Free Printable Practice Examination

1.

The arithmetic means between 1 and 25

a)

4, 9, 16

b)

7, 13, 19

c)

8, 14, 20

d)

5, 10, 17

2.

If $h=-1$ , then $h - h^2 + h^3 - h^4$ is

a)

-4

b)

-2

c)

0

d)

2

3.

What is the simplest form of $\dfrac{2^{-3}x^{-5}y^{-2}}{4^{-2}x^{-4}y^{-1}}$ ?

a)

$\dfrac{2}{xy}$

b)

$2xy$

c)

$\dfrac{xy}{2}$

d)

$\dfrac{2x}{y}$

4.

If in a given year, February 24 falls on Saturday, what day of the week is February 12 of that year?

a)

Monday

b)

Tuesday

c)

Wednesday

d)

Thursday

5.

If x & y are positive integers, $x^2 + y^2 = 80$ and $x^2 - y^2 = 8$ , then y is equal to

a)

5

b)

6

c)

7

d)

8

6.

Law of Cosines can be used to solve the following oblique triangle cases EXCEPT

a)

SAA

b)

ASA

c)

SAS

d)

AAA

7.

How many numbers n will make $300/n$ a whole number?

a)

9

b)

12

c)

18

d)

20

8.

If a, b, c, and d are consecutive odd integers and $a<b<c<d$ , then $c+d$ is how much greater than $a+b$ ?

a)

2

b)

4

c)

6

d)

8

9.

Perform the indicated operations: $4 + \dfrac{4-2}{\dfrac{8}{3-(-1)}}$

a)

5

b)

4

c)

3

d)

6

10.

What does the figure show?

a)

same (+) correlation

b)

same (-) correlation

c)

perfect (+) correlation

d)

perfect (-) correlation

11.

Who is the first mathematician who attempted to classify curves according to the types of equations that produce them and also made contributions to the theory of equations

a)

Blaise Pascal

b)

Rene Descartes

c)

Pierre De Fermat

d)

John Napier

12.

The domain and range, respectively, of the function f(x) = √(x+2) − 3 is

a)

x ∈ R | x ≠ −2 ∧ ( y ∈ R ∨ y ≥ −3 )

b)

x ∈ R | x ≠ −2 ∧ ( y ∈ R ∨ y ≠ −3 )

c)

x ∈ R | x ≥ −2 ∧ ( y ∈ R ∨ y ≤ −3 )

d)

x ∈ R | x ≥ −2 ∧ ( y ∈ R ∨ y ≥ −3 )

13.

What are the solutions of $x^2 - 5x + 10 = 0$ ?

a)

$\dfrac{5}{12} \pm \dfrac{\sqrt{65}}{12} i$

b)

$-\dfrac{5}{12} \pm \dfrac{\sqrt{65}}{12} i$

c)

$\dfrac{5}{2} \pm \dfrac{\sqrt{15}}{2} i$

d)

$-\dfrac{5}{2} \pm \dfrac{\sqrt{15}}{2} i$

14.

Which of the following identities is $\tan x = \dfrac{1}{\cot x}$

a)

Fermat

b)

Pythagorean

c)

Quotient

d)

Reciprocal

15.

The originator of the concepts behind the present-day computer

a)

Charles Babbage

b)

Alan Turing

c)

John Napier

d)

Blaise Pascal

16.

What is the minimum number of faces a prism may have?

a)

4

b)

5

c)

6

d)

8

17.

What is the appropriate statistical test needed when birth order is related to academic performance?

a)

Pearson-r

b)

t-test

c)

F-test

d)

Spearman-rho

18.

In a group of 150 students, 60 are taking Physics, 48 are taking Chemistry, and 24 are taking both. A student is selected at random from those taking Physics. What is the probability that the student is taking Chemistry?

a)

3/5

b)

1/5

c)

4/5

d)

2/5

19.

Find the sum of the series 1/3 + 1/(3*5) + 1/(5*7) + 1/(7*9) + 1/(9*11)

a)

1/11

b)

5/11

c)

3/33

d)

5/33

20.

A coin is tossed five times in succession. What is the probability of getting a head on the first toss and tails on the other succeeding tosses?

a)

1/8

b)

1/32

c)

1/16

d)

5/32

21.

