Mathematics Grade 9 - Set Theory, Computation, Measurement, Algebra, Relations, Functions and Graphs, Consumer Arithmetic, Geometry, Trigonometry

Flashcards for Mathematics Grade 9, covering topics such as set theory, computation, measurement, algebra, relations, functions and graphs, consumer arithmetic, geometry, and trigonometry.

What do curly brackets or braces {} mean in set notation?

The set of' or 'the set'.

What type of letters are used to represent a set?

Capital letters

In set notation, what does the symbol ∈ mean?

Is an element of

In set notation, what does the symbol ∉ mean?

Is not an element of

What is set builder notation?

A way to describe a set using an algebraic expression that states a condition only satisfied by the elements of the set.

What is a Venn diagram?

A diagram that shows all possible logical relations between a finite collection of different sets.

What is the complement of a set A, denoted as A'?

The set of all elements in the universal set U that are not in set A.

If every member of set A is also a member of set B, how is this relationship written?

A ⊆ B (A is a subset of B)

If A is not a subset of B, how is this written?

A ⊈ B

What is the symbol for the empty set?

∅ or {}

What is the formula used to determine the number of subsets in a set?

S = 2^n, where n is the number of members in the set.

What is the intersection of two sets A and B?

The set of all elements that are common in both set A and set B. A Ո B = {𝑥: 𝑥 ∈ A and 𝑥 ∈ B }

What does A Ո B represent?

The intersection of A and B.

What is the union of two sets A and B?

The set of all elements that are in either A or B. A U B = {𝑥: 𝑥 ∈ A or 𝑥 ∈ B or both}

What does A U B represent?

The union of A and B

What is the formula for the number of elements in the union of two sets?

n(A ∪ B) = n(A) + n(B) – n(A ∩ B)

What is the general formula for three sets?

n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A ∩ B) - n(A ∩ C) - n(B ∩ C) + n(A ∩ B ∩ C)

What does 'rounding off' numbers mean?

Reducing the digits in a number while trying to keep its value almost the same.

When rounding, what happens if the digit to be rounded is less than 5?

The value of the previous digit remains the same.

When rounding, what happens if the digit to be rounded is greater than or equal to 5?

The value of the previous digit is increased by one.

What are significant figures?

The digits of a number that have meaning or contribute to the value of the number.

Which digits are always significant?

All non-zero digits.

Which digits are not significant?

Trailing zeros to the left of the decimal point and leading zeros to the right of the decimal point.

How do you square a number?

Multiply it by itself.

What is a perfect square?

A number that can be written as the square of an integer.

What is a square root?

A factor of a given number that, when multiplied by itself, gives the original number.

How is a square root written?

With a radical symbol √

What is the base of an exponential number?

The number being multiplied to a power or index

What is an index in an exponential number?

Also known as either: Power or Exponent

What rule applies to multiplying quantities with the same base?

Add their Indices

What rule applies to division of indices where the bases are the same?

Subtract the power.

What happens when we raise the power of a quantity to a power?

We multiply the indices

What happens when anything is raised to the 0 power?

The result is one.

What has a fractional (or rational index)

The denominator is the root and the numerator is the power to which the quantity is to be raised.

What is place value?

The value represented by a digit in a number based on its position in the number.

What is the result of using distributive law on 𝑎𝑥 + 𝑎𝑦?

𝑎(𝑥 + 𝑦)

What is used to factorize an expression when there are common factors in pairs of terms?

Grouping

What is the formula when using Factorization of Quadratic expression that can be expressed as difference of squares?

(𝑎 + 𝑏)(𝑎 − 𝑏)

What is the general form of a quadratic Expression?

𝑎𝑥² + 𝑏𝑥 + 𝑐

What is the general form of a quadratic Equation?

𝑎𝑥² + 𝑏𝑥 + 𝑐 = 0

What is used to graphically identify a function?

A graph – if a vertical line passes through two or more points of the graph, then the relation is not a function.

What is a linear function graphically?

A straight line

Given 𝒇: 𝒙 → 𝟑𝒙. What does this state?

𝒇 is a function such that x is mapped onto 3𝑥

What two names are used to describe vertical and distance to describe a line?

Slope or Gradient

What is the gradient of a line?

The ratio of the increase in the vertical rise to the increase horizontal run.

What is the formula for gradient?

𝑚 = rise / run

What is the general form of the equation of a straight line?

𝒚 = 𝒎𝒙 + 𝒄

What is the 'c' used for the equation of a straight line?

y-intercept (where the line cuts the y-axis)

What is the formula for profit?

