Geometry(Pt.1), Geometry(Pt.2:Equations), Algebra, Mathematics Knowledge and Operations
An Acute angle is more than _ degrees but less than _.
0, & 90
How to find a Common denominator in a fraction of 3/5 and 3/10?
1. Divide the larger denominator by the small denominator(10 / 5=2) 2. Take the Fraction with the smaller denominator (3/5) and multiply both the numerator and denominator by 2( 3 x 2=6, 5x2= 10) 3. Replace the Numerator and denominator with the numbers from step 2 (3/5=6/10) and add both fractions together(6/10 + 3/10 = 9/10)
Method two on Preparing to Add and Subtract a fraction Question: Cousin ate 3/5 of one pizza and your little sister eats 1/6 (cut into 6 slices instead of 6) of another pizza and you want to know how much pizza was eaten. (NEED TO ADD 3/5 and 1/6)
1. Multiply the denominator of the first fraction by the denominator of the second fraction(5 x 6 =30) 2. Express the first fraction in terms of the new common denominator (3/5 = ?/30) 3. Multiply the numerator by the number that was multiplied by to result in the new denominator (5=30 "so multiply 6 by 3" to get 18/30) 4. Next express the second fraction in terms of the new common denominator (1/6= ?/30) 5. Multiply the numerator by the second number that was multiplied by to result in the denominator (6=30 " so multiply 5 by 1" to get 5/30) 6. Add the new numbers together (18/30 + 5/30 = 23/30)
How to Multiply fractions
1. Multiply the numerator.(1/2 x 3/4 x 3/5 "1 x 3 x 3=9") 2. Multiply the denominator. (1/2 x 3/4 x 3/5 "2x4x5=40") Final 9/40 3. Reduce to the lowest term if necessary.
Steps on Dividing Fractions
1. Obtain the reciprocal of a number by flipping the number (ex: 5=1/5"same as 5/1=5") 2. To divide a fraction use the inverse of the number that follows the division symbol and substitute a multiplication symbol for the division sign. 3. Therefore 1/3 / 2 goes to 1/3 x 1/2=1/6
How to find a common denominator for three fraction(1/2 + 2/3 + 3/5)?
1. Take the largest denominator and multiply it by whole numbers starting with 1,2,3,4 (until you find a denominator the other denominators also divide evenly) 2. So in this class 30 is the common denominator (2x15=30, 3x10=30, 5x6=30) 3. Make the denominators the same as the LCD (1x15/2x15 + 2x10/3x10 + 3x6/5x6= 15/30 + 20/30 + 18/30) 4. Add the numbers together (15 + 20+ 18=53) final =53/30
How many degrees is a Straight line?
180 degrees
What is a Prime number?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, & 97
A circle has how many degrees?
360
What does a Quadrilateral(a shape with four sides such as square or rectangle) Angles add up to?
360 degrees
What does a circle always have?
360 degrees
Solve the Fraction 20/21 x 14/25 1. Multiply numerators then denominator
8/15
What is a Polynomial?
A expression that uses one or more variable.(Ex: 3ab-2x^2+2y^3-7)
Circle What is Diameter?
A measured as a line passing through the center of the circle from a point on one side of the circle all way way to a point on the other side of the circle (ALSO the Diameter of a circle is always TWICE as long as the radius of a circle d=2r)
What is a Reciprocal?
A number by which another number can be multiplied to produce 1.
What are Coefficient?
A number part of a algebraic term (ex: 8a-12b=-4 "8 and 12 are it")
What is a common factor?
A number that can divide into both the numerator and the dominator. (6/10 "6/2=3, 10/2=5") Final 3/5
What is a Base number?
A number yea used as a factor a specific number of times- its a number raised to an exponent ( 4^3 "4x4x4" base is 4)
What is a Exponent?
A shorthand method of indicating repeated multiplication ( 15^2 "15x15" small number written on top)
What is a Equilateral triangle?
A triangle with three equal sides that each measure 60 degrees
What is a Scalene triangle?
A triangle with three unequal sides
Numerical Factor What is a Composite number?
A whole number that can be divided evenly by itself and by 1, as well as by one or more other whole numbers "other words has more than two factors" (6= 1,2,3 &6)
How to find the Area of a Trapezoid?
A= a+b/2 h (a=length of one base"one of the parallel lines" b=the length of the other base "other parallel line" , h=height measured between the two parallel lines)
How to find the Area of a Circle?
