Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

ACT Test-taking > Math > Flashcards

Math Flashcards

You may prefer our related Brainscape-certified flashcards:
SAT® Prep flashcards
1
Q

What do you read first on long word problems?

A

Beginning and end

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What are natural numbers?

A

Positive counting numbers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What are integers

A

Natural numbers with their negative counterparts

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What are rational numbers

A

Numbers that can be written as a fraction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What are irrational numbers

A

Numbers that can’t be written as a fraction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What are conplex numbers.

A

Imaginery numbers

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Difference of two squares

A

(A^2+B^2)(A^2-B^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Square of a sum

A

A^2+2AB+B^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Square of a difference

A

A^2-2AB+B^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Difference of two cubes

A

(A-B)(A^2+AB+B^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

Sum of two cubes

A

(A+B)(A^2+AB+B^2)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Cube of a sum

A

A^3+3A^2B+3AB^2+B^3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Cube of a difference

A

A^3-3A^2B+3AB^2-B^3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the inverse of a log?

A

An exponential function
(Log3x=5)=(3^5=x)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is a reciprocal?

A

Inverse fraction

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is prime factorization?

A

Factoring a number down until its no longer divisible by natural numbers.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is cosecant or csc of Theta?

A

Reciprocal of sin or 1/sin

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is secant or sec of theta?

A

1/cos

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What is cot of theta?

A

1/tan

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is the standard equation of a circle?

A

(X-H)^2 + (Y-K)^2=R^2
H,K= Circle’s center

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

How do you factor by grouping?

A

Section parts of the polynomial, factor common factors, then rewrite the equation.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What are A and B in A[sin(Btheta)]

A

A=amplitude
B=period

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What are special trig identities?

A

Sin^2theta + cos^2theta = 1
Sin of theta/ cos of theta = tan of theta

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Whatis the formula for averages?

A

TAN
Total=Average×Number of items
Ex: 522 total test points divided by 6 test means the average score is 87

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

How can you rewrite multiplying logarithms?

A

Add them
Log(xy) = Log(x)+log(y)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

What do you do when dividing logarithms?

A

You subtract them
Log (x/y) = log(x)-log(y)

27
Q

What’s the formula for simple interest?

A

I=PRT
Interest=principle×annual rate×total time

28
Q

What’s the determinant of a 2by2 matrix?

A

[Ab over cd] = ad-bc

29
Q

Whats the equation for finding the hypotenuse of an isoceles right triangle?

A

The hypotenuse equals the product of one of the sides and the root of 2

30
Q

What is the expected value formula?

A

Multiplying the number of items in a row by their own probability then adding those outcomes together.

31
Q

How do you find the area of a circle?

A

πr^2

32
Q

How do you find the circumference of a circle?

A

2πr

33
Q

How do you solve combination problems?

A
  1. Figure out the number of slots you need to fill.
  2. Fill in those slots with how many times its value can change according to the rule.
  3. Multiply each slot together.
    Ex: In the word HAWKS, how many ways can you rearrange the letters so none repeat and W goes last?
    4×3×2×1×1=24
34
Q

How do you write a quadratic function in vertex form?

A

f(x) = a(x^2-h)+k
(h,k) = vetices
h = -b/2a
k = -determinant/4a
Determinant = b^2-4ac

35
Q

How do you convert radians to degrees?

A

Degrees(π)/180

36
Q

How do you convert radians to degrees?

A

Multiply degrees by 180 then divide by π

37
Q

20^2

A

400

38
Q

30^2

A

900

39
Q

25^2

A

625

40
Q

Multiplying matrices

A

Multiply each row of the first matrix by each column of the second matrix.

41
Q

What’s a substitute for the distance formula?

A

Picture the distance like the hypotenuse of a right triangle

42
Q

Commom right triangles

A

3-4-5
6-8-10
5-12-13
7-24-25

43
Q

Standard equation of an eclipse

A

(x-h)^2/a^2 + (y-k)^2/b^2 = 1

Here, (h, k) represents the center of the ellipse, “a” is the semi-major axis (the distance from the center to the farthest point on the ellipse in the x-direction), and “b” is the semi-minor axis (the distance from the center to the farthest point on the ellipse in the y-direction).

Note that if “a” and “b” are equal, then the ellipse is a circle. Additionally, if “a” is greater than “b,” the major axis is along the x-axis, and if “b” is greater than “a,” the major axis is along the y-axis.

I hope this helps! Let me know if you have any further questions.

44
Q

Exponential growth formula

A

y = a * (1 + r)^t

Here,
- “y” represents the final value or the value at time “t” in the exponential growth.
- “a” is the initial value or starting point.
- “r” is the growth rate expressed as a decimal (not a percentage).
- “t” is the time period or the number of intervals elapsed.

In this formula, the exponential term (1 + r)^t represents the factor by which the initial value “a” grows over time. By multiplying the initial value “a” with this exponential factor, we can calculate the final value or the value at any specific time “t”.

45
Q

What is the hypotenuse of a 30-60-90 triangle

A

Smallest side time 2

46
Q

How do you find the second longest side of a 30-60-90 triangle?

A

Smallest side times the root of 3

47
Q

What is GCF

A

The biggest factor that goes into all numbers being factored.

48
Q

What’s the area of a triangle?

A

Base times heighth divided by 2

49
Q

What’s the pythagoream theorm?

A

A^2×B^2=C^2

50
Q

How do you divide fractions?

A

Invert the second fraction and multiply horizontally

51
Q

Area of a pyramid

A

Area of the base, times the heighth, divided by 2.

52
Q

What is the least commom multiple?

A

The smallest multiple two numbers can go into.

53
Q

What is a prime number?

A

A number only divisible by 1 and itself?

54
Q

What is a multiple?

A

A number divisible by other numbers.

55
Q

How do you add matrices?

A

Add their corresponding parts.

56
Q

What are supplementary angles?

A

Numbers that add to 180°

57
Q

What is an opposite reciprical?

A

Opposite sign and inverse fraction.

58
Q

What’s the standard form of a quadratic function?

A

f(x) = ax^2+bx+c

59
Q

How do you square root an imperfect square?

A

Factor the imperfect square and attach its remainder

60
Q

What is a factorial

A

The product of all of a numbers factors.

61
Q

Tough problem guessing tricks

A

Plug and chug
Plug in C

62
Q

What’s the area of a trapazoid?

A

((a+b)/2)h
Average of the top and bottom times the height

63
Q

What do you do with an inequality when yoh divide by a negative?

A

Flip the inequality

ACT Test-taking (5 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions