ACT
if a b and c are positive integers such that a^b=x and c^b=y then xy=?
(ac)^b
equation for a circle
(x-h)^2 + (y-k)^2 = r^2
how do you rewrite (3-x)
-1(x-3)
If g(x) is a transformation that moves f(x) three units to the right and then reflects it across the x-axis, then g(x) =
-f(x- 3)
sin^2 + cos^2 =
1
tan 45°
1
circumference of an arc
2πr times (degree measure of arc/360)
Volume of a sphere
4/3πr³
surface area of a cube
6s²
a hexagon always has how many distinct diagonals
9
The triangular shape is an illusion resulting from one significant addition to the process__ dust.
:
i^0 i^1 i^2 i^4
= 1 = i = -1 = -i (repeats)
Which of the following figures in a plane separates it into half-planes?
A line (not a line segment)
misplaced modifier
A modifier that is not placed near the word it modifies (The jacket was too small on the clothes rack, should be- the jacket on the clothes rack was too small)
Area of a trapezoid
A=1/2h(b1+b2)
Area of a parallelogram
A=bh
area of a circle
A=πr²
oxford comma
ALWAYS USE
affect vs effect
Affect is usually a verb meaning "to influence." Example: His opinion will affect my decision. Effect is usually a noun meaning "result" or "force." Example: His opinion had a great effect on my decision
Among vs. Between
Among is used with more than two items. Example: The scientist is living among a group of native people. Between is used with two items. Example: The race between Amy and Jenny was very close.
amount vs number
Amount is used to denote a quantity of something that cannot be divided into separate units. Example: There was a small amount of water in the glass. Number is used when the objects involved are discrete or can be counted. Example: A large number of students participated in the festivities.
Assure, Ensure, Insure
Assure means "to convince," or "to guarantee" and usually takes a direct object. Example: I assure you that I will not be late. Ensure means "to make certain." Example: Ensure that the door is locked when you leave. Insure means "to guard against loss." Example: Please insure this package for $100
all proteins contain
C, H, O and N
Compare to vs Compare with
Compare to means "assert a likeness." Example: My grandmother often compares me to my mother. Compare with means "analyze for similarities and differences." Example: The detective compared the photograph with the drawing.
Complement vs Compliment
Complement is a noun or verb implies "something that completes or adds to" something else. Example: The dessert was a tasty complement to my meal. Compliment is a noun or verb that implies "flattery or praise." Example: Pam appreciated Mike's compliment on her high test scores.
Convoluted
Complicated
Percent Change Formula
Difference/original *100
Might of
Doesn't exist (it's might have)
An isosceles triangle contains three angles that measure 40°, x°, and y°. Which of the following CANNOT be true?
Every triangle has three angles that add up to 180°, and an isosceles triangle has two equivalent angles. Therefore, the three angles of this triangle are either 40° + 40° + 100° or 40° + 70° + 70°. In any case, this triangle can't include a 50° angle
farther vs further
Farther refers to distance. Example: Matt traveled farther than all of the others. Further indicates "additional degree, time, or quantity." Example: The airline representative told us to expect further delays.
fewer vs less
Fewer refers to units or individuals in general quantities Example: Fewer students went on the class trip this year. Example: I weigh fewer pounds this year than I did last year. Less refers to quantities that can be counted Example: There is less air in my bicycle's front tire than in its rear tire. Example: I weigh less this year than I did last year.
if 2⁵ⁿ⁻²=8⁴ⁿ⁺⁷, then what does n equal?
First, both the bases have to be the same to set the exponents equal, recognize that 8= 2³, so multiply 8's exponent by 3 to make the base 2 and then set the exponent equal
Rational symmetry
If a figure can be rotated less than 360 about a point so that the image and the pre-image are indistinguishable, the figure has rotational symmetry
If I'm lucky, there is a creek, or a pond, to discover
If I'm lucky, lucky, there is a creek or a pond Nouns conjoined with "or," as in the highlighted portion, stand on equal footing. They should not have any intervening commas.
On Friday, a computer was originally priced at $800. On the following Wednesday, the price was reduced by 15%. On the following Friday, the price was further reduced by 20%. What percent of the original price was the final price?
If a price is reduced by 15%, then 85% of the original price is retained. Likewise, if a price is reduced by 20%, then 80% of the original price is retained. If a price is reduced by 15% and then again by 20%, the percent of the original price that remains is (85%)(80%) = (0.85)(0.80), or 0.68, which is equivalent to 68%.
Given similar rectangles QUAD and RECT, the ratio of sides QU to RE is 1:4. If the area of QUAD is 12, what is the area of RECT?
If the ratio of the sides of the two rectangles is 1:4, the ratio of the areas is (1:4)2 = 1:16. Set up a proportion to get x=192
ascending order
In order from the lowest value to the highest. e.g. 1-9 or A-Z.
