Math

Question 1

Area of a rectangle

Answer 1

Area = length × width

Question 2

True or False: The formula for the slope of a line is (y2 - y1) / (x2 - x1).

Answer 2

True

Question 3

Fill in the blank: The quadratic formula is used to find the roots of the equation ax^2+ bx + c = 0, and is given by __________.

Answer 3

x = (-b ± √(b² - 4ac)) / (2a)

Question 4

What is the formula for the perimeter of a triangle?

Answer 4

Perimeter = side1 + side2 + side3

Question 5

What is the standard form of a linear equation?

Answer 5

Ax + By = C

Question 6

Formula for the volume of a cylinder…

Answer 6

πr²h

Question 7

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

Answer 7

True

Question 8

Fill in the blank: The formula for the sum of the first n natural numbers is __________.

Answer 8

n(n + 1) / 2

Question 9

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

Answer 9

Distance = √((x2 - x1)² + (y2 - y1)²)

Question 10

Multiple choice: Which of the following is the formula for the area of a circle? A) 2πr B) πr² C) πd

Answer 10

B) πr²

Question 11

What is the formula for the difference of squares?

Answer 11

a² - b² = (a - b)(a + b)

Question 12

True or False: The Pythagorean theorem states that a² + b² = c² for a right triangle.

Answer 12

True

Question 13

Fill in the blank: The formula for the sum of a geometric series is __________.

Answer 13

S_n = a(1 - r^n) / (1 - r) for r ≠ 1

Question 14

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

Answer 14

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Question 15

Multiple choice: Which formula represents the exponential growth model? A) y = mx + b B) y = a(1 + r)^t C) y = a(1 - r)^t

Answer 15

B) y = a(1 + r)^t

Question 16

What is the formula for the area of a triangle?

Answer 16

Area = 1/2 × base × height

Question 17

True or False: The formula for the circumference of a circle is C = 2πr.

Answer 17

True

Question 18

Fill in the blank: In a linear equation, the slope-intercept form is given by __________.

Answer 18

y = mx + b

Question 19

What is the formula for converting Fahrenheit to Celsius?

Answer 19

C = (F - 32) × 5/9

Question 20

Multiple choice: What is the formula for compound interest? A) A = P(1 + r/n)^(nt) B) A = P(1 + rt) C) A = P + Prt

Answer 20

A) A = P(1 + r/n)^(nt)

Question 21

What is the formula for the roots of a cubic equation?

Answer 21

There is no simple formula; numerical methods are often used.

Question 22

The area of parallelogram…

Answer 22

parallelogram = base × height

Question 23

Fill in the blank: The formula for the binomial theorem is __________.

Answer 23

(a + b)ⁿ = Σ (n choose k) a^(n-k) b^k

Question 24

What is the formula for the factorial of a number n?

Answer 24

n! = n × (n - 1) × (n - 2) × … × 1

Question 25

Multiple choice: Which of the following is the formula for the area of a trapezoid? A) (b1 + b2)h/2 B) b1h C) bh

Answer 25

A) (b1 + b2)h/2

Question 26

What is Ohm's Law?

Answer 26

The relationship between voltage, current, and resistance, stated as V = IR.

Question 27

True or False: Voltage is the measure of electrical current.

Answer 27

False

Question 28

Fill in the blank: The unit of electrical resistance is _____.

Answer 28

Ohm

Question 29

What is the formula for electrical power?

Answer 29

P = VI, where P is power, V is voltage, and I is current.

Question 30

Multiple Choice: What is the unit of electric current?

Answer 30

Ampere

Question 31

What is the principle of conservation of charge?

Answer 31

The total electric charge in an isolated system remains constant.

Question 32

True or False: A series circuit has the same current flowing through all components.

Answer 32

True

Question 33

What is a parallel circuit?

Answer 33

A circuit where components are connected across common points, providing multiple paths for current.

Question 34

Fill in the blank: The unit of capacitance is _____.

Answer 34

Farad

Question 35

Multiple Choice: What does a capacitor do?

Answer 35

Stores electrical energy

Question 36

What is the formula for capacitance?

Answer 36

C = Q/V, where C is capacitance, Q is charge, and V is voltage.

Question 37

True or False: Inductance is the property of a conductor to oppose changes in current.

Answer 37

True

Question 38

What is the unit of inductance?

Answer 38

Henry

Question 39

Fill in the blank: The total resistance in a series circuit is the ____ of individual resistances.

Answer 39

sum

Question 40

Multiple Choice: What is the effect of increasing resistance in a circuit?

Answer 40

Decreases current

Question 41

What is Kirchhoff's Voltage Law?

Answer 41

The sum of the electrical potential differences (voltage) around any closed network is zero.

Question 42

True or False: In a parallel circuit, the voltage across each component is the same.

Answer 42

True

Question 43

What is the formula for the total resistance in a parallel circuit?

Answer 43

1/R_total = 1/R1 + 1/R2 + ... + 1/Rn

Question 44

Fill in the blank: The measure of how much energy is used by a device per unit of time is called _____.

Answer 44

Power

Question 45

Multiple Choice: Which of the following is not a type of electrical circuit?

Answer 45

None of the above (series, parallel, and series-parallel are types)

Question 46

What is the formula for calculating energy consumption?

Answer 46

Energy (in kWh) = Power (in kW) × Time (in hours)

Question 47

True or False: The power factor is the ratio of real power to apparent power.

Answer 47

True

Question 48

What is the unit of frequency?

Answer 48

Hertz (Hz)

Question 49

Fill in the blank: The frequency of an AC signal is measured in _____.

Answer 49

Hertz

Question 50

Multiple Choice: What does an oscilloscope measure?

Answer 50

Voltage over time

Question 51

What is the formula for calculating the impedance in an AC circuit?

Answer 51

Z = √(R² + (XL - XC)²), where XL is inductive reactance and XC is capacitive reactance.