Math Subtest II Flashcards
Ways to Classify Trangles: SSS, SAS, ASA, AA
Side / Side / Side : If the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Side/Angle/Side (SAS) : If two sides and the angle between the sides of one triangle are congruent to the corresponding sides and the angle between them of another triangle, then the two triangles are congruent.
Angle/Side/Angle (ASA) : If two angles and the side between them of one triangle are congruent to the corresponding angles and side between them of another triangle, then the two triangles are congruent.
Angle/Angle (AA) : If two angles of one triangle are congruent to two corresponding angles of a second triangle, then the two triangles are similar.
What is the order of operations in math? PEMDAS
(PEMDAS)
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
What is Frequency (when discussing EM waves)?
The number of oscillations the wave undergoes in a certain amount of time
What does this picture represent?
This is a factoring tree. It is one way that a student can perform the prime factorization of a number. In this instance, the number 1960 has been factored into the prime factorization 1960 = 2 × 2 × 2 × 5 × 7 × 7 = 2³ × 5¹ × 7².
Area Formulas
- Triangle
- Parallelogram
- Reactangle
- Square
- Circle
triangle A=1/2bh
parallelogram A=bh
rectangle =A=L(w)
square A=S^2
circle= A=(pi)r^2
What is Exponentiation
Exponentiation is repeated multiplication. An exponent is often called a power. For example, the third power of 2 is
2³ = 2 × 2 × 2 = 8
What is the divisibility test for 3?
If the sum of the digits is divisible by 3, then the number is also. For example, 177 is divisible by 3 since the sum of its digits is 15 (1 + 7 + 7 = 15), and 15 is divisible by 3.
Convert to decimal notation.
5.913 x 10^-8
0.00000005913
What are the 3 M’s - Measures of Central Tendency?
Mean: average of n data points is the sum of the values divided by n
Median: the middle value of the data set in the sense that there are an equal number of values above and below the median
Mode: the most frequently occurring values in the data set
The table shows the percent change in a Consumer Price Index from the previous year for 1996 and 1997. Which category shows the greatest change from 1995 to 1996?
A. Public transportation
B. Private transportation
C. Food
D. Apparel & Upkeep
Public Transportation
Use the diagram to find the area of the rectangle. Give your answer in lowest terms.
The area of the rectangle is _______ square foot.
Correct answer is 3/49
What are the 4 basic types of human tissue?
connective, epithelial, muscle, and nerve.
What is the fundamental unit of measurement for length, mass and time?
Meter, Kilogram, Second
Name of 2D figure with X sides
3
4
5
6
7
8
9
10
12
20
triangle 3
quadrilateral 4
pentagon 5
hexagon 6
heptagon 7
octagon 8
nonagon 9
decagon 10
dodecagon 12
icosagon 20
What is the distributive Property of MULTIPLICATION?
The product of a number with a sum equals the sum of the products of the number with each term of the sum.
2 × (3 + 5) = (2 × 3) + (2 × 5)
Name the first 10 prime numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, …
What is the Associative Property of ADDITION?
When adding three or more numbers, the sum is the same regardless of the way in which the numbers are grouped.
2 + (3 + 5) = (2 + 3) + 5
What is the sequence of squares?
The square of the list of natural numbers, for instance:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 …
What is the identity property of ADDITION?
Adding zero to a number does not change it.
2 + 0 = 2
Your students have been growing plants and measuring the growth per week. You want them to graph this data to show the small changes over time. What is the best type of graph to use?
- Bar Graph
- Pie Chart
- Line Graph
- an X-Y Plot
- Line Graph
Line graphs are used to track changes over periods of time. When smaller changes exist, line graphs are better to use than bar graphs. Line graphs can also be used to compare changes over the same period of time for more than one group.
What is a composite number?
A natural number that is greater than 1 and not prime.
Label the parts of this plant cell
What are the three basic properties of addition?
commutative associativite and identity.
Define Homeostasis
The ability to maintain a state of internal balance. For example, if the environmental temperature increases, the human body begins to perspire, and the cooling effect of evaporation decreases the surface temperature of the skin. Likewise, a disruption in any system will set off a diverse set of control mechanisms that return the organism to a state of internal balance.
Transitive Property
if a number is equal to b, and number b is equal to number c, then number a is also equal to number c
a=b, b=c, c=a
Reflexive Property
every number is equal to itself x=x
Label the parts of a flower
What is the divisibility test for 6?
If the number is divisible by both 3 and 2, then it is also divisible by 6. For example, 168 is divisible by 6 since it is divisible by 2, and it is divisible by 3.
There are 5 strategies for estimating (never use the phrase “guess” or “educated guess” with young students!). Name and define at least 2.
- Front-end strategy. The front-end strategy focuses on the left-most or highest place-value digits. For example, you can estimate the sum 67 + 91 by adding the highest place-value digits, 6 and 9. Thus, approximate 67 + 91 by 60 + 90 to obtain 150.
- Rounding strategy. Using the rounding strategy to estimate 67 + 91 would round 67 to 70 and would round 91 to 90 to yield 70 + 90 = 160 as an estimate for the sum.
- Clustering strategy. When operating with numbers that are clustered close to one another in value, group the operations to make the calculations easier. For example, to estimate the sum 594 + 603 + 622 + 586, notice that each of the 4 terms is approximately 600. So, the sum is approximately 4(600) = 2400.
