maths basic

Question 1

What is the formula for the area of a circle?

Answer 1

The formula for the area of a circle is A = πr².

Question 2

True or False: The sum of the angles in a triangle is 180 degrees.

Answer 2

True.

Question 3

Fill in the blank: The Pythagorean theorem states that in a right triangle, a² + b² = _____

Answer 3

c².

Question 4

What is the value of sin(90 degrees)?

Answer 4

The value of sin(90 degrees) is 1.

Question 5

What is the quadratic formula?

Answer 5

The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a.

Question 6

What is the value of cos(0 degrees)?

Answer 6

The value of cos(0 degrees) is 1.

Question 7

True or False: The circumference of a circle is given by C = 2πr.

Answer 7

True.

Question 8

What is the formula for the volume of a cylinder?

Answer 8

The formula for the volume of a cylinder is V = πr²h.

Question 9

Fill in the blank: The derivative of x² is _____

Answer 9

2x.

Question 10

What is the relationship between the sides of a 30-60-90 triangle?

Answer 10

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2.

Question 11

What is the formula for the sum of an arithmetic series?

Answer 11

The formula is S_n = n/2 (a + l), where n is the number of terms, a is the first term, and l is the last term.

Question 12

True or False: The slope of a line is defined as the change in y over the change in x.

Answer 12

True.

Question 13

What is the standard form of a linear equation?

Answer 13

The standard form of a linear equation is Ax + By = C.

Question 14

Fill in the blank: The integral of x dx is _____

Answer 14

(1/2)x² + C.

Question 15

What is the value of tan(45 degrees)?

Answer 15

The value of tan(45 degrees) is 1.

Question 16

What is the formula for the area of a triangle?

Answer 16

The formula for the area of a triangle is A = 1/2 * base * height.

Question 17

True or False: The median is the middle value in a set of data.

Answer 17

True.

Question 18

What is the formula for the distance between two points (x1, y1) and (x2, y2)?

Answer 18

The formula is d = √((x2 - x1)² + (y2 - y1)²).

Question 19

What is the value of e (Euler’s number) approximately?

Answer 19

The value of e is approximately 2.718.

Question 20

Fill in the blank: The factorial of n (n!) is the product of all _____ numbers from 1 to n.

Answer 20

positive.

Question 21

What is the formula for the area of a trapezoid?

Answer 21

The formula for the area of a trapezoid is A = 1/2 * (b1 + b2) * h.

Question 22

True or False: A function is a relation where each input has exactly one output.

Answer 22

True.

Question 23

What is the formula for the surface area of a sphere?

Answer 23

The formula for the surface area of a sphere is A = 4πr².

Question 24

What is the value of log10(100)?

Answer 24

The value of log10(100) is 2.

Question 25

Fill in the blank: The limit of a function as x approaches a value is _____ if the function approaches a specific value.

Answer 25

defined.

Question 26

What is the formula for the binomial theorem?

Answer 26

The binomial theorem is (a + b)ⁿ = Σ (n choose k) * a^(n-k) * b^k.

Question 27

What is the value of the derivative of sin(x)?

Answer 27

The derivative of sin(x) is cos(x).

Question 28

True or False: The range of the function y = x² is all real numbers.

Answer 28

False.

Question 29

What is the formula for the perimeter of a rectangle?

Answer 29

The formula for the perimeter of a rectangle is P = 2(l + w), where l is length and w is width.

Question 30

Fill in the blank: The cosine rule states that c² = a² + b² - 2ab cos(C) where C is the angle opposite side c. True or False?

Answer 30

True.

Question 31

What is the value of the integral from 0 to 1 of x dx?

Answer 31

The value is 1/2.