Selling Price (SP) - Cost Price (CP)

What is the formula for Loses?

Cost Price (CP) - Selling Price (SP)

What do you call the part of earning not taxed?

Tax-free income

What do you call the spouse, young children, or even old not working parents

Dependents

What is hire purchase?

A type of credit system where you are allowed to purchase an item buy paying some money down (down payment or deposit) then paying the remainder in equal monthly instalments.

What items are normally bought under a special hire purchase?

Cars, machinery, properties, etc.

What is a Mortgage?

A special hire purchase agreement between a bank and home owner.

Can the bank lend a 100% of deposit on a Mortgage?

The purchaser pays a deposit on the item and the bank lends him/her the remainder (loan/mortgage) to pay for the item.

What does it mean, that the item is legally the property of the bank?

The item is legally the property of the bank until the mortgage is repaid.

When does a purchaser own the property?

The item is legally the property of the bank until the mortgage is repaid

What is a Principal

The amount of money borrowed

What is Rate, R -

The percentage rate charged by the bank

What is Time, T -

The period for the loan to be repaid

What is called a simple interest in a bank?

The interest paid to a bank is called simple interest, providing the principal (amount borrowed) in calculating the interest remains the same during the period of the loan.

What are the formulas for Simple Interest?

I=PRT

What is principal?

When money is invested, it is called the principal

What happens in the coming years?

Each year the principal achieves an interest. If the interest payable is reinvested at the end of each year in the same fixed deposit, then the principal at the beginning of each New Year is greater than the principal of the previous year.

What are the depreciation assets that value tends to decrease?

Many assets such as cars, mini bus, speed boat engine, furniture, etc. tend to decrease in value over time as a result of wear and tear due to constant use.

What is called a Pythagoreas Theorem is used for?

To find for the missing side of a right-angled triangle.

What is a Hypotenuse?

Is the side opposite the right angle

What is it called when triangles are equal-angular triangles?

Similar triangles

If triangles are the same and similar, what name is given?

Congruent Triangles

What does the formula SAS stand for? (Congruent)

Side Angle side

What does the formula ASA stand for? (Congruent)

Angle Side Angle

What does the formula SSS stand for? (Congruent)

Side Side Side

What dies it mean (Angle at the segment )?

Lies on the arc made by the segment

What is a segment?

Area made around the arc to diameter

What is cyclic quadrilateral?

A quadrilateral whose vertices all lie on the circumference of a circle.

What's the name for where exterior angle of cyclic quadrilateral is equal to interior of opposite angle?

Theorem 5

what does that a tangent line to do with circle?

A tangent to a circle is a straight line which touches the circle at only one point

Where tangent to a circle is perpendicular to?

Radius

What is SOH in trigonometry?

Sine = Opposite / Hypotenuse

What is CAH in trigonometry?

Cosine = Adjacent / Hypotenuse

What is TOA in trigonometry?

Tangent = Opposite / Adjacent

What are the two types of Triangles is used for Pythagoras Theorem?

right-angled

What are the properties of similar triangles?

All corresponding angles are congruent and all corresponding sides are proportional

What are the properties of a Congruent triangle

They are exactly the same and having all measurements as Side Angel Side, SAS etc

What is known as Circle, where the opposite sides adding with value 180?

Cyclic quadrilateral

In a right triangle, the ratio of the length of the side opposite an angle to the length of the hypotenuse is called the ____.

Sine

In a right triangle, the ratio of the length of the side adjacent to an angle to the length of the hypotenuse is called the ____.

Cosine

In a right triangle, the ratio of the length of the side opposite an angle to the length of the side adjacent is called the ____.

Tangent

What are the Trigonometric ratios?

Sine, Cosine and Tangent.

Define 'perimeter' in the context of measurement.

The distance around a plane shape.

What is the formula for the perimeter of a triangle?

Perimeter = a + b + c (sum of all sides)

What is the formula for the perimeter of a square?

Perimeter = 4 × a (a = length of side)

How is the distance around a circle defined?

Circumference

What is the formula for measuring the circumference?

C = πd or C = 2πr (where d is diameter and r is radius)

What is the formula for the area of a square and rectangle?

Length x Breadth

How is an area calculated in a square or a rectangle?

Multiply the Base and Height size.

What is the formula for Area of square and Rectangle

Length x Breadth

What is the formula for calculating the area of Parallelogram?

Base x Hight

What is the formula for calculating the area of Area of triangle?

1/2 x base x height