A=πr^2 Ex: Find the area of 9 inch diameter pie 1. Multiply π by the square of 4.5^2(4.5 is from being half the diameter of 9) 2. A=πx(4.5 x 4.5)=60.585 square inches
How to Multiply terms with same bases?
Add the exponents: x^2 (x^3)=x^2+3=x^5
What is a constant?
Algebraic expression that contains only a number (14d+12a+5 "5 is it")
Quadrilaterals What do Rectangles have?
All (four) right angles and the opposite sides have equal lengths
What is a Reflex angle?
An angle greater than 180 degrees
What is a Quadratic equation?
An equation that includes the square of a variable (ex:x^2-2x=15→x^2-2x-15=0)
What is a Vertical angle?
Angles oppose each other when two lines cross and their always equal
How do you calculate a factorial?
By finding the product of (multiplying) whole number and all the whole numbers less than it down to 1 (6 factorial 6!=6x5x4x3x2x1=720)
What does Arcs of a circle and sizes of angles measure in?
Degrees and in minutes or even seconds (1 degree = 60 minutes and 1 minute =60 seconds)
When adding or subtracting fractions what must they have the same ?
Denominator "called common denominator"
What happens when a product has a exponent?
Each factor is raised to that power:(xy)^3=x^3 y^3
How to divide an Inequality equation?
Ex: -2x<14 by -2 1. Divide both sides by -2 (2x<14→x>-7)
How to solve Combining equation ?
Ex: 12x-9y=37, 8x+9y=23 1. Add the two equations to figure out just one of the variable (12x-9y=37 ,+ 8x+9y=23 "20x =60") 2. After solving x you get x=3 and you plug 3 in for the x value in either the original equation to figure out the value of y (8(3) +9y=23, 24+9y=23, 9y=23-24, 9y=-1, y=-1/9)
How to solve an Inequality?
Ex: 3+x≥4 1. Simply isolate x by subtracting 3 from both sides (3+x≥4→3+x-3≥4-3→x≥1)
How to multiply an Inequality equation?
Ex: 3<4 by -4 1. Multiply both side by -4 ( 3<4→-12<-16)
How to covert an Improper fraction to a mixed number?)Look at pic if need help
Ex: 7/3 1. Divide the numerator by denominator (7/3= quotient of 2 with the remainder of 1) 2. There is something left over b/c 3 doesn't divide evenly into 7 3. So the reminder becomes a numerator over the original denominator (1/3 is left over "7/3 is the same as 2 ,1/3)
Combining equation How to solve when a problem requires you to change one equation entirely to figure out the answer?
Ex: 7x+10y=36, 2x-y=--9 1.Multiply the bottom equation by 10 ( 2x-y=-9 → 20x-10y=-90) 2. Add it to the first equation to eliminate y (7x+10y=36, + 20x-10y=-90 → 27x=-54) then divide to get x=-2 3. Take the x value "2" and plug it in to the original equation to solve for y ( 2x-y=-9 → 2(2)-y=-9, → -4-y=-9 → y=-5)
How to solve a Quadratic equation?
Ex: x^2-2x-15=0 1. Factor: x^2-2x-15=0(x-5),(x+3)=0 2. Solve separate x-5=0, x+3=0 → x=5 &-3
What is a Right angle?
Exactly 90 degrees
Quadrilaterals What do Trapezoids have?
Exactly two sides that are parallel
What is A Numerical Factor?
Factors are integers that can be divided evenly into another integer.
Quadrilaterals What do Squares have?
Four sides of equal length and all the angles are right angles
Quadrilaterals What do Rhombuses have?
Four sides of equal length but the angels don't have to be right angles
What does ≥ mean ?
Greater than or equal to(x≥3)
What is a Obtuse triangle?
Has a angle greater than 90 degrees
What is the Area of a shape?
Is all the flat space within the boundary
What is a Integer?
Is any Positive or Negative WHOLE Number or ZERO(-4.0, 29)
What happens when a base has a Negative exponent?
It equals to its reciprocal (inverse) with a positive exponent : x^-3=1/x^3
What are Two dimensional "flat shapes" measure by?
Length x width
What does ≤ mean?
Less than or equal to(x≤4)
What does < mean?
Less than(3<4)
An Obtuse angle is what?
More than 90 and less than 180
How to find the Rectangular prisms?
Multiply Length x width(depth) x height:V=lwh (remember cubic =in^3)
What is a real number?
Numbers that can be found on a number line (negative and positive, rational and irrational).
What is a Factorial?
Operation represented by an exclamation point.
