Grade 8 Math Review Flashcards

Flashcards generated from Grade 8 math textbook notes to assist in exam preparation.

What is a rational number?

A number that can be written in the form of a/b where a and b are integers and b ≠ 0.

How are positive and negative rational numbers represented on a number line?

Positive rational numbers are represented on the right side of zero, and negative rational numbers are represented on the left side of zero.

What is the relationship between a rational number and its opposite?

Two rational numbers are said to be opposite if they have the same distance from 0 but are on different sides of 0.

Describe the relationship among the sets of natural numbers (ℕ), whole numbers (W), integers (ℤ), and rational numbers (ℚ).

Each set is contained within the next larger set: ℕ ⊂ W ⊂ ℤ ⊂ ℚ.

Define the absolute value of a rational number 'x'.

|x| = x, if x ≥ 0; |x| = -x, if x < 0. The absolute value describes the distance from zero on a number line without considering direction.

What is the rule for adding rational numbers with the same denominators?

To add two or more rational numbers with the same denominators, add all the numerators and write the common denominator. (a/b) + (c/b) = (a+c)/b

Describe the steps for adding rational numbers with different denominators.

I. Make all the denominators positive. II. Find the LCM of the denominators. III. Find equivalent rational numbers with the common denominator. IV. Add the numerators and take the common denominator.

What is the rule for finding the sum of two rational numbers where both are negative?

i) Sign: Negative (−) ii) Take the sum of the absolute values of the addends. iii) Put the sign in front of the sum.

What is the process of subtraction of rational numbers?

Subtracting c/d from a/b means adding the negative of c/d to a/b. Thus a/b − c/d = a/b + (−c/d)

What is the rule for multiplying two rational numbers?

Multiply the numerator with the numerator and the denominator with the denominator. Then reduce the final answer to its lowest term.

What are the rules for determining the sign of the product of two rational numbers?

Positive x Positive = Positive, Negative x Negative = Positive, Positive x Negative = Negative, Negative x Positive = Negative

What is the rule for dividing rational numbers?

Multiply by the reciprocal. a/b ÷ c/d = a/b × d/c = ad/bc (where c ≠ 0).

What is the simple interest formula?

Interest (I) = Principal (P) x Rate (R) x Time (T), I = PRT

What is squaring of a number?

The process of multiplying a number by itself.

What is a perfect square?

A rational number x is called a perfect square if and only if x = m^2 for some m ∈ ℚ.

What is the relationship between squaring and square root?

Extracting square root is the inverse of the operation squaring.

Define the cube root of a given number.

The cube root of a given number is one of the three identical factors whose product is the given number.

What are common uses for squares, square roots, cubes, and cube roots?

Used often in carpentry, engineering, designing buildings, and technology. Cube root is used to solve for the dimensions of a three-dimensional object of a certain volume.

What are the quadrants of a Cartesian coordinate plane?

Quadrant I: (+, +), Quadrant II: (-, +), Quadrant III: (-, -), Quadrant IV: (+, -).

What is the equation of a vertical line through the point P(a, b)?

x = a. This line is parallel to the y-axis.

What is the equation of a horizontal line through the point P(a, b)?

y = b. This line is parallel to the x-axis.

What is the form of a linear equation, with a graph passes through the origin?

y = mx (m ∈ ℚ, m ≠ 0)

If m > 0 for the line y = mx, which quadrants does the graph pass through?

Quadrants I and III. If m < 0?, Quadrants II and IV.

Give the rules for Equivalent Transformations for Inequalities

For any rational numbers a, b, and c
I. If a < b, then a + c < b + c II. If a < b, then a − c < b − c III. If a < b and c > 0, then ac < bc IV If a < b and c > 0, then a/c < b/c V If a < b and c < 0, then ac > bc
VI If a < b and c < 0, then a/c > b/c

Define 'similar' in geometric figures.

Having the same shape, but not necessarily the same size.

What are the two conditions for polygons to be similar?

i) All pairs of corresponding angles are congruent, ii) The ratio of the lengths of all pairs of corresponding sides are equal.

What is a 'scale factor'?

The ratio of two corresponding sides of similar polygons, also known as the constant of proportionality (k).

Angle-Angle Similarity (AA)

If two angles of one triangle are congruent to the corresponding two angles of another triangle, then the two triangles are similar

Side-Angle-Side Similarity

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are proportional, then the triangles are similar.

Side-Side-Side Similarity

If the three sides of one triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

If two triangles are similar, state their perimeter relationship?

If the ratios of the corresponding sides of two similar triangles is k, then the ratio of their perimeters is given by: p1/p2 = s1/s2 = k

If two triangles are similar, state their areas relationship?

If the ratios of the corresponding sides of two similar triangles is k, then the ratio of their areas is given by: A1/A2 = (s1/s2)^2 = k^2.

Give the Angle-Sum Theorem

The sum of the degree measures of the interior angles of a triangle is equal to 180°

What is the relationship between an exterior angle and its two remote interior angles?

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

What is Euclid’s Theorem?

In a right-angled triangle with an altitude to the hypotenuse, the square of the length of each leg of a triangle is equal to the product of the hypotenuse and the length of the adjacent segment into which the altitude divides the hypotenuse.

What is Pythagoras' Theorem?

In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. If the lengths of shorter sides are a & b, and the length of hypotenuse is c, then a^2 + b^2 = c^2

What is the positional relationship between a line and a circle?

The line may intersect the circle at no points, one point (tangent), or two points (secant).

Define the intercepted arc

Arc ACB is said to be intercepted by ∠AOB and ∠AOB is said to be subtended by arc ACB.

What is the measure of minor arc, intercepted by a central angle ∠AOB?

(m∠AOB) = m(ACB)

A measure of a(n) _ angle equals one-half of the measure of its intercepted arc?

Inscribed

What is the measure of one chord intersecting two others?

m(∠APD) = 1/2 ( m (AD) + m (BC))

Prisms and Cylinder Surfaces

The sum of the areas of lateral faces for an object where all is enclosed

Solid Prism

2 parallel and congruent polygons where others connect them

Cylinder is

Two parallel and congruent non-polygons (circular) solid.

If the lateral edges of the prism are perpendicular to the bases is..

A right prism, such as Right Triangle

Volume Definition in Solid space

The measure of space occupied by it

Equal heights and equal volume

base heights are all equal in measure

Equally Likely

All events have the same occurrence in sampling