If $10^{10}+10^{10}+\dots+10^{10}=10^x$ , what is x? ten terms

a)

10

b)

11

c)

100

d)

101

22.

If the sum of the first 50 odd integers is 2500, what is the sum of the first 100 even integers?

a)

2,500

b)

2,550

c)

10,000

d)

10,100

23.

A gardener receives a salary of 45,000.00 pesos a year with a contract of 550.00 pesos annual increase for 7 years. What is his total income for 7 years?

a)

326,550.00

b)

9,979,200

c)

318,850.00

d)

318,300.00

24.

The missing terms in 1, 1, 2, 4, 7, 13, __, __

a)

23, 43

b)

23, 44

c)

24, 43

d)

24, 44

25.

What is the 6th term in the expansion of $(x-2y)^6$

a)

$-32\,x\,y^5$

b)

$-32\,x^5\,y$

c)

$-192\,x\,y^5$

d)

$-192\,x^5\,y$

26.

Celia argues that $15\equiv -9\pmod{6}$ . Is she correct? Why?

a)

Yes, because 6 divides $15-9$

b)

Yes, because 6 divides $15+9$

c)

No, because 6 does not divide $15+9$

d)

No, because $15\ne -9+6(1)$

27.

What is the last digit of $2023^{2024}$

a)

3

b)

1

c)

9

d)

7

28.

How many distinct permutations can be made using all the letters in the word MATHEMATICS?

a)

4,989,600

b)

9,979,200

c)

19,958,400

d)

39,916,800

29.

A particular examination in Statistics with 100 students was known to be approximately normally distributed with a mean of 84 and a standard deviation of 6. Find the z-score of a student whose score is 90.

a)

1.20

b)

1.00

c)

-1.00

d)

0.17

30.

How many positive real roots are there in $P(x)=x^3+3x^2-x-3$

a)

0

b)

1

c)

2

d)

3

31.

If p is prime, then $(p-1)! \equiv -1 \mod(p)$ . This belongs to what theorem?

a)

Diophantine’s

b)

Euler’s

c)

Fermat’s

d)

Wilson’s

32.

If three children eat 4 kilos of rice in 5 days, how long will twelve children eat 48 kilos of rice?

a)

12

b)

15

c)

18

d)

21

33.

The sum of angles of a triangle in hyperbolic geometry is

a)

$90^\circ$ < A + B + C < $180^\circ$

b)

$180^\circ$ < A + B + C < $540^\circ$

c)

A + B + C < $180^\circ$

d)

A + B + C > $90^\circ$

34.

One of the greatest mathematicians who is said to have claimed that “Mathematics is the queen of sciences and number theory is the queen of mathematics.”

a)

Carl Gauss

b)

Aristotle

c)

Albert Einstein

d)

Isaac Newton

35.

Among the following statements, which of these cannot be applied in Excel?

a)

Graph an equation

b)

Find the measures of variation

c)

Create tables and worksheets

d)

Graph data

36.

If the letters in the word MATHEMATICS are repeatedly and consecutively written, what is the 2023rd letter?

a)

T

b)

I

c)

C

d)

S

37.

What is $\varphi(37)$ equal to?

a)

36

b)

1

c)

19

d)

37

38.

Find the slope of the line normal to the curve $x^2 + y^2 - 6x + 10y + 5 = 0$ at $(1,0)$ .

a)

$2/5$

b)

$-5/2$

c)

$-2/5$

d)

$5/2$

39.

A ladder of 50 feet long is leaned on the wall, its lower end forms an angle of 30 degrees from the ground. Find the distance of the upper end of the ladder to the ground.

a)

100 feet

b)

40 feet

c)

25 feet

d)

20 feet

40.

What is the midpoint of the line segment joining the points $(2,-3)$ and $(6,7)$ ?

a)

$(2,2)$

b)

$(4,4)$

c)

$(2,4)$

d)

$(4,2)$

41.

Who is the greatest mathematician that died tragically at the age of 20 for being shot in the abdomen during duel speculated out to be a conflict over a woman?

a)

Carl Gauss

b)

John Napier

c)

Evariste Galois

d)

Francois Viete

42.

It is the ultimate goal of mathematical investigation

a)

conjecture

b)

extension

c)

generalization

d)

pattern observation

43.

