A Glossary of Mathematical Terms and Concepts for ESL Students

CUNYMath

A - E

ABSOLUTE VALUE
Absolute value of a number is the number itself if the number is non-negative, otherwise it is the opposite of the number. (See also non-negative number and opposite number.)
| x | = { x if x > = 0
-x if x < 0
Examples: Read as:
| 3 | = 3 absolute value of 3 is 3
| -4 | = 4 absolute value of -4 is 4
| -.2 | = .2 absolute value of .2 is .2
ADDITION +
add 2 to 3 3 + 2
4 plus 5 equals 9 4 + 5 = 9
x increased by 6 x + 6
the sum of 7 and y 7 + y
4 more than n n + 4
ANGLES
diagram of several intersecting and non-intersecting lines forming various types of angles acute angle (< 90°): 1, 2, 4, 6
obtuse angle (> 90°): 5, 7
right angle (= 90°): 3
straight angle (= 180°): 8
alternating angles: 5 & 7;
4 & 6
corresponding angles: 1 & 6
complementary angles (sum = 90°): 1, 2
opposite angles: 1 & 4
supplementary angles (sum = 180°): 1, 2, 3;
4, 5;
6, 7;
2, 3, 4;
1, 5
AREA
Area of a:  
square = side multiplication sign side
rectangle = length multiplication sign width
circle = mathematical symbol piradius multiplication sign radius = mathematical symbol pi multiplication sign radius2
ASSOCIATIVE LAW
The associative law of:
addition: a + (b + c) = (a + b) + c
multiplication: a(bc) = (ab)c
AVERAGE (MEAN)
The average of x1, x2, ... , xn = (x sub 1 + x sub 2 + ... + x sub n) / n
(pronounced "x sub 1'' and so on)
The mean of 2, 5, 7, 11 =   2 + 5 + 7 + 11
4		   =  6.25
Mean is the same as average.
CIRCLE
center: (0, 0) a circle whose center is (0,0) and radius is 3
radius: 3
equation of circle: x2 + y2 = 9
center: (h, k) a circle whose center is (h, k) and radius is r
radius: r
equation of circle: (x - h)2 + (y - k)2 = r2
COMMUTATIVE LAW
The commutative law of:
addition: a + b = b + a
multiplication: ab = ba
COMPLEX NUMBER
The sum of a real number and an imaginary number is called a complex number. (See also number and imaginary number.)

Examples:
1 + i,   -3 + 2i,   -3.7 - i   are complex numbers.
CONIC SECTIONS
Conic sections are curves cut by a plane with a double cone. They may be:

a double cone with circle, ellipse, point, parabola, intersecting lines, and hyperbola identified
COORDINATES (CARTESIAN COORDINATES)
The origin: (0, 0)      x and y axes with points P : (3, 2), Q :(-4, 1), R : (0, -2), and Origin: (0, 0) labeled
Coordinates of points: P : (3, 2)
Q :(-4, 1)
R : (0, -2)
Abscissa (x -coordinate) : 3, -4 , 0
Ordinate (y -coordinate) : 2, 1, -2
CONSTANT
A constant is a number in an algebraic expression. (See also polynomial and variable.)

Example:
4 is a constant in the expression 3x + 2y + 4.
DISTANCE
Distance between points P (x1, y1) and Q (x2, y2) x and y axes with points P: (x sub 1, y sub 1) and Q: (x sub 2, y sub 2) labeled
PQ = the square root of [ (y sub 2 - ysub 1)^2 + (x sub 2 - x sub 1)^2 ]
DISTRIBUTIVE LAW
The distributive law in algebra and arithmetic:
a (b + c) = ab + ac
DIVISION
3 divided by 5 3
5
x divides into 8 8
x
the quotient of n and y n
y
the ratio of 7 to 2 7
2
Quotients of above examples: 3
5		 , 8
x		 , n
y		 , 7
2
Dividends of above examples: 3, 8, n, 7
Divisors of above examples: 5, x, y, 2
(See also ratio and quotient.)
ELLIPSE
center: (0, 0) an ellipse with center (0, 0) and vertices V1, V3, V2, and V4 labeled counterclockwise from V1 which crosses the positive x axis
major axis (longer) : 2a
minor axis (shorter): 2b
equation of ellipse:
vertices: V1 (a, 0)
V2 (-a, 0)
V3 (0, b)
V4 (0, -b)
EQUATION
An equation is a statement of equality between two algebraic expressions with one or more unknowns. (See also system of equations.)

Linear equation in one unknown: 3x -1 = 5
To solve 3x - 1 = 5  
3x = 6  
x = 2 (root/solution)

Quadratic equation in one unknown: x2 - x - 2 = 0
To find the solution of x2 - x - 2 = 0  
(x - 2)(x + 1) = 0  
x - 2 = 0 x + 1 = 0  
x = 2 x = -1 (solutions)

Linear equation in two unknowns: 2x + y = 3
EQUATION OF A STRAIGHT LINE
General Form:
Ax + By + C = 0
2x + 3y + 4 = 0

Intercept Form:
x
a		 + y
b		 = 1            a straight, diagonal line from the second quadrant to the fourth quadrant, passing through the first quadrant; the y axis from y=0 to y-intercept is labeled 'b'; the x axis from x=0 to x- intercept is labeled 'a'
x-intercept: (a, 0), (3, 0)
y-intercept: (0, b), (0, 2)

Slope-Intercept Form:
y = mx + b
y = 4x - 3
slope: m, 4
intercept: (0, b) , (0, -3) 		           a straight, diagonal line from the first quadrant to the third quadrant, passing through the second quadrant; the y axis from y=0 to y-intercept is labeled 'b'

Point-Slope Form:
y - y1 = m (x - x1)
y - 5 = 2 (x - 3)
point: (x1, y1), (3, 5)
slope m, 2 		           a straight, diagonal line from the first quadrant to the second quadrant, passing through no other quadrants; a point which lies on the line within the first quadrant is labeled '(x sub 1, y sub 1)'

Two Points Form:
y - y1 = (y sub 2 - y sub 1) divided by (x sub 2 - x sub 1) (x - x1)            a straight, diagonal line from the first quadrant to the second quadrant, passing through no other quadrants; a point which lies on the line within the first quadrant is labeled '(x sub 1, y sub 1)'; a second point, also lies on the line within the first quadrant, is labeled '(x sub 2, y sub 2)'
two points: (x1, y1), (x2, y2)
EVALUATE
To evaluate is to find the value of a mathematical expression.

Examples:
Evaluate 3 - 2 (4 + 1)
3 - 2 (4 + 1) = 3 - 2 (5)
  = 3 -10
  = -7

Evaluate a2 - 2ab - b2 when a = -1 and b = 2
a2 - 2ab - b2 = (-1)2 - 2(-1)(2) - (2) 2
  = 1 + 4 - 4
  = 1
EXPONENTIAL FUNCTION
An exponential function is a function of the form
y = ax where a > 0.
(See also function and power.)
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