The length of one side of any triangle is always _______ the sum and ________ the difference of the lengths of the other two sides.
LESS THAN the sum GREATER THAN the difference
lay vs lie
Lay means "to put" or "to place," and takes a direct object. Example: Please lay your scarf on the back of the chair. Lie means "to recline, rest, or stay," or "to take a position of rest." This verb does not take a direct object. Example: Carrie likes to lie down when she gets home from school.
Maria posted a time of 37 minutes and 29 seconds for a 5-mile running course. About how many miles per hour did she average during the run?
Maria ran 5 miles in 37 minutes 29 seconds, which is about 37.5 minutes. To solve for miles per hour, first calculate how long it took Maria to travel one mile. 37.5 minutes/5 miles=7.5 minutes/1 mile, or 1 mile in 7.5 minutes. To convert this into miles per hour, simply multiply by the number of minutes there are in one hour: (60 minutes/1 hour)×(1 mile/7.5 minutes)=8 miles per hour.
Credulity
Naivete
Conviction
Strongly held belief
Sin/Cos =
Tan
Contentious
Quarrelsome
Constraint
Repression of feelings
Weather conditions at this facility, which sits atop its namesake's 6,288-foot peak in New Hampshire, HAS earned the location the nickname "Home of the worlds worst weather."
Should be HAVE EARNED, because it was the weather conditions (plural) that earned the location its name
that vs which
That is used to introduce an essential clause in a sentence. Commas are not normally used before the word that. Example: This is the book that Jenny recommended I read. Which is best used to introduce a clause containing nonessential and descriptive information. Commas are required before the word which. Example: That book, which is old and tattered, is a favorite of mine.
Rhombus Diagonals
The diagonals of a rhombus are perpendicular, and they bisect each other (you can make a right triangle with the 90 angle and use the Pythagorean therom to find the length of each side)
A cylindrical can of pineapple juice contains 350cm3 of liquid. If the can is 14πcm tall, what is the diameter?
The formula for the volume of a cylinder is πr2h. The question is asking for diameter, so first solve for r, then double it. 350= πr2(14π) r2= 25 cm r= 5 cm Since the radius is 5 cm, the diameter is 10 cm. Thus the answer is 10 cm.
set vs sit
The verb set takes a direct object, while the verb sit does not. Example: Please set the glass down on the table. Example: Please sit in the chair next to mine.
What is the y-coordinate of the point of intersection of the lines y = 3x - 7 and y = 5x + 5 in the standard (x, y) coordinate plane?
This can be solved easily by the substitution method. 5x + 5 = 3x - 7 is equivalent to 2x = -12. Therefore x = -6. But we were asked for the y-coordinate. Using the equation y = 3x - 7 and substituting (-6) for x we find that y = 3(-6) - 7 = -25
Two trains running on parallel tracks are 600 miles apart. One train is moving east at a speed of 90 mph, while the other is moving west at 75 mph. How long, in hours rounded to the nearest hundredth, will it take for the two trains to pass each other?
This is a standard Rate × Time = Distance problem. Since the two trains start 600 miles apart, you know that their combined distance traveled must equal 600. Using the R×T=D formula, you can say that (Rate of Train 1 × Time of Train 1) + (Rate of Train 2 × Time of Train 2) = 600. You know how fast the trains are moving, and their total distance, but you do not know the time, so solve for T. Train 1 travels at 90 mph for T hours, while Train 2 travels at 75 mph for T hours. Your equation will look like this: 90 T + 75 T = 600 165 T = 600 T= 3.64 hours Thus the answer is 3.64 hours.
At the company YouGroove, 35 employees work in the sales department and 50 employees work in the operations department. Of these employees, 15 work in both the sales and the operations departments. How many of the 110 employees at YouGroove do NOT work in either the sales or the operations departments?
To solve this problem, use the group formula: Total = Group1 + Group2 - Both + Neither. In this problem, that means 110 employees = (35 sales) + (50 operations) - (15 both) + Neither. Solve for Neither = 40
compound verbs
Two or more verbs in one sentence that have the same subject, never use a comma to separate them example: Comparison of a child's development to universal standards and norms is discouraged, since it is believed that children naturally develop in different ways and acquire skills at different times.
