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РК 2 каз новый платонус студенты

Total questions: 76

Worksheet time: 38mins

Name
Class
Date
1.

Which of the following best defines a function in mathematical terms? 

a)

A map f: X → Y such that for every x ∈ X there exists exactly one y ∈ Y with f(x) = y

b)

A map where each y ∈ Y corresponds to multiple x ∈ X 

c)

A set of ordered pairs without any restriction 

d)

An expression containing only numerical constants

e)

A graph that passes the horizontal line test 

2.

Which graph represents a quadratic function?

a)

A U-shaped curve (parabola)

b)

A straight line

c)

An S-shaped curve

d)

A hyperbola

e)

A step graph

3.

Choose the correct statement about functions:

a)

A function has one output for each input

b)

A function can have two outputs for one input

c)

A function must be a straight line

d)

A function is always increasing 

e)

All graphs are functions

4.

Choose the incorrect statement about functions:

a)

A function may assign multiple outputs to one input

b)

A linear function has the form y = mx + b 

c)

A quadratic function has a parabolic graph

d)

The vertical line test is used to check if a graph is a function

e)

Functions can be increasing or decreasing 

5.

Translate the term “piecewise function” into English:

a)

A function defined by different expressions over different intervals

b)

A function with a broken graph

c)

A function with a hole

d)

A function that is constant

e)

A function with variables only 

6.

Fill in the gap: A (an) __________ function has a graph that never touches the x-axis

a)

exponential

b)

linear

c)

quadratic

d)

absolute value

e)

constant

7.

Which of the following graphs is not a function?

a)

A circle

b)

A straight line

c)

A parabola opening upwards

d)

An exponential curve

e)

A linear decreasing graph

8.

Identify the function type: y = 1/x

a)

Rational function

b)

Linear function

c)

Quadratic function

d)

Exponential function

e)

Absolute value function

9.
a)

five

b)

a proper fraction

c)

radicand of a root 25\sqrt[]{25}

d)

0

e)

the value of a logarithm log⁡28\log_28

10.

If the surface area of a cube is 384 cm2, what is the volume of the cube? 

a)

512 cm3

b)

45 cm3 

c)

5978 cm3

d)

98 cm3

e)

25 cm3

11.

Which of the following is the midpoint of a line with endpoints at (-2,-8) and (8,0)?

a)

(3,–4)

b)

(-2, 5)

c)

(6,–8)

d)

(0,5)

e)

(3,4)

12.

If  30%  of  r is  equal to 75%  of   s, what is  50%  of  s  if  r = 30?

a)

6

b)

3

c)

solution of the question   x-8=0

d)

-1

e)

12

13.

What is the correct translation of “Функция формуламен берілген”?

a)

The function is given by a formula 

b)

The function is defined as a rule

c)

The function has a structure

d)

The function is written as a text

e)

The function is set by condition

14.

What is the correct translation of “Функция болмайды”?

a)

is not a function

b)

has no function

c)

isn’t functioning

d)

cannot be a function

e)

does not function

15.

What is the correct translation of “функция таблица түрінде берілген”? 

a)

The function is given by a table

b)

The function is written by hand

c)

The function is shown by numbers

d)

The function has a data set

e)

The function is described by a graph

16.

Which of the following is an exponential function? 

a)

y = 2^x

b)

y = x^2

c)

y = √x

d)

y = x + 3

e)

y = log(x)

17.

What is the domain of y = 1/x?

a)

All real numbers except 0

b)

All real numbers

c)

Only positive numbers

d)

Only negative numbers

e)

All integers

18.

Which of the following is a rational function? 

a)

y = (x + 1)/(x - 2)

b)

y = 3x² + 2x - 1

c)

y = |x|

d)

y = 2^x

e)

y = √x

19.

Which function has a horizontal asymptote?

a)

Exponential function

b)

Linear function

c)

Quadratic function

d)

Absolute value function

e)

Cubic function

20.

