ECT MATHEMATICS

Question 1

What is the solution to the equation 2x + 5 = 17?

x = 8
x = 7
x = 12
x = 6

Answer 1

x = 6

Question 2

If 3x - 8 = 10, what is the value of x?

x = 6.5
x = 6
x = 4
x = 3

Answer 2

x = 6

Question 3

What is the volume of a triangular prism with a triangular base of area 14 square units and a height of 6 units?

72 cubic units
48 cubic units
84 cubic units
42 cubic units

Answer 3

84 cubic units

Question 4

If an angle measures 220 degrees, what type of angle is it?

Reflex
Acute
Obtuse
Right

Answer 4

Reflex

Question 5

Simplify the expression i to the power of 105.

i
-i
-1
1

Answer 5

i

Question 6

If a location follows UTC+3 and it is 12:30 UTC, what time is it there?

09:30
14:30
10:30
15:30

Answer 6

15:30

Question 7

What is the name of a shape with five sides?

Pentagon
Hexagon
Octagon
Heptagon

Answer 7

Pentagon

Question 8

What shape has opposite sides parallel and equal in length?

Parallelogram
Rhombus
Trapezoid
Rectangle

Answer 8

Parallelogram

Question 9

What are the fixed points inside an ellipse, such that the sum of the distances from any point on the ellipse to these points is constant?

Axis
Foci
Center
Vertices

Answer 9

Foci

Question 10

A fruit salad requires a mix of 3 different fruits from a selection of 4. How many combinations of fruits can be used?

8
10
4
12

Answer 10

4

Question 11

What is an angle that measures 360 degrees called?

Straight angle
Reflex angle
Perigon
Right angle

Answer 11

Perigon

Question 12

What property states that the order of elements in an operation doesn’t affect the result?

The Distributive Property
The Commutative Property
The Identity Property
The Associative Property

Answer 12

The Commutative Property

Question 13

Solve for y if 2y + 5 = 19.

x = 14
x = 10
x = 7
x = 21

Answer 13

x = 7

Question 14

What is a three-sided polygon called?

Triangle
Pentagon
Hexagon
Quadrilateral

Answer 14

Triangle

Question 15

Simplify the expression 3(x + 4) - 2(2x - 1).

x + 11
5x - 11
-x + 14
7x + 5

Answer 15

-x + 14

Question 16

Which shape is characterized by being perfectly round in three dimensions?

Cylinder
Cone
Sphere
Prism

Answer 16

Sphere

Question 17

If 18 workers can paint a house in 12 days, how many days will it take for 12 workers to paint the same house?

16 days
24 days
20 days
18 days

Answer 17

18 days

Question 18

The base of a triangle is 8 cm, and its height is 6 cm. Find the area of the triangle.

24 sq. cm
16 sq. cm
32 sq. cm
12 sq. cm

Answer 18

24 sq. cm

Question 19

A book originally priced at $60 is sold at a 40% discount. How much is discounted from the original price?

$24
$18
$20
$12

Answer 19

$24

Question 20

Which property states that any number added to zero remains unchanged?

The Commutative Property
The Associative Property
The Distributive Property
The Identity Property

Answer 20

The Identity Property

Question 21

If five years ago, Sarah was three times the age of David, and the sum of their ages is 50 now, how old is Sarah?

Answer 21

35 years old

Question 22

What is the sum of the interior angles of a nonagon?

1440 degrees
1620 degrees
1260 degrees
1800 degrees

Answer 22

1260 degrees

Question 23

An angle that is formed by two rays in opposite directions and measures 0 degrees is called a:

Perigon
Zero angle
Reflex angle
Straight angle

Answer 23

Zero angle

Question 24

In how many ways can a committee of 3 people be chosen from a group of 5 people?

15
20
10
5

Answer 24

10

Question 25

What is a polygon with equal sides and equal angles called? Concave polygon Irregular polygon Regular polygon Convex polygon

Answer 25

Regular polygon

Question 26

A box contains 6 chocolates, 4 of which are dark chocolate. If two chocolates are chosen randomly, what is the probability of selecting two dark chocolates consecutively without replacement? 1/6 1/12 2/5 1/8

Answer 26

2/5

Question 27

What theorem is used to determine the length of the diagonal of a rectangular solid with sides of lengths a, b, and c? Heron's formula Pythagorean theorem Law of Sines Euler's formula

Answer 27

Pythagorean theorem

Question 28

What type of triangle has all sides of equal length? Scalene triangle Equilateral triangle Right-angled triangle Isosceles triangle

Answer 28

Equilateral triangle

Question 29

Which shape has four equal sides and opposite angles equal but not 90 degrees? Parallelogram Rhombus Rectangle Square

Answer 29

Rhombus

Question 30

Solve for x in the equation x^2 + 5x + 6 = 0. x = 1 or x = 6 x = 2 or x = 3 x = -2 or x = -3 x = -1 or x = -6

Answer 30

x = -2 or x = -3

Question 31

Which type of angle measures exactly 90 degrees? Obtuse angle Straight angle Right angle Acute angle

Answer 31

Right angle

Question 32

Which theorem connects the concepts of differentiation and integration? The Limit Theorem The Fundamental Theorem of Calculus The Intermediate Value Theorem The Mean Value Theorem

Answer 32

The Fundamental Theorem of Calculus

Question 33

What is a solid with two parallel and congruent bases connected by rectangular faces? Prism Cone Pyramid Cylinder

Answer 33

Prism