TSIA2 STUDY GUIDES: MATH EXAM
QUESTIONS AND ANSWERS 100% PASS
Adding with same denominator - ANS (a/b)+c/b)=((a+c)/b)
Subtracting with same denominator - ANS (a/b)-(c/b)=((a-c)/b)
Adding with different denominator - ANS (a/b)+(c/d)=((ad)+(cb))/bd
Subtracting with different denominator - ANS (a/b)-(c/d)=((ad)-(cb))/bd
Multiplying Factors - ANS (a/b)*(c/d)=(a*c)/(b*d)
Dividing Factors - ANS (a/b)/(c/d)=(ad)/(bc)
Factoring numbers - ANS a(c/d)= a+(c/d)= (ad+c)/d
Intergers - ANS {...,−3,−2,−1,0,1,2,3,...}
Real Numbers - ANS All numbers that are on number line. Integers plus fractions, decimals,
and irrationals
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, PEMDAS - ANS Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Percentages - ANS part = (percent / 100) x whole
percent of change - ANS ((New value - old value)/old value) X 100
Distance from A to B - ANS √(x2 − x1)^2 + (y2 − y1)^2
Parallel and Perpendicular lines - ANS Parallel lines have equal slopes. Perpendicular lines
(i.e., those that make a 90∘90° angle where they intersect) have negative reciprocal slopes:
𝑚1m1 .𝑚2=−1m2=−1.Parallel Lines (l ∥∥ m)
Mid-point of the segment AB - ANS M (𝑥1+𝑥2/2),(𝑦1+𝑦2/2)
Slope of the line - ANS (𝑦2−𝑦1)/(𝑥2-𝑥1)=𝑟𝑖𝑠𝑒/𝑟𝑢𝑛
Point-slope form - ANS y-y1=m(x-x1), where (x1,y1) is any point on the line and m is the slope
of the line
Slope-intercept form - ANS y=mx+b, where m is the slope and b is the y-intercept of the line.
Factoring - ANS "FOIL"
(𝑥+𝑎)(𝑥+𝑏)(x+a)(x+b)=
𝑥2+(𝑏+𝑎)𝑥+𝑎𝑏=
x2+(b+a)x+ab
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
QUESTIONS AND ANSWERS 100% PASS
Adding with same denominator - ANS (a/b)+c/b)=((a+c)/b)
Subtracting with same denominator - ANS (a/b)-(c/b)=((a-c)/b)
Adding with different denominator - ANS (a/b)+(c/d)=((ad)+(cb))/bd
Subtracting with different denominator - ANS (a/b)-(c/d)=((ad)-(cb))/bd
Multiplying Factors - ANS (a/b)*(c/d)=(a*c)/(b*d)
Dividing Factors - ANS (a/b)/(c/d)=(ad)/(bc)
Factoring numbers - ANS a(c/d)= a+(c/d)= (ad+c)/d
Intergers - ANS {...,−3,−2,−1,0,1,2,3,...}
Real Numbers - ANS All numbers that are on number line. Integers plus fractions, decimals,
and irrationals
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
, PEMDAS - ANS Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Percentages - ANS part = (percent / 100) x whole
percent of change - ANS ((New value - old value)/old value) X 100
Distance from A to B - ANS √(x2 − x1)^2 + (y2 − y1)^2
Parallel and Perpendicular lines - ANS Parallel lines have equal slopes. Perpendicular lines
(i.e., those that make a 90∘90° angle where they intersect) have negative reciprocal slopes:
𝑚1m1 .𝑚2=−1m2=−1.Parallel Lines (l ∥∥ m)
Mid-point of the segment AB - ANS M (𝑥1+𝑥2/2),(𝑦1+𝑦2/2)
Slope of the line - ANS (𝑦2−𝑦1)/(𝑥2-𝑥1)=𝑟𝑖𝑠𝑒/𝑟𝑢𝑛
Point-slope form - ANS y-y1=m(x-x1), where (x1,y1) is any point on the line and m is the slope
of the line
Slope-intercept form - ANS y=mx+b, where m is the slope and b is the y-intercept of the line.
Factoring - ANS "FOIL"
(𝑥+𝑎)(𝑥+𝑏)(x+a)(x+b)=
𝑥2+(𝑏+𝑎)𝑥+𝑎𝑏=
x2+(b+a)x+ab
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED.
