ACT MATH QUESTIONS WITH COMPLETE ANSWERS
(100% ACCURATE)
Question 1.
the distance formula
ANSWER
d = [( x₂ - x₁)² + (y₂ - y₁)²]
OR think of distance between two points as the hypotenuse of a right triangle use
pythagorean theorem
Question 2.
matrices
ANSWER
mxn
array of numbers organized in m rows and n columns
to multiply matrix by constant a... multiply every number by that constant a
to add two matrices of the same dimension... add corresponding elements
the determinant of 2 x 2 : ad-bc
*only need to know determinant of 2 x 2
multiplying matrices:
-use calc when can
-to find product multiply elements in each row of the first matrix by the corresponding
elements in each column of the second matrix and then add the products
-you can only do this if the # of columns in the first matrix = the # of rows in the second
matrix
mxn x nxp = mxp
*matrices are also used to represent a system of linear equations
,Question 3.
four-sided figure facts
ANSWER
in a quadrilateral
-all four angles add up to 360º
in a parallelogram
-opposite sides are parallel and equal
-opposite angles are equal
-adjacent angles are supplementary (add up to 180º)
-area= base x height
-the height is the perpendicular distance from the base to the opposite side
in a rhombus
-opposite sides are parallel
-opposite angles are equal
-adjacent angles are supplementary (add up to 180º)
-all 4 sides are equal
-area= base x height
-the height is the perpendicular distance from the base to the opposite side
-the diagonals are perpendicular
in a rectangle
-are considered special parallelograms (same facts as parallelograms apply)
-all 4 angles are each equal to 90º
-area= length x width
-perimeter= 2(length) + 2(width)
-the diagonals are equal
in a square
-considered special rectangles (same facts as rectangles apply)
-all 4 sides are equal
-area= (side)^2
-perimeter= 4(side)
-the diagonals are perpendicular
Question 4.
single digit prime numbers
ANSWER
2, 3, 5, 7
, Question 5.
logarithms
ANSWER
another way to express an exponent
logbn=x is the same as b^x=n
*is no value is given for base (b)...b=10
Question 6.
geometry questions
ANSWER
use basic word problem approach
1) know the question
2) let the answers help (eliminate)
3) break problem up into pieces
AND
write all the information given in the problem on the given picture (or draw your own
picture)
write down any formulas you need, and fill in given info
Question 7.
real numbers
ANSWER
All rational and irrational numbers
Question 8.
parts to wholes topics
ANSWER
i. percentages
ii. probabilities
iii. ratios
(100% ACCURATE)
Question 1.
the distance formula
ANSWER
d = [( x₂ - x₁)² + (y₂ - y₁)²]
OR think of distance between two points as the hypotenuse of a right triangle use
pythagorean theorem
Question 2.
matrices
ANSWER
mxn
array of numbers organized in m rows and n columns
to multiply matrix by constant a... multiply every number by that constant a
to add two matrices of the same dimension... add corresponding elements
the determinant of 2 x 2 : ad-bc
*only need to know determinant of 2 x 2
multiplying matrices:
-use calc when can
-to find product multiply elements in each row of the first matrix by the corresponding
elements in each column of the second matrix and then add the products
-you can only do this if the # of columns in the first matrix = the # of rows in the second
matrix
mxn x nxp = mxp
*matrices are also used to represent a system of linear equations
,Question 3.
four-sided figure facts
ANSWER
in a quadrilateral
-all four angles add up to 360º
in a parallelogram
-opposite sides are parallel and equal
-opposite angles are equal
-adjacent angles are supplementary (add up to 180º)
-area= base x height
-the height is the perpendicular distance from the base to the opposite side
in a rhombus
-opposite sides are parallel
-opposite angles are equal
-adjacent angles are supplementary (add up to 180º)
-all 4 sides are equal
-area= base x height
-the height is the perpendicular distance from the base to the opposite side
-the diagonals are perpendicular
in a rectangle
-are considered special parallelograms (same facts as parallelograms apply)
-all 4 angles are each equal to 90º
-area= length x width
-perimeter= 2(length) + 2(width)
-the diagonals are equal
in a square
-considered special rectangles (same facts as rectangles apply)
-all 4 sides are equal
-area= (side)^2
-perimeter= 4(side)
-the diagonals are perpendicular
Question 4.
single digit prime numbers
ANSWER
2, 3, 5, 7
, Question 5.
logarithms
ANSWER
another way to express an exponent
logbn=x is the same as b^x=n
*is no value is given for base (b)...b=10
Question 6.
geometry questions
ANSWER
use basic word problem approach
1) know the question
2) let the answers help (eliminate)
3) break problem up into pieces
AND
write all the information given in the problem on the given picture (or draw your own
picture)
write down any formulas you need, and fill in given info
Question 7.
real numbers
ANSWER
All rational and irrational numbers
Question 8.
parts to wholes topics
ANSWER
i. percentages
ii. probabilities
iii. ratios