Factorize $2x^2+7x-15$

a)

$(2x-3)(x+5)$

b)

$(2x+3)(x-5)$

c)

$(x-5)(2x+3)$

d)

$(2x+5)(x-3)$

44.

There are 6 orange, 5 blue and 11 pink balls. What is the probability that I will pick orange balls randomly?

a)

5:22

b)

6:22

c)

3:11

d)

11:22

45.

Which of the following is NOT considered to be a fundamental property?

a)

weight

b)

length

c)

time

d)

mass

46.

Find the equation of the line perpendicular to $2x-3y=7$ , passing through $(1, 2)$

a)

$2x+3y=8$

b)

$3x+2y=7$

c)

$2x-3y=4$

d)

$3x-2y=-1$

47.

Which is the numerical characteristic of a sample?

a)

mean

b)

statistic

c)

parameter

d)

standard deviation

48.

Amount due on 2.5 years if 8,000.00 invested at 12% simple interest

a)

$10{,}400.00$

b)

$9{,}300.00$

c)

$10{,}782.79$

d)

$5{,}600.00$

49.

If July 12, 2003 fell on Tuesday, on what day will July 12, 2005 fall?

a)

Thursday

b)

Friday

c)

Sunday

d)

Monday

50.

A recipe calls for 2 cups milk for every 7 cups of flour. A chef will use 28 cups of flour, how many cups of milk must he have?

a)

10

b)

8

c)

12

d)

14

51.

Two positive integers are relatively prime if they have no common factor other than 1. How many two-digit number relatively prime with 24?

a)

8

b)

6

c)

7

d)

5

52.

Solve for a: $\log_4$ $3a-4$ $=2$ .

a)

3

b)

20/3

c)

4

d)

20

53.

Most scores of the examinees are above the mean. What is the graphic representation of the score distribution?

a)

leptokurtic

b)

perfect normal curve

c)

negatively skewed

d)

positively skewed

54.

How many ways are there to select 3 candidates from 8 equally qualified recent graduates for opening in an accounting firm?

a)

6

b)

24

c)

56

d)

336

55.

He has been described as the greatest “might-have-been” in the history of mathematics.

a)

Blaise Pascal

b)

Gaspard Monge

c)

Bonaventura Cavalier

d)

Gregorio de Saint

56.

The inventor of a more complex protractor

a)

Lorenz

b)

Joseph Huddart

c)

Marin Mersenne

d)

De Moivre

57.

On a farm there are cows and chickens. Altogether, they have 41 heads and 100 legs. How many chickens are there?

a)

32

b)

26

c)

21

d)

20

58.

In a party there are 8 people. If everyone at the party shakes hands with everyone else, how many handshakes would there be?

a)

64

b)

28

c)

35

d)

7

59.

Which of these materials help the students explore the perimeter and area of polygons?

a)

clinometer

b)

geoboard

c)

fraction kit

d)

string and ruler

60.

How many squares does a chessboard have?

a)

55

b)

91

c)

140

d)

204

61.

Which of the following are relatively prime?

a)

17 and 51

b)

19 and 57

c)

11 and 131

d)

13 and 39

62.

If it is 5 o’clock and you have to leave for the airport at 39 hours, what time do you need to leave?

a)

10

b)

6

c)

8

d)

2

63.

What do numbers 495, 585, 675 have in common? I. these numbers are divisible by 5 II. these numbers are divisible by 7 III. these numbers are divisible by 9 IV. these numbers are divisible by 11

a)

I and III

b)

II and IV

c)

II and III

d)

I and IV

64.

Which among the measures of central tendency is not influenced by outliers?

a)

mean

b)

weighted mean

c)

median

d)

mode

65.

Which among the distribution is used for rare events in large population?

a)

Binomial distribution

b)

Normal distribution

c)

Poisson distribution

d)

Frequency distribution

66.

Which of the following statements are both true to Euclidean and non-Euclidean geometry

a)

a triangle cannot have two right angles

b)

any two coplanar lines intersect

c)

perpendicular lines form right angles

d)

if a circle has a radius r, its circumference in 2πr

67.

Find the $\det A = \begin{bmatrix} x - y & x \ x & x - y \end{bmatrix}$ .

a)

$-2xy - y^2$

b)

$-2xy$

c)

$y^2$

d)

$-2xy + y^2$

68.