Quadrilaterals What do Parallelogram have ?
Opposite sides that are parallel and their opposite sides and angles are equal (the angles don't have to be right angles)
What triangle does the Pythagorean theorem(a^2+b^2=c^2) work with?
Right triangle
What are Rational numbers?
Set of real numbers, fraction, and terminating decimals. (Ex: 1/2, 5, 0.25)
How to factor a Number?
Simply determine the numbers that you can divide into it.(8= 4&2)
How to Divide terms with the same Bases?
Subtract the exponents: x^5 / x^2=x^5-2=x^3
What does ≥ ≤ mean on a number line?
That the circle is closed
What does > < mean on a number line?
That the circle is opened
What happens when a Transversal line crosses a parallel line?
The angles formed make pairs that have the same measure
What is a Denominator?
The bottom number in a fraction(2/6)
What is a Perimeter of a shape?
The distance around a shape
Where is the Vertex located for a angle?
The middle letter (ex: <DRJ "R")
Circle What is Circumference?
The posts forming the circle that is the distance around the circle
Circle What is Radius?
The straight line measurement from the center of the circle to any point on the circle to any point on the circumference of the circle
What is a numerator?
The top number in a fraction (2/6)
What is a Flat shape?
Triangle, Circle, Rectangles, Squares
True or False: Parallel lines Never intersect?
True (Always in the same distance apart and they never meet)
Reciprocal What happens if you have a Fraction ?
Turn the fraction upside down ( 3= 1/3)(1/6=6/1) (2/3=3/2=0 "does have a reciprocal")
What is a Supplementary angle?
Two angles that add up to 180 degrees
What are Alternate Exterior angles?
Two angles that are on opposite sides of the transversal (when they are equal its a parallel line)
What are Alternate interior angles?
Two angles that are on the opposite sides of the transversal and between the parallel lines lie between the two lines and on opposite sides of the transversal
What are Consecutive Interior angles?
Two angles that are on the same side of the transversal between the parallel lines (If these angles add up to 180 then your dealing with parallel lines)
What is a Complementary angles?
Two angles that equal 90 when added together
What are Corresponding angles?
Two angles that have the same measure with them being on the same side of the transversal and both either are above or below the parallel lines (*They have to be equal if the lines are parallel*)
How to find the Surface area of a Cylinder?
Use SA = 2πr² + 2πrh (r=radius)
How to find the Surface Area of any Prism?
Use SA=2B+ph (B= area of the base, p=perimeter of the base, h=height)
How to find the Surface of a Rectangular prism?
Use SA=2ab+2bc+2ac (a,b,c= the lengths of the three sides)
How to find the Surface area of a Cube?
Use SA=6s^2 (s=length of the side of each edge)
How to solve Circumference?
Use equation C=π(3.14)d Ex:Suppose you know that the pie you just baked has a diameter of 9 inches. what is the circumference? 1. use the equation and input what its in the problem (C=3.14x9=28.26 in)
How to find the Area of a Rhombus?
Use equation: A= pq/2 (p= the length of one diagonal, q= the length of the other diagonal)
How to find the Area of a Parallelogram?
Use equation: A=bh (height is measured by the base perpendicular to the parallel side)
How to find the Area of a Square and Rectangle?
Use equation: A=lw
How to find the Area of the Triangle?
Using equation A=1/2bh (b=base"bottom or the length", h=height "the distance drone perpendicular from the base to the opposite vertex")
How to find the Perimeter of a triangle?
Using equation a+b+c(basically adding all the sides together)
How to find the Volume of Spheres?
V=4/3 πr^3
How to find the Cylinders volume?
V=πr^2h
What is a Improper Fraction?
When a numerator is larger than or equal to the denominator (ex:13/5)
What is a Isosceles triangle?
When two sides have equal length
Numerical Factor What is a Prime Number?
Whole number that can be divided evenly by itself and by 1 but not by any other number "which means it has exactly two factors" (2=1&2, 5= 1 & 5)
What is the special rule for inequalities?
You multiply or divide both side of the inequity by a negative number(inequality sign is reversed)
What does > mean?
greater than(4>3)
Any base raised to the zero power equals?
one
What is the equation for Slope-intercept?
y = mx + b (m=slope, b=point where lines cross the y-axis , x&y= coordinates of points) Ex: Find the y-intercept of the straight line that has a slope of 4 and passes through the point (-1,-6) 1. Use y = mx + b→ -6=4(-1)b→-6=-4b→-2=b
