Mathematics Flashcards - Ratios, Proportions, Numbers, Probability, Algebra, Geometry, and Trigonometry

Flashcards covering key concepts from ratios, proportions, numbers, probability, algebra, geometry, and trigonometry.

What is direct proportion?

Two quantities change together at a constant ratio; y = kx where k is the constant of proportionality.

What is inverse (indirect) proportion?

As one quantity increases, the other decreases; their product is constant (xy = k), or y = k/x.

How do you read and simplify a ratio like A:B?

Read as A to B and simplify by dividing both terms by their greatest common divisor.

What is the cross-multiplication rule for proportions?

If A:B = C:D, then AD = BC.

What does a map scale of 1:200 mean?

1 unit on the map represents 200 units in real life; real distance = map distance × 200.

What is x% of a number?

Multiply the number by x/100; for example, 25% of 80 is 80 × 0.25 = 20.

How do you calculate percentage change?

Percentage change = (New value − Original value) / Original value × 100%.

How do you find a fraction of a number?

Multiply the number by the fraction (e.g., 1/4 of 20 = 20 × 1/4 = 5).

What is a triangular number?

A number in the form n(n+1)/2; examples: 1, 3, 6, 10, 15.

What is a square number?

A number that is a square of an integer (0, 1, 4, 9, 16, 25, …).

What is an even number?

An integer divisible by 2.

What is an odd number?

An integer that is not divisible by 2.

What is a rational number?

A number that can be expressed as a fraction p/q with integers p and q and q ≠ 0.

What is an irrational number?

A number that cannot be expressed as a simple fraction; decimal representation does not terminate or repeat (e.g., √2, π).

What is a real number?

All rational and irrational numbers; every point on the number line.

What is a natural number?

Positive integers starting from 1: 1, 2, 3, …

What is a whole number?

Natural numbers including 0: 0, 1, 2, 3, …

What is an integer?

All positive and negative whole numbers including 0: …, −2, −1, 0, 1, 2, …

What is the area of a circle formula?

Area = πr²; if given diameter d, use r = d/2 and A = π(d/2)².

What is probability?

The chance of an event happening; value between 0 and 1 (or 0% to 100%).

What is a probability tree diagram used for?

To represent sequential events and their probabilities along branches.

What is the gradient of a line in y = mx + c?

m is the gradient (slope); it shows the rate of change (rise over run).

What is the y-intercept?

The value of y when x = 0; where the line crosses the y-axis.

What is Pythagoras theorem?

In a right-angled triangle, a² + b² = c²; c is the hypotenuse.

What is the volume of a rectangular prism?

Volume = length × width × height (V = l × w × h).

What is the surface area of a rectangular prism?

Surface area = 2(lw + wh + lh).

How do you expand brackets like 3(3x+2)?

Distribute to get 9x + 6.

How do you expand -2(2x+5)?

Distribute to get -4x − 10.

How do you factor x^2 + 7x + 12?

(x + 3)(x + 4).

What are substitution and elimination methods used for?

Both are methods to solve simultaneous linear equations; substitution replaces a variable, elimination adds equations to remove a variable.

What are sine, cosine and tangent definitions?

Sine = opposite/hypotenuse; Cosine = adjacent/hypotenuse; Tangent = opposite/adjacent.

What is an angle of elevation?

The angle between the horizontal and the line of sight upward to an object.

What is an angle of depression?

The angle between the horizontal and the line of sight downward to an object.