- Compatible numbers strategy. Adjust the numbers so that they are easier to work with: in division, adjust the divisor, the dividend, or both, so that they are easier to compute. For example, to estimate 67 ÷ 3, observe that 67 is close to 66, which is divisible by 3. So, an estimate for 67 ÷ 3 is 66 ÷ 3 = 22.
- Special numbers strategy. Look for special numbers that are close to values that are easy to combine, such as one-half, or the powers of ten. For example, to estimate 51% of 89, observe that 51% is close to and that 89 is close to 90. So, 51% of 89 is approximately one-half of 90, or 45. This estimate is very close to the actual value of 45.39.
What is a compound machine?
two or more simple machines working together.
A wheelbarrow is an example of a complex machine that uses a lever and a wheel and axle. Machines of all types make work easier by changing the size or direction of an applied force.
Symmetric Property
if a number is equal to another number, then the converse is also true
x=y then y=x
Regarding a Circle, what is a
Chord
Arc
Sector
A line segment connecting any two points on a circle
the intersection of the interior of a central angle of the circle with the circle itself
What is the set of Natural Numers?
N = {1, 2, 3, 4, 5, 6, . . . }
When is an X-Y plot used?
X-Y plots are used to determine relationships between the two different things. The x-axis is used to measure one event (or variable) and the y-axis is used to measure the other. If both variables increase at the same time, they have a positive relationship. If one variable decreases while the other increases, they have a negative relationship. Sometimes the variables don’t follow any pattern and have no relationship.
Substitition Property
if two number are equal to one another, they are interchangeable
x=y, they x+z=y+z
Slope-Intercept Form of a Line
y = mx + b
What is the difference between an autotroph and a heterotroph?
Autotropic organisms are capable of harnessing energy from sunlight and using it to produce glucose, the main source of energy for the organism. Heterotropic organisms capture energy by eating plants or other animals.
What is the difference between a constant and a variable?
Constants are symbols that represent fixed values. In the expression 3x + 7, the constants are 3 and 7.
Variables are symbols that stand for changing values. Most often we use letters of the alphabet for variables. In the expression 3x + 7, the letter x is a variable. The value of the expression depends on the specific number we substitute for x. For example, if we substitute 2 for x, the value of the expression is 3(2) + 7 = 13.
What is a function?
A set of ordered pairs that pairs each element x of one set, called the domain (input) of the function, with a unique element f(x) of another set, called the range (output) of the function.
What are the difference between an operator, grouping symbols and relations.
Operators are symbols such as +, -, × and / that represent operations such as addition, subtraction, multiplication, and division.
Grouping symbols are symbols such as parentheses ( ) and brackets [] that indicate the order in which we should interpret the operations and the relations in a mathematical expression.
Relations are symbols that compare expressions. Common relations are =, , ≤, and ≥.
What is the commutative property of ADDITION?
When adding two numbers, the sum is the same regardless of the order in which the numbers are added.
2 + 3 = 3 + 2
Label the parts of the animal cell.
Least Common Multiple
the smallest multiple that they have in common
3: 3,6,9,12,[15],18,21,24
5: 5,10,[15]
What are irrational numbers?
are any numbers that ‘cannot’ be expressed as fractions, such as an infinite, non-repeating decimal
irrational have non-terminating and non-repeating decimals (ex. PI)
What are organelles?
Smaller structures inside plant an animals cells, which are specialized to fulfill specific functions within the cell.
Mitochondria, for example, break down glucose to provide energy to the cell. Bacterial cells lack most of these organelles.
Equations
consists of two expressions related by an equals sign. For example,
2x − 3 = 5
is an equation.
If an equation contains a variable, then a solution of the equation is a value which, when substituted for the variable, yields a true equality. For example, 4 is a solution of 2x − 3 = 5 because when 4 is substituted for x, the equation is a true statement:
2(4) − 3 = 8 - 3 = 5
What is the divisibility test for 9?
If the sum of the digits is divisible by 9, then the number itself is also divisible by 9. For example, 369 is divisible by 9 since the sum of its digits is 18 (3 + 6 + 9 = 18), and 18 is divisible by 9.
Be able to convert a fraction to a percentage and a percentage to a fraction.
2/5 = ?
65% = ?
example: 2/5 = .4 = 40%
65% = 65/100
Fundamental Counting Principle
states that if there are ‘m’ ways one thing to happen, then there is another thing that happens, there are ‘mxn’ ways for both to happen (tree diagram)
What equations calculate the Circumference, Area, and Diameter of a Circle.
C = 2πr
A = πr²
d = 2r
Polyhedra
three-dimensional solid with faces that are polygons joined at their edges.
The term polyhedron comes from the Greek “poly” meaning many, and “hedra” meaning faces.
The edges of a polyhedron are the line segments where the faces meet, and the vertices (singular, vertex) of the polyhedron are the points where the edges meet.
Calculating Slope of a Line
Find the slope of the line that passes through the points (2 , 0) and (3 , 4).
Find the slope of the line that passes through the points (2 , 0) and (3 , 4).
Greatest Common Factor
the largest factor that they have in common
20: 1,2,[4],5,10,20
24: 1,2,3,[4],6,8,12,24
