80 inches(C) must be 280 inches

(D) must be 160 inches

Diagonals of a rhombus are perpendicular and bisect each other.

Using Phytagorean Triple 3-4-5.

Multiply 3-4-5 by 4 it becomes 12-16-20

The hypotenuse is 20. Therefore one side of a rhombus measures 20 inches. The

perimeter of a rhombus is inin 80420 !v

16We just divide 32 by 2

We just divide 24 by 2

12






24.Simplify:

q p

pq

q

p

q

q p

x x

x

x

¹¹ º ¸©©

ª¨

¹¹ º

¸©©ª

¨

(A)

22 p pq

x

(B)

22 q pq

x

(c) pq

x2

(D) pq

x

Solution:

q p

pq

q

p

q

q p

x

x

x

x

¹¹ º

¸©©ª

¨

¹¹ º

¸©©ª

¨

q p p

p p

x

x

!

pq p

p

x

x! 2

2

pq x!

p x

p x






25. Determine the solution of the following equation.

? A 462143122 ! x x x x

(A) 0 (B)3

2 (C)

2

1(D)

2

3

Solution:

? A 462143122 ! x x x x

? A 46843222 ! x x x x

x21 !

2

1! x

distribute -2 distribute 4

cancel






26. A car traveled 3 miles south, 9 miles east, and then another 9 miles south.

What is the straight-line distance (in miles) between the point where the car started

and where it stopped?

(A) 21 (B) 36 (C) 37 (D)15

Solution:

To solve this problem, we can use the coordinate plane. The car started at the

origin and stopped at the point 12,9 . We get the distance between 0,0 and

12,9 using the distance formula:

2

12

2

12 y y x xd !

22129 !

225!

15!

9 miles

3 miles

9 miles

12 miles below the x-axis






A(5,8)

B(-2,2)

27. Find the y-intercept of the perpendicular bisector of AB where A(5,8) and B(-2,2)

(A) 6.75 (B) 7.75 (C) 8.75 (D) 8.75

Solution:

First we get the slope of AB using the formula

12

12

x x

y ym

!

25

28

!m

7

6!m

The slope of the line perpendicular to AB is the negative reciprocal of 7

6 which is

67 .






Next we get the midpoint of AB using the formula

¹ º

¸©ª

¨ !

2,

2, 2121 y y x x y x mm

¹ º

¸©ª

¨ !2

82,

2

52

5,2

3!

Next we get the equation of the line with slope of 6

7 and passing through the

point 5,2

3 using the point-slope form of the equation of the line.

11 x xm y y !

¹ º

¸©ª

¨!

2

3

6

75 x y , transpose -5 to the right

52

3

6

7¹

º

¸©ª

¨! x y , distribute

67

512

21

6

7! x y

5

4

7

6

7! x y

4

27

6

7! x y , already in the form ,bmx y ! where b is the y-

intercept

Answer:6.75

y-intercept = 27/4 or 6.75






28. For what value of k will the graph of k x x y ! 23 2 be tangent to the x-axis?

(A)2

1(B)

3

2(C)

3

1(D)

4

3

Solution:

The number of points of intersection of the parabola cb xax y ! 2 and the x-axis

is

±°

±¯

®

!

!!

!"

axis-xtheintersectnotdoes parabolathen the,04I

axis-xthetangentis parabolathen the,04I

pointsat t o parabolatheintersects parabolathen the,04I

22

22

22

cb xa x yacb

tocb xa x yacb

cb xa x yacb

k x x y ! 23 2 is tangent to the x-axis when 03422 ! k

31! k

29. The sum of the first five terms of a geometric sequence is 93. If its common

ratio is 2, what is the first term?

(A) 2 (B) 3 (C) 4 (D) 5

Solution:

Let x be the first term of the geometric sequence

9316842 ! x x x x x

9331 ! x

3! x






30. A certain number was to be added to2

1 but by mistake

2

1was divided by the

number. However, the correct result was obtained. Find the number.

(A) 1or 2 (B) 1or 2 (C) 1-or 2

1

(D) 1or 4

1

Solution:

212

1

! x x

, multiply both sides by x2 , the result is

x x ! 221

0122 ! x x

0112 ! x x

1or 2

1 !! x x

ANSWER KEY IN UPCAT PR ACTICE TEST 2

1 A 11 D 21 B

2 C 12 B 22 A

3 B 13 C 23 B

4 B 14 B 24 D

5 C 15 B 25 C

6 B 16 B 26 D

7 A 17 D 27 A

8 B 18 A 28 C

9 A 19 A 29 B

10 C 20 D 30 C

UPCAT review tips next page






UPCAT review tips

MATHEMATICS SCIENCE AND TECHNOLOGY

I. ARITHMETIC I. GENERAL SCIENCE

1. Whole Numbers 1. Effect of earth's motion, shape and inclination

2. Rational Numbers on time and seasonal changes

3. Decimal/Money/Percent 2. Force and motion

4. Measurement 3. Improving, conserving and protecting

5. Ratio and Proportion man's environment

4. Forms and transformation of energy

5. Investigating Matters

II. ALGEBRA

BIOLOGY

1. Integers

2. Algebraic Expressions 1. Reproduction

3. Quadratic Equations 2, Chemical and cellular basis of life

4. Linear Equations/ Inequalities/Equalities 3. Organ Systems

5. Polynomials 4. Life Energy

6. Rational Expression 5. Ecosystem

7. Exponents/ Scientific Notation/ Radicals 6. Genetics -Mendellian patterns of heredity

8. Sequences and Series 7. Diversity of life

III. Statistics CHEMISTRY

IV. Geometry 1. Properties of Colloids

2. Changes of Matter

1. Plane Coordinates/ Lines 3. Restless Molecules -Behavior of Gases

2. Graphs/ Angles 4.Structure of Atom

3. Triangles/ Rectangles/ Circles 5. carbon and its Compounds

6. Properties of Elements

V. WORD PROBLEMS 7. Nature of Solution





b t t b it th l ti ti th h il dd

PHYSICS

1. Conversion of one unit of measure to another

2. Adding vector quantities (graphically)

3. Acceleration of a Falling Body

4. Object's Motion with rfespect to a

reference point

5. Differentiating distance from displacement

6. Solving average velocity

VERBAL ABILITY

ENGLISH AND FILIPINO

1. Communication Skills- Grammar and

Correct Usage Verbal relationship2. Reading Comprehension Skills

3. Logical Organization

4. Vocabulary

5. Analogy

30215924 upcat reviewer practice test 2

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