Which function is not defined at x = 0?

a)

y = 1/x

b)

y = x²

c)

y = |x|

d)

y = 2x + 1

e)

y = √x

21.

Which of these represents a logarithmic function?

a)

y = log(x)

b)

y = 3x

c)

y = x² + 1

d)

y = 2^x

e)

y = 1/x

22.

What type of function is y = √x?

a)

Square root function

b)

Quadratic function

c)

Exponential function

d)

Linear function

e)

Cubic function

23.

Which function grows the fastest as x increases?

a)

Exponential function

b)

Linear function 

c)

Quadratic function

d)

Absolute value function

e)

Logarithmic function

24.

Which function represents exponential decay?

a)

y = (1/2)^x

b)

y = 2^x

c)

y = x²

d)

y = x³

e)

y = log(x)

25.

What is the inverse of y = 2^x?

a)

y = log₂(x)

b)

y = x²

c)

y = 1/x

d)

y = √x

e)

y = |x|

26.

What is the domain of the square root function y = √x?

a)

x ≥ 0

b)

x ≤ 0

c)

All real numbers

d)

x ≠ 0

e)

Only positive integers

27.

Which function is not continuous over all real numbers?

a)

y = 1/x

b)

y = x²

c)

y = x³

d)

y = 2^x

e)

y = log(x)

28.

What is the range of y = |x|? 

a)

y ≥ 0

b)

All real numbers

c)

y ≤ 0

d)

y ≠ 0

e)

y > 0

29.

At which point does the function y = |x| have a sharp corner?

a)

x = 0

b)

x = 1

c)

x = −1

d)

x = 2

e)

It has no corner

30.

If 3x-y=2 and 2y-3x=8

2y – 3x = 82y – 3x = 8

, which of the following is equal to xy\frac{x}{y} ? 

a)

2/5

b)

mixed fraction

c)

negative number

d)

3/4

e)

improper fraction

31.

What is the minimum value of the function y = x² + 2x + 1?

a)

0

b)

1

c)

-1

d)

2

e)

-2

32.

Which one of the following sets does not represent (A∩B)C\frac{\left(A\cap B\right)}{C} ?

a)

b)

c)

d)

e)

33.

How many of the following statements are true?  

I. The set of integers contains the set of natural numbers.  

II. The set of natural numbers is a subset of the set of integers.  

III.  z=z+∪z−z=z^+\cup z^-

IV. Every positive integer is greater than 1.  

V. The smallest integer is -1.  

a)

2

b)

1

c)

3

d)

4

e)

5

34.

What is 12−3[4+5−42÷8]12-3\left[4+5-4^2\div8\right] ? Use the BEDMAS rule.

a)

-9

b)

33

c)

-33

d)

9

e)

39

35.
a)

8

b)

-8

c)

-12

d)

28

e)

16

36.

What property of indefinite integrals is wrong:

a)

b)

c)

d)

e)

37.
a)

25 degrees

b)

50 degrees

c)

110 degrees

d)

85 degrees

e)

60 degrees

38.

Point the right equivalent of this term integration by parts 

a)

бөліктеп интегралдау

b)

анықталған интеграл

c)

меншіксіз интеграл

d)

интеграл 

e)

анықталмаған интеграл

39.

Point the right equivalent of this term difference of the sets

a)

жиындардың айырымы

b)

жиындардың қиылысуы

c)

жиындардың бірігуі 

d)

бос жиын 

e)

жиынның толықтырылуы

40.

The set A has 6 elements and the set В has 4 elements. What is the least number of subsets of А ∪\cup В? 

a)

64

b)

value of a root   678\sqrt[]{678}

c)

index of a root 25\sqrt[]{25}

d)

24

e)

32

41.
a)

The value of expression is equal to ( −1330-\frac{13}{30} ).

b)

The value of expression is equal to ( −59-\frac{5}{9} )

c)

The value of expression is logarithmic expression

d)

The value of expression is inverse trigonometric functions

e)

The value of expression is equal to 23\frac{2}{3}

42.

