PREPARE FOR MATHEMATICAL TUTOR EXAM

Algebra, Pre-Algebra, Basic Math, Calculus, Pre-Calculus, Probability, Statistics, Geometry, Trigonometry

Find the sum of the series 1/(1×2) + 1/ (2×3)+ 1/(3×4)+...+1/(n×(n+1))+...

• A.
• 1
• B.
• e
• C.
• 3/2
• D.
• 1/2

70% of the counties of the particular state received some rain on Monday, and 65% of the counties received some rain on Tuesday. No rain fell either day in 25% of the counties. What % of the counties received some rain on Monday and Tuesday?

• A.
• 45.5%
• B.
• 40%
• C.
• 12.5%
• D.
• 60%

A supermarket raised the price of a loaf of bread by exactly 30%. Which of the following could NOT be the resulting price of the item:

• A.
• $2.60
• B.
• $1.17
• C.
• $3.90
• D.
• $1.50

The sides of the trapezoid ABCD (BC//AD) are: AB=BC=CD=a and AD=2a.The line segment BE//CD, BE X AD = p.E. If the area of the triangle ABE= 5/2, then area of ABCD is:

• A.
• √5
• B.
• 5
• C.
• 3√5 / 2
• D.
• 2√5

Calculate the volume of the solid, bounded by the surfaces: z=4x2 +4y2; z=x2+y2; z=4.

• A.
• 2π
• B.
• 8π
• C.
• 6π
• D.
• 35/4

6

Solve the exponent equation: 4 × 9x -13 × 6x + 9 × 4x = 0

• A.
• (1; 9/4)
• B.
• (0; 1)
• C.
• (0; 2)
• D.
• (1; 1)

7

There are 3 black and 7 white balls in the box, identical in touch. You draw 3 balls randomly. If you find 1 black ball among the drawn ones, you will win $1, if you find 2 black balls, you win $2 and you will win $10, if all 3 are black. What are the chances to win at least 1 buck?

• A.
• 7/24
• B.
• 1/2
• C.
• 13/24
• D.
• 17/24

8

(sin4x – cos4x)' is:

• A.
• 2sin(2x)
• B.
• tan3(x)
• C.
• -cos(2x)
• D.
• -2sin(4x)

9

Only one pair of the following vectors is orthogonal. Which one is it?

• A.
• 3i+4j & 1/3i + 1/4j
• B.
• -j+5k & j - 1/5k
• C.
• 3j & -5k
• D.
• 2i + 4j & -1/2i +1/4k

10

Which of the following standard forms might represent conic section x2 -3x + 4xy +y2 + 21y - 15 = 0

• A.
• x2/a2 + y2/b2 = 1
• B.
• x2+y2=R2
• C.
• y2=4ax
• D.
• x2/a2 - y2/b2 = 1
• E.
• x2/a2-y2/b2=0

11

(2^sin^2(3x))'=

• A.
• ln8 × 2^sin^2(3x) × sin6x
• B.
• ln2× 2^sin^2(3x) × cos3x
• C.
• e^sin^2(3x) × ln2 × cos^2(3x)
• D.
• 6cos3x × ln2 × 2 × sin^2(3x)

12

How many integers between 10 and 60, inclusive, can be evenly divided by neither 2 nor 3?

• A.
• 43
• B.
• 17
• C.
• 34
• D.
• 37

13

A(-1; 0; 1); B(-1;1;0); C(1;0;0) and D(0;1;1) are the vertices of the pyramid. Find the volume of this pyramid.

• A.
• 1/2
• B.
• 0
• C.
• 1/3
• D.
• 1/6

14

What is the area of the figure bounded by the lines: x=0; x=π/2; y=sin(x); y=1?

• A.
• 1
• B.
• π
• C.
• 2 - π
• D.
• π/2 - 1

15

Find the normal vector n to the plane, containing vectors: A = 3i +j - k and B = -i +k.

• A.
• n = i -2j + k
• B.
• n = i + 2j + k
• C.
• n = 2i - 2j - k
• D.
• n = i + 4j + k

16

(1+tan2x)4 - 1/cos8x is:

• A.
• >0
• B.
• <0
• C.
• =0
• D.
• =1

17

When x->0 lim TAN(x2)/ x =

• A.
• 0
• B.
• 1
• C.
• Infinity
• D.
• Undefined

18

3 individuals take the elevator in 15-story building. What are the odds they all will get off on the same floor? Notice: they are all strangers to one another.

• A.
• 1/196
• B.
• 1/3375
• C.
• 1/2744
• D.
• 3/225

19

Number 1100101 in binary system represents the number in decimal system. Which one?

• A.
• 110
• B.
• 101
• C.
• 96
• D.
• 77

20

Find the sum of the series 1 + 1/3 + 1/9 + ... + 1/3k-1 + ...

• A.
• e
• B.
• 2/3
• C.
• 3/2
• D.
• Infinity

21

If A is a true statement, which of the following is correct?

• A.
• A & not A <=> TRUTH
• B.
• A=> not A
• C.
• A or not A <=> TRUTH
• D.
• A or not A <=> LIE

22

Simplify expression: not (A & not A):

• A.
• not A & not A
• B.
• not A & A
• C.
• A=> not A
• D.
• not A or A

23

A three-character password consists of 2 different digits between 0 and 9, inclusive, and 1 letter of the English alphabet. The letter must appear as first or second character. How many different passwords are possible?

• A.
• 2340
• B.
• 94348800
• C.
• 188697600
• D.
• 4680

24

Find the false statement:

• A.
• No three positive integers a,b,c can satisfy the equation an+bn=cn for any integer n > 2.
• B.
• If connect North Pole, Paris and Kyiv on the globe, the sum of the inner angles of the obtained triangle is 180 degrees.
• C.
• The series 1+1/2+1/3+...+1/n+... is divergent.
• D.
• The nonzero rational numbers form a group under multiplication.

25

An employer must hire 3 programmers from among 6 applicants and 1 product manager from among 4 applicants. What is a total number of possible ways in which he can make his selection?

• A.
• 80
• B.
• 120
• C.
• 1400
• D.
• 132

26

The function * is defined by the equation a*b=ab/(b-a), where a is not = b. Which of the following has a value of 3?

• A.
• 1*3
• B.
• 3*0
• C.
• 2*6
• D.
• 6*2
• E. 4*-1

27

What is the S to the 10-th power, if S is the sum of the solutions of the equation 2x2 - 2ix +10=0, where i=√(-1).

• A.
• -1
• B.
• 1024
• C.
• -1024i
• D.
• 1