Download act math review answers

ACT MATH REVIEW
1) What is a ratio? MATHEMATICAL COMPARISON. A:B OR A/B
2) A fraction is a DIVISION problem.
3) What is the formula for the area of a trapezoid? THE AVERAGE OF THE BASES TIMES
THE HEIGHT. (BASE ONE + BASE TWO / 2) TIMES HEIGHT
4) For arithmetic sequences, find the common DIFFERENCE
5) For geometric sequences, find the common RATIO
6) What is distance in relation to speed (rate) and time? DISTANCE = RATE X TIME
7) What is the relationship between radii and tangent lines to a circle? THEY ARE
PERPENDICULAR
8a) Pi is a ratio between what two measurements of a circle? PI = CIRCUMFERENCE
DIVIDED BY DIAMETER
8b) What is the formula for the area of a circle? AREA = PI X RADIUS SQUARED
9a) The legs of a right triangle are 3 and 4, what is the hypotenuse? 5
9b) What if the legs were 5 and 12? 13
10) All composite numbers can be expressed as a product of PRIME numbers.
11) What is the difference between rational and irrational numbers? RATIONAL NUMBERS
ARE THE RATIO OF TWO WHOLE NUMBERS. IRRATIONALS CAN’T BE EXPRESSED
AS SUCH.
12) Square roots of prime numbers are rational or irrational? IRRATIONAL
13) What is the result when any number is raised to the 0 power? IT EQUALS ONE
14) Straight lines are produced from algebraic equations with up to three variables when the
variables are raised to the power of ZERO or ONE.
15) What do the “m” and the “b” stand for in the equation y=mx + b? M = SLOPE AND B =
Y-INTERCEPT OR THE POINT WHERE THE LINE INTERSECTS THE Y-AXIS.
16) To find LCM (lowest common multiple) using prime factorization, multiply each unique
factor to the HIGHEST degree. To find the GCF (greatest common factor), multiply common
factors to the LOWEST degree common.
17) If y=Kx or y/x=K, then this is a(n) DIRECT variation. K is some constant.
18) If y=K/x or yx=K, then this is a(n) INVERSE variation. K is some constant.
19) What does SOHCAHTOA stand for? SINE = OPPOSITE/HYPONETUSE, COSINE =
ADJACENT/HYPOTENUSE AND TANGENT = OPPOSITE/ADJACENT
20) Slope is a ratio between the LEFT/RIGHT direction or X variable and the UP/DOWN
direction or Y variable.
21) If two points on a line in a plane are (2,8) and (-7, -3), what is the slope? 8-(-3)/2-(-7)=11/9
22) In a 30, 60, 90 right triangle, if the side opposite the 30 degree is 2, what is the hypotenuse?
2 X 2 =4 What is the side opposite the 60 degree angle? 2 X SQUARE ROOT OF 3.
23) In a 45, 45, 90 right triangle, if the hypotenuse is 4, what are the legs? ROOT 2 X ? = 4 SO
X = 2 ROOT 2.
24) State the average formula SUM OF ALL INDIVIDUAL ELEMENTS DIVIDED BY THE
NUMBER OF ELEMENTS
25) Probabilities are always values between ZERO and ONE because ZERO OR 0% is the
probability that something will never happen and 1 OR 100% is the probability that some
phenomenon will always happen.
26) State the Pythagorean Theorem A SQUARED PLUS B SQUARED EQUALS C
SQUARED. A AND B ARE THE LEGS AND C IS THE HYPOTENUSE OF A RIGHT
TRIANGLE.
27) If two lines are both perpendicular to a third line, what relationship exists between the two
lines? THEY ARE PARALLEL
28) In an isosceles or equilateral triangle, what does the altitude from one base do to both the
vertex angle and the base? ALTITUDE BISECTS THEM BOTH.
29) If you only know the distance and average speed for a journey, how do you find the time for
such a journey? TIME EQUALS DISTANCE DIVIDED BY RATE.
30) The longest side of a triangle is always opposite the LARGEST angle.
31) If you have four horses and seven riders, how many different horse/rider pairs can be
formed? FOUR TIMES SEVEN EQUALS 28.
32) What is the formula for the circumference of a circle? C=2 PI TIMES RADIUS (2Pi R) OR
PI TIMES DIAMETER.
33a) The angles of a triangle determine its SHAPE, while the sides determine its SIZE.
33b) Similar triangles are equal in PROPORTION.
33c) If two corresponding angles are equal in two different triangles, then the two triangles are
at least SIMILAR BY THE NO CHOICE THEOREM.
34a) How do you find the x-intercept for non-horizontal straight lines? SET Y = 0
34b) How do you find the y-intercepts for non-vertical straight lines? SET X = 0
35a) What is true about the slopes of parallel lines? THEY ARE EQUAL
35b) What is true about slopes of perpendicular lines? THEY HAVE OPPOSITE
RECIPROCAL SLOPES
36) The intersection point of two straight lines in a plane is the SOLUTION in a systems of
equations problem.
37) A team won 18 of its 30 games, with no ties. What fraction of the 30 games did it lose? 12
OVER 30 OR 2 FIFTHS.
38) State the distance formula SQUARE ROOT OF THE SUM OF THE SQUARES OF THE
X COORDINATES AND THE Y COORDINATES.
39) State the mid-point formula SUM OF THE X COORDINATES OVER 2, SUM OF Y
COORDINATES OVER 2.
40) What degree measure is formed when an angle is inscribed in a semicircle? 90 DEGREES
41) When solving for a variable in an inequalities problem, if you multiply or divide by a
negative number, what do you need to do to the inequality sign? SWITCH THE SIGNS
42) If an angle is created from a straight line, what do the two angles add up to? 180 DEGREES
43) Percents break anything into ONE HUNDRED parts.
44) Reciprocals are two numbers when multiplied equal ONE
45) The set of inputs into a function is called the DOMAIN and the set of outputs is called the
RANGE.
46) State the zero product property IF TWO OR MORE FACTORS ARE MULTIPLED WITH
PRODUCT EQUALING ZERO, ONE OF THE FACTORS MUST EQUAL ZERO.
47) i equals the square root of NEGATIVE ONE. i squared equals NEGATIVE ONE
48) The diagonals of a squares and rhombi are PERPENDICULAR BISECTORS.
49) What to the diagonals of a parallelogram do to each other? THEY BISECT EACH OTHER