If 40% of j is equal to 50% of k, then j is 

a)

25 % larger than k

b)

20% larger than k

c)

10% larger than k

d)

80% larger than k

e)

15% larger than k

43.

A dormitory now houses 30 men and allows 42 square feet of space per man. If five more men are put into this dormitory, how much less space will each man have? 

a)

6 square feet

b)

4 square feet

c)

8 square feet

d)

7 square feet

e)

5 square feet

44.

At which x does the function y = 1/x have a vertical asymptote?

a)

x = 0

b)

x = 1

c)

x = −1

d)

x = ∞

e)

x = 2

45.

What is the value of the function f(x) = ln(x) at x = 1?

a)

0

b)

1

c)

e

d)

Undefined

e)

-1

46.

Which of the following statements is true for y = tan(x)? 

a)

The function has vertical asymptotes at x = ±π/2, ±3π/2, ...

b)

The function is bounded between −1 and 1

c)

The function is even

d)

The function has a period of 2π

e)

The function has no asymptotes

47.

How many real zeros does the function f(x) = x² + 1 have?

a)

0

b)

1

c)

2

d)

Infinite

e)

3

48.

Which value of x is a zero of the function f(x) = (x − 2)(x + 3)?

a)

2

b)

1

c)

0

d)

-1

e)

5

49.

If a function crosses the x-axis at x = −4, what is true?

a)

f(−4) = 0

b)

f(−4) = 1

c)

f(−4) = −4

d)

f(−4) is undefined

e)

f(−4) > 0 

50.

What are the zeros of f(x) = x(x − 1)(x + 2)?

a)

0, 1, −2

b)

−1, 1, 2 

c)

0, −1, −2

d)

1, 2, 3

e)

0, 1, 2

51.

What does the derivative of a function represent?

a)

The rate of change of the function

b)

The total value of the function

c)

The graph of the function

d)

The area under the curve

e)

The maximum value

52.

Which of the following functions is not differentiable at x = 0? 

a)

f(x) = |x|

b)

f(x) = x²

c)

f(x) = sin(x)

d)

f(x) = x³

e)

f(x) = ln(x)

53.

What is the English equivalent for «Бірлік шеңбер»?

a)

unit circle

b)

one circle

c)

circle of one

d)

unity circle

e)

basic circle

54.

What is the English equivalent for «Функцияның периоды»? 

a)

period

b)

phase

c)

range

d)

interval

e)

wave

55.

What is the English equivalent for «амплитуда»?

a)

amplitude

b)

height

c)

volume

d)

frequency

e)

level

56.

What is the sum of interior angles in a quadrilateral?

a)

360°

b)

180°

c)

270°

d)

540°

e)

90°

57.

Which triangle has all sides equal?

a)

Equilateral triangle

b)

Isosceles triangle

c)

Scalene triangle

d)

Right triangle

e)

Acute triangle

58.

In an isosceles triangle, how many sides are equal? 

a)

2

b)

3

c)

1

d)

0

e)

4

59.

Which formula is used to find the area of a triangle? 

a)

(1/2) × base × height

b)

base × height

c)

side × side

d)

π × r²

e)

length × width

60.

Which triangle has no equal sides?

a)

Scalene triangle

b)

Equilateral triangle

c)

Isosceles triangle

d)

Right triangle

e)

Obtuse triangle 

61.

What is the name of a quadrilateral with two pairs of parallel sides?

a)

Parallelogram

b)

Trapezoid

c)

Kite

d)

Rhombus

e)

Rectangle

62.

Which quadrilateral has four right angles and equal sides?

a)

Square

b)

Rectangle

c)

Rhombus

d)

Trapezoid

e)

Parallelogram

63.