What is the vertex of the parabola $y = x^2 - 2x + 3$ ?

a)

$(2,3)$

b)

$(-1,2)$

c)

$(1,2)$

d)

$(2,1)$

69.

How many minutes after 2 o’clock will the hands of the clock extend in opposite direction for the first time?

a)

43.64 minutes

b)

42.64 minutes

c)

41.64 minutes

d)

40.64 minutes

70.

The cost C of a product is a function of the quantity x of the product: $C(x) = x^2 - 23000x + 1000$ . Find the quantity for which the cost is minimum

a)

11,500

b)

13,500

c)

12,500

d)

10,500

71.

Given the dimension of the transpose of the matrix [ -1 2 ; 0 1 ; 3 1 ].

a)

3 × 2

b)

2 × 3

c)

3 × 3

d)

2 × 2

72.

On a 12-hour clock, find x so that $3 + x = 1$ .

a)

7

b)

11

c)

10

d)

9

73.

Compute det⁡(A^T) if

A = [ −2 3]

[ 4 1 ].

a)

14

b)

1/14

c)

−14

d)

−1/14

74.

Which measure of central tendency is affected by extreme measures?

a)

mean

b)

weighted mean

c)

median

d)

mode

75.

Find c in A = [ c+3 −1

4 c−2 ] so that det⁡(A)=0\det(A)=0det(A)=0 .

a)

c = −2; c = 1

b)

c = 2; c = −1

c)

c = −3; c = 2

d)

c = 3; c = −2

76.

Anthony has two sticks of lengths 5 cm and 8 cm. He needs a third stick to form a triangle. what it the range of the values for the possible length of the third stick in order to form a triangle

a)

5 < x < 8

b)

3 < x < 13

c)

5 < x < 15

d)

8 < x < 13

77.

Find c in A =

[ c+3 −1 ]

[ 4 c−2 ]

so that det⁡(A) = 0

a)

c = −2; c = 1

b)

c = 2; c = −1

c)

c = −3; c = 2

d)

c = 3; c = −2

78.

Which pair is relatively prime?

a)

(18 , 4)

b)

(13, 7)

c)

(24, 18)

d)

(6 , 45)

79.

which two angle are complementary?

a)

22 degrees and 78 degrees

b)

56 degrees and 24 degrees

c)

67 degrees and 23 degrees

d)

140 degrees and 40 degrees

80.

One of the legs of a right triangle is 5cm long and its hypotenuse is 15 cm, how long is the other leg?

a)

10 cm

b)

8 √10 cm

c)

10 √2 cm

d)

8 cm

81.

Find the distance between A (4, -3) and B (-2, 5)

a)

11

b)

8

c)

9

d)

10

82.

find the derivative of f(x) = 7x + 4

a)

7

b)

7x

c)

0

d)

-7

83.

A tin cam is to be painter blue on its surface. What will be the total area of the tin can that will covered by paint if its radius is 3 cm and height is 7 cm

a)

56.52

b)

154.26

c)

188.4

d)

131.88

84.

there were two outstanding astronomers who contributed notably to mathematics in the early part of the equation of the seventeenth century; the german Johann kepler and the italian

a)

Johanna Muller

b)

Nicholas Chuquet

c)

Galileo Gallilei

d)

Nicholas Cusa

85.

if the distance between the point (8, 7) and (3, y) is 13, what is the values of y

a)

5

b)

-19

c)

19 and -5

d)

5 and -19

86.

if x and y are both odd numbers, which of the following numbers must be an even number

a)

x + y

b)

xy

c)

2x + y

d)

xy + 2

87.

which of the following identities is tan x = sinsinx/coscosx

a)

Fermat's Identities

b)

Pythagorean Identities

c)

Quotient Identities

d)

Reciprocal Identities

88.

Find the equation of the x-axis

a)

x = 0

b)

x + y = 0

c)

y = 0

d)

x-y =0

89.

In three dimension, where is the point located if x = y = z = 0

a)

yz plane

b)

origin

c)

xz plane

d)

xy plane

90.

His greatest contributions include such groundbreaking texts in the invention of dividing rods used as multiplication tables

a)

Francois Viete

b)

Marin Mersenne

c)

Johannes Kepler

d)

Jhon Napier

Practice Examination – EC2 Mathematics

Total questions: 90

Worksheet time: 45mins

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