1st quarter review

Test is Friday!!!

Number Patterns

• arithmetic patterns:– have a common difference between all terms

• geometric patterns:– common ratio between all terms

• think of it as:– arithmetic: we add or subtract to get the next term– geometric: we multiply or divide to get the next term

Example

• Give the next 5 terms in the patterns:

• 2, 4, 6, 8,…

• 2, 6, 18,…

Another sequence…

• What is the pattern?

• 1, 2, 9, 16, 25, 36, …

Primes & Composites

• prime number:– has only two different factors, one and the

number itself

• composite number:– has more than two factors

• the number one (1) is neither prime nor composite!

Greatest Common Factor

• using two or more numbers

• find the prime factorization of both numbers

• find what they have in common, and that is the GCF

• example: 190 360

Least Common Multiple

• find the GCF

• then, multiply in the leftover numbers

• example: 32 100

Fractions Vocabulary Review

• fraction:

• improper fraction:

• mixed fraction:

Least Common Denominator

• uses the least common multiple of the denominators

• Example:

• What is the LCD for:16

15,

24

11,

12

5

Adding/Subtracting Fractions

• must have common denominators• adding mixed numbers:

– add fractions first– add whole numbers– reduce the fraction, if needed

• subtracting mixed numbers:– subtract fractions first, borrowing if needed– subtract whole numbers– reduce the fraction, if needed

Examples

• Find the sum or difference:

9

52

9

73

10

34

2

16

Examples

• Find the sum or difference:

4

32

5

19

Multiplying/Dividing Fractions

• multiplying fractions:– multiply numerators– multiply denominators– reduce, if needed

• dividing fractions:– flip the second fraction– multiply the fractions– reduce, if needed

• mixed numbers:– change into improper fractions

Examples

• Find the product or quotient:

7

6

3

2

4

3

12

5

Vocabulary Review

• Mean:

• Median:

• Mode:

Percents

• means per hundred or divided by 100

• you can change percents to a reduced fraction or a decimal

• use multiplication to find the percent of a number

Example

• Find 5% sales tax on a CD selling for $12.95.

Example

• Estimate 74% of 840.

Example

• A sale sign says 20% off, save $30! What is the original cost of the item?

Example

• Margo knows that the tax on the new coat she bought was $12.60 and that the sales tax rate was 7%. What was the cost of her new coat?

Multiplication Properties of Exponents

• When two powers have the same base, add the exponents and keep the base

• When finding a power of a power, multiply the exponents

• When finding the power of a product, “distribute” the power to each part of the product

23 xx

43x 423yx

Negative & Zero Exponents

• Negative exponents make the number or variable a reciprocal

• Anything raised to a zero exponent is 1

2b

0m

Division Properties of Exponents

• When dividing two powers with the same base, subtract the exponents

• When finding a power of a quotient, “distribute” the power to top and bottom

3

8

x

x

4

2

3

b

a

Scientific Notation

• Uses powers of 10 to write decimal numbers

• Contains a number between 1 and 10 that is multiplied by a power of 10

Example 1

• Write expressions for the perimeter and the area of the rectangle:

3x+5

x

Example 2• Evaluate each expression if m = 4, n = -3,

and t = 0:

• 2m + 3(4n)3

• (5n3 – 2s7)t

• 9m – 4m2 – m2 + m + 5n2

Example 3

• Write an expression for the perimeter of:

n

3n

n

n

Example 1

• Solve each equation:

4

32

3

1x 855 x

Example 3

• Solve: 3x + 5 = 6

Example 5

• Solve:34

3

13

x

x

Perimeter

• The distance around a polygon, shape, object, etc.

• When you have a flat figure, add up all the sides

• Circles: use the formula C = 2πr = πd

Area

• Area of square = (side)2

• Area of rectangle/parallelogram = base x height

• Area of triangle = ½ x base x height

• Area of trapezoid = ½ x height x (base + base)

• Area of circle = πr2

Surface Area

• Surface area is the sum of the areas of all its bases and faces

• i.e. like wrapping a present

Formulas

• Surface Area of a Rectangular Prism

• Surface Area of a Cylinder

• Surface Area of a Cone

whlhlwSA 2

rhrSA 22 2

2rrsSA

Volume of a Prism

BhV

Area of the base

Height

Volume of a Pyramid

BhV3

1

Area of the Base

Height

Volume of a Cylinder

hrV 2

Volume of a Cone

hrV 2

3

1

Volume of a Sphere

3

3

4rV