Which shape has only one pair of parallel sides?

a)

Trapezoid

b)

Rectangle

c)

Square

d)

Parallelogram

e)

Rhombus

64.

Which quadrilateral has all sides equal and opposite angles equal? 

a)

Rhombus

b)

Rectangle

c)

Trapezoid

d)

Kite

e)

Square

65.

Which formula finds the perimeter of a rectangle? 

a)

2 × (length + width)

b)

length × width

c)

4 × side

d)

2 × length

e)

length + width

66.

What is the Pythagorean Theorem?

a)

a² + b² = c²

b)

a² − b² = c²

c)

a × b = c²

d)

a + b = c

e)

a/b = c

67.

What is the height in a triangle?

a)

The perpendicular from a vertex to the opposite side

b)

The longest side

c)

The base

d)

The diagonal

e)

The midpoint

68.

Which of the following has two equal angles and two equal sides? 

a)

Isosceles triangle

b)

Scalene triangle

c)

Equilateral triangle

d)

Square

e)

Rhombus

69.

If a triangle has angles of 45°, 45°, and 90°, what type is it?

a)

Isosceles right triangle

b)

Equilateral triangle 

c)

Scalene triangle

d)

Acute triangle

e)

Obtuse triangle

70.

Which of the following is the correct way to state the definition of a function? 

a)

A function is a relation in which each input has exactly one output

b)

A function is a set of ordered pairs where inputs are not repeated

c)

A function is a set of elements where the output equals the input 

d)

A function is a relation that can have multiple outputs for one input

e)

A function is a rule that does not depend on the input 

71.

Which of the following is the correct statement for the Pythagorean Theorem? 

a)

In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides

b)

In any triangle, the sum of the squares of the sides is equal to the square of the hypotenuse

c)

The sum of the squares of the sides of a triangle equals the sum of the squares of the angles

d)

The sum of the squares of the sides equals the square of the triangle

e)

The square of the hypotenuse equals the sum of the angles of the triangle 

72.

Which of the following uses the correct mathematical language for the Law of Sines?

a)

The ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle

b)

The ratio of the sine of an angle to the length of its opposite side is constant 

c)

The sum of the angles of a triangle is always equal to one

d)

The sine of an angle in a triangle is equal to its cosine

e)

The ratio of the angles to the sides is always constant 

73.

Which is the correct mathematical formulation of the triangle inequality theorem? 

a)

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side 

b)

The sum of the angles of any triangle must be greater than 180°

c)

The sum of the lengths of two sides of a triangle must equal the length of the third side 

d)

The sum of the angles of any triangle is equal to 360° 

e)

The length of the longest side of a triangle is always greater than the sum of the other two

74.

Which is the correct way to state the definition of an isosceles triangle? 

a)

An isosceles triangle is a triangle with at least two sides equal 

b)

An isosceles triangle is a triangle with all sides equal

c)

An isosceles triangle has one angle greater than 90°

d)

An isosceles triangle has two angles equal 

e)

An isosceles triangle is a triangle with no equal sides

75.

Which is the correct mathematical language for the definition of a parallelogram? 

a)

A parallelogram is a quadrilateral with opposite sides parallel and equal

b)

A parallelogram is a quadrilateral with equal sides and angles 

c)

A parallelogram is a quadrilateral with two pairs of parallel sides

d)

A parallelogram is a figure with only one pair of parallel sides

e)

A parallelogram is a quadrilateral with opposite angles equal 

76.

Which is the correct formulation for the Law of Cosines? 

a)

In any triangle, the square of one side equals the sum of the squares of the other two sides minus twice their product times the cosine of the included angle 

b)

In any triangle, the sum of the squares of all sides equals the square of the hypotenuse 

c)

The square of one side of a triangle is equal to the sum of the squares of the angles

d)

In any triangle, the angles are equal to the square of the sides 

e)

The square of the longest side of a triangle is equal to the sum of the other two sides 

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