Volume of a rectangular prism
V=lwh
Volume of a cylinder
V=πr²h
aqueous solution
a solution in which water is the solvent
isosceles triangle
a triangle with at least two congruent sides
dangling modifier
a word or phrase that modifies a word not clearly stated in the sentence (Coating the sidewalk, we walked through the snow. Should be-We walked through the snow coating the sidewalk)
Determinant of Matrix
ad/bc
cotangent
adjacent/opposite (reciprocal of tangent)
Proteins are composed of
amino acids
angles of a trapezoid
angles along the same leg are supplementary
Acclaim
applaud
nth term of a geometric sequence
aₙ= a₁×r ⁿ⁻¹
nth term of an arithmetic sequence
aₙ=a₁+(n-1)d
use a colon...
before a list after an independent clause that is followed by information that directly modifies or adds to the clause Colons may also precede direct quotations and should be used in business salutations and titles.
organic
carbon containing
prokaryotic cell
cell in which the DNA is in a nucleoid
Although these snowflakes appear to have a triangular shape___ they actually have a hexagonal pattern
comma
In general, details introduced by the word "including" must be set apart from the clause with a ...
comma "The Louvre contains some of the most famous works of art in the history of the world including the Mona Lisa by Leonardo DaVinci and the Venus de Milo by Michelangelo."
indiscriminate
confused
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Frighten
daunt
its'
does not exist
Articulate
effective
Parallel lines have ____ slopes, Perpendicular lines have ____ slopes
equal neg. reciprocal
intreped
fearless
the number of solutions that a polynomial has is represented by its
greatest exponent
lament
grieve
inscrutable
hard to understand
Detrimental
harmful
the decimal construction of 5/13 repeats and can be written as .384615384615... what is the 99th digit to the right of the decimal point
look for a pattern, this decimal repeats in a 6-digit pattern. That means that the 6th digit is 5, and so is the 12 digit, the 18th digit, and the 24th digit and so on. Because 96 is a multiple of 6, the 96th digit is also 5, the 97th digit is 3, the 98th is 8 and the 99th is 4
secant
hypotenuse/adjacent (reciprocal of cosine)
Cosecant
hypotenuse/opposite (reciprocal of sine)
When data points are graphed on a XY-graph, independent variables are usually on the ______, and dependent variables on the ______
independent = x-axis dependent = y-axis
both a colon and a semicolon must be after an
independent clause (complete sentence)
Eukaryotic cell
is any organism whose cells contain a nucleus and other organelles enclosed within membranes (as opposed to cells like bacteria that are prokaryotic)
Use a semicolon to...
join closely related independent clauses when a coordinate conjunction is not used with conjunctive adverbs to join independent clauses. to separate items that contain commas and are arranged in series. separate coordinate clauses when they are joined by transitional words or phrases.
A square root function is undefined in the real number system whenever the expression under the radical is
less than zero
Convert radians to degrees
multiply by 180/π
Convert degrees to radians
multiply by π/180
enigma
mystery
semicolons and colons
neither a semicolon nor a colon should be used before the phrase such as
Probability of two, mutually exclusive, outcomes both happening is
number of desired outcomes divided by total number of possible outcomes
Eccentric
odd
elucidate
odd
DNA contains the genetic information needed for making
proteins (protein synthesis)
IC__IC
semicolon
geometric mean
the mean of n numbers expressed as the n-th root of their product ex: The geometric mean of 3 positive numbers is the cube root of the product of the 3 numbers. What is the geometric mean of 2, 4, and 27? find the cube root of 2x4x27=216, Anwser=6
Amplitude
the measure of a wave from the vertical center to the crest
add an apostrophe and a s to form
the possessive of singular nouns, plural nouns, or indefinite pronouns that do not end in "s". My friend's house is at the end of the street.
on a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that are 2 1/2 inches apart?
there are five .5 inches in 2.5 inches, so multiple 18 and 5, (18)(5)=90
add an apostrophe
to form the possessive of plural nouns ending in "s" to the last noun to indicate joint possession to all nouns to indicate individual possession to indicate contractions *Do not use an apostrophe with a possessive pronoun*
forgo
to obstain from
average speed
total distance divided by total time
comma splice
two sentences joined incorrectly with only a comma (when you choose an option on the ACT that changes the sentence, always re-read the sentence and determine if the new sentence contains a comma splice)
Ambiguous
unclear
reflectional symmetry
when one half is a mirror image of the other half
That vs. Who
who is the pronoun for a person or people, and that is the pronoun for everything else.
Which of the following mathematical expressions is equivalent to the verbal expression "A number, x, squared is 39 more than the product of 10 and x" ?
x2 = 39 + 10x
Inverse proportion equation
y = k/x
Direct proportion equation
y = kx
Inversely proportional relationship
y is increasing as x is decreasing
equation of a parabola
y=ax^2+bx+c
if g(X)= cscX (tanX), then what does g(X)=
you need to use reciprocal trig ratios, tanX= sinX/cosX, to rewrite the expression write: cscXtanX= 1/sinX x sinX/cosX=1/cos= secX (reciprocal of cos)
area of an arc
πr^2 times (degree measure of arc/360)
