8th Grade Math Packet Key Concepts

Question and answer flashcards covering integers, rational numbers, operations, expressions, equations, inequalities, proportions, percents, geometry, measurement, and probability from the 8th Grade Math Packet.

What are integers?

The set of positive whole numbers, their opposites, and zero.

Which number is farther left on the number line, -2 or 0?

-2 is farther left, so it is less than 0.

State the rule for adding two integers with the same sign.

Add their absolute values; keep the common sign.

How do you add integers with different signs?

Subtract the lesser absolute value from the greater and keep the sign of the integer with the greater absolute value.

Describe the rule for subtracting integers.

Add the opposite of the number being subtracted, then follow addition rules.

What sign will the product of two integers with different signs have?

Negative.

When dividing integers, when is the quotient positive?

When the two integers have the same sign.

Explain how to multiply two decimals.

Multiply as with whole numbers, then place the decimal point in the product so the number of decimal places equals the sum in the factors.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator.

Convert 0.75 to a fraction in simplest form.

3/4

Evaluate 5y − 8 when y = 7.

27

Write an algebraic expression for “4 less than x.”

x − 4

Simplify: 6m + 10 − 2m + 4.

4m + 14

What inverse operation solves n − 6 = −36?

Add 6 to each side.

Solve the one-step equation −2x = 8.

x = −4

What does the inequality symbol ‘<’ mean?

Less than.

On a number line graph, do you use an open or closed circle for x ≥ 3?

Closed circle because the boundary value is included.

State the rule when multiplying or dividing an inequality by a negative number.

Reverse the direction of the inequality sign.

Define a unit rate.

A rate with a denominator of 1.

What is the unit price of 18 oz of juice for $1.26?

$0.07 per ounce.

Give the proportion cross-product rule.

If a/b = c/d, then ad = bc.

Shawn fills 8 bags in 2 hours. How many in 6 hours?

24 bags.

What is the constant of proportionality in y = 3x?

3

State the two conditions for similar polygons.

Corresponding angles are congruent, and corresponding side lengths are proportional.

Write 45% as a fraction in simplest form.

9/20

Find 10% of 40.

4

Solve 60 is 5% of n.

n = 1,200

Percent of change formula.

(Amount of change ÷ Original amount) × 100%.

Classify a 40° angle.

Acute angle.

What is the area formula for a parallelogram?

A = base × height (bh).

Formula for the area of a triangle.

A = ½bh

Write the trapezoid area formula.

A = ½h(b₁ + b₂)

Circumference formula using diameter.

C = πd

Give the area formula for a circle.

A = πr²

Define surface area of a prism.

The sum of the areas of all its faces.

Volume formula for a right prism.

V = Bh, where B is the area of the base and h is the height.

How do you find the mean of data?

Divide the sum of the data values by the number of values.

Theoretical probability formula.

P(event) = favorable outcomes ÷ total possible outcomes.

Complementary probability relationship.

P(event) + P(not event) = 1

Define experimental probability.

Probability based on the results of repeated trials: (number of times event occurs) ÷ (total trials).

How many outcomes are in the sample space of flipping a coin and rolling a six-sided die?

12 outcomes (2 × 6).

Independent events definition.

Events where the outcome of one does not affect the outcome of the other.

Dependent events definition.

Events where the outcome of one affects the outcome of the other.

Probability of rolling an even number on a standard die.

3/6 = 1/2 = 0.5 = 50%.

Opposite of −7.

7

Order the numbers −4, 5, −2, 0, 1 from least to greatest.

−4, −2, 0, 1, 5

Simplify the expression 6n + 2(4n + 5).

14n + 10

State the distributive property.

a(b + c) = ab + ac

Solve 4(x − 7) = 12.

x = 10

Graphing x ≤ −3: open or closed circle?

Closed circle at −3, arrow left.

Write the inequality for “a number w plus 1 is at most 4.”

w + 1 ≤ 4

Find the product: (−2.07)(−4.9).

10.143

Divide 38.25 by 1.5.

25.5

Convert 3/8 to a decimal.

0.375

Convert 1.5 to a fraction in simplest form.

3/2

Solve the proportion 10/n = 15/25.

n = 16.67 (or 10*(25/15) = 16⅔).

Give the percent equivalent of 0.16.

16%

If the price rises from 12 to 18, what is the percent increase?

50% increase.

Complementary angles sum to what measure?

90°

Supplementary angles sum to what measure?

180°

Surface area of a cylinder formula.

SA = 2πr² + 2πrh

Write 25% as a decimal.

0.25

Unit price comparison: Which is cheaper, 2 pairs of socks for $3.50 or 6 pairs for $9.00?

2 pairs for $3.50 ($1.75 each) is cheaper than 6 pairs for $9.00 ($1.50 each)? Actually $1.50 is cheaper, so 6 pairs for $9.00.

Identify like terms in 3x + 5 + 7x − 2.

3x and 7x are like terms; 5 and −2 are like terms.

How do you find the missing side in similar triangles?

Set up a proportion of corresponding sides and solve for the unknown.

State the counting principle.

If one event has m outcomes and another has n outcomes, there are m × n total outcomes for both events.

Mean of 5, 7, 8, 10.

(5 + 7 + 8 + 10)/4 = 7.5

Experimental probability of drawing a blue chip 7 times in 20 draws.

7/20 = 0.35 = 35%.

Probability of selecting a vowel from the letters in "HAPPINESS."

3 vowels out of 9 letters = 3/9 = 1/3 ≈ 33.3%.

When solving −4y ≥ 16, why is the inequality reversed?

Because you divide by a negative number.

Write a verbal model for “p + 2p.”

A number p plus twice the same number.

What are vertical angles?

Opposite angles formed by two intersecting lines; they are congruent.

Formula for percent of decrease from 20 to 12.

((20 − 12)/20) × 100% = 40% decrease.