Algebra, Geometry, and Statistics Review

Flashcards reviewing concepts from lecture notes on expanding algebraic expressions, including brackets, highest common factors, factorising, rounding, measuring rise and run, ratios, equations, and congruence.

Expanding a Pair of Brackets

To expand a pair of brackets, multiply the first term in the first bracket by every term in the second bracket, then multiply the second term in the first bracket by every term in the second bracket; (a + b)(c + d) = ac + ad + bc + bd.

Perfect Squares

The formulas for the perfect squares shortcut expansions are: (a + b)(a + b) = a2 + 2ab + b2 and (a − b)(a − b) = a2 − 2ab + b2.

Difference of Two Squares

The formula for the difference of two squares shortcut expansion is: (a + b)(a − b) = a2 − b2.

Expanding Brackets

To expand brackets, multiply each term in the brackets by the coefficient in front of the brackets.

Highest Common Factor (HCF)

The highest common factor (HCF) of two terms is the largest factor that divides into both terms without a remainder.

Finding the HCF

List the factors of the coefficients for each term, select the highest number present in both lists, state the common pronumeral, and combine into a term.

Factorising by Finding the HCF

To factorise an algebraic expression by finding the highest common factor, find the HCF of both terms, rewrite each term, and take the HCF out to the front of a set of brackets.

Congruent Figures

Congruent figures are identical figures that have the same shape and size; they can be superimposed exactly using reflection, rotation, or translation.

Side-Side-Side (SSS) Congruence

If all of the corresponding sides of two triangles are equal, the triangles are congruent

Side-Angle-Side (SAS) Congruence

If two triangles have two corresponding sides that are equal, and the angles between those corresponding sides are equal, the triangles are congruent.

Angle-Side-Angle (ASA) Congruence

If two triangles have two corresponding angles that are equal, and a side that is also equal, the triangles are congruent.

Right Angle-Hypotenuse-Side (RHS) Congruence

If the hypotenuse and one other side of two right-angled triangles are equal, the triangles are congruent.

Proof

An argument that shows why a statement is true.

Theorem

A statement that can shown to be true.

Supplementary Angles

Angles that add up to 180°.

Complementary Angles

Angles that add up to 90°.

Vertically Opposite Angles Theorem

Vertically opposite angles are equal.

Parallel Lines Properties

If two lines are parallel and cut by a transversal, co-interior angles are supplementary, corresponding angles are equal, and alternate angles are equal.

Interior Angles of a Triangle Theorem

The sum of the interior angles of a triangle is 180°.

Equilateral Triangle Angles

Each interior angle of an equilateral triangle is 60°.

Exterior Angle of a Triangle Theorem

The exterior angle of a triangle is equal to the sum of the opposite interior angles.

Congruent Triangles

Triangles that have the same size and the same shape—that is, they are identical in all respects.

Isosceles Triangle Theorem

The angles at the base of an isosceles triangle are equal.

Simplifying Fractions

Divide both numerator and denominator by the highest common factor (HCF).

Simplifying Ratios

To simplify a ratio, divide both numbers by their highest common factor (HCF). Ratios must contain only whole numbers.

Rounding to Decimal Places

To round a decimal to a given number of decimal places, count out the required number of decimal places and consider the next digit.

Converting Minutes to Seconds

Multiply by 60 in order to convert minutes to seconds.

Equivalent Rates

An equivalent rate is obtained when both quantities are multiplied or divided by the same number.

Rate

A rate compares two quantities.

Finding the Lowest Common Denominator

To obtain the lowest common denominator (LCD) of two or more common fractions, find the lowest common multiple (LCM) of the denominators of these fractions.

Run

The horizontal distance between two points on a line.

Rise

The vertical distance between two points on a line

The Mean

The average of all values in a set of data.

Median

The middle score of a set of numbers.

Mode

The score occurs most frequently.