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ATI TEAS 7. > Mathematics > Flashcards

Mathematics Flashcards

1
Q

What is the Pythagorean theorem used for?

A

To find the length of a side in a right triangle when the lengths of the other two sides are known (a² + b² = c²).

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2
Q

What does the slope of a line represent?

A

The rate of change of the line, showing how much the y-value changes for a unit increase in the x-value.

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3
Q

How do you calculate the perimeter of a triangle?

A

Add the lengths of all three sides.

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4
Q

What is an integer?

A

A whole number that can be positive, negative, or zero, not including fractions or decimals.

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5
Q

How do you solve the inequality 5x - 7 > 18?

A

Add 7 to both sides and then divide by 5 (x > 5).

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6
Q

How do you find the mode of a data set?

A

The mode is the number that appears most frequently in the data set.

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7
Q

How do you calculate the area of a parallelogram?

A

Base multiplied by height (Area = Base × Height).

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8
Q

What is the formula for calculating the volume of a rectangular prism?

A

Volume = Length × Width × Height.

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9
Q

How do you solve the equation 2x² = 18 for x?

A

Divide both sides by 2 to get x² = 9, then take the square root of both sides (x = ±3).

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10
Q

How can you determine if a number is divisible by 3?

A

A number is divisible by 3 if the sum of its digits is divisible by 3.

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11
Q

How do you calculate the diagonal of a square with side length s?

A

Use the formula
𝑑 = 𝑠 √ 2, where d is the diagonal.

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12
Q

What is the formula for the area of a trapezoid?

A

Area = 1/2 × (𝐵𝑎𝑠𝑒1 + 𝐵𝑎𝑠𝑒2) × 𝐻𝑒𝑖𝑔ℎ𝑡.

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13
Q

How do you convert a decimal to a percent?

A

Multiply the decimal by 100 and add the percent sign (%).

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14
Q

What is the difference between permutations and combinations?

A

Permutations consider order as important, while combinations do not.

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15
Q

How do you find the range of a data set?

A

Subtract the smallest value from the largest value in the set.

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16
Q

What is the formula for calculating simple interest?

A

Interest = Principal × Rate × Time.

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17
Q

How do you calculate the volume of a cylinder?

A

Volume = 𝜋𝑟^2ℎ, where 𝑟 is the radius of the base and ℎ is the height.

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18
Q

What is the Least Common Multiple (LCM) of two numbers, and how do you find it?

A

The LCM is the smallest number that is a multiple of both numbers. Find it by listing multiples or using the prime factorization method.

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19
Q

What is the complement of an angle measuring 30 degrees?

A

The complement is the angle that, when added to 30 degrees, equals 90 degrees. So, it is 60 degrees.

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20
Q

How do you simplify the expression (𝑥^2 𝑦)^3 ?

A

Use the power of a power property: 𝑥^6 y^3.

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21
Q

uestion: How do you find the slope of a line given two points on the line, (x1, y1) and (x2, y2)?

A

Use the formula slope =𝑦^2 − 𝑦^1 / 𝑥^2 − 𝑥^1

22
Q

How do you factor a quadratic expression like 𝑥^2 − 9 ?

A

Recognize it as a difference of squares: (x+3)(x−3).

23
Q

What is the Absolute Value of a number, and how is it represented?

A

he absolute value of a number is its distance from zero on a number line, represented as ∣𝑎∣.

24
Q

How do you solve the equation 2 / 3𝑥 = 8 ?

A

Multiply both sides by the reciprocal of 2/3 (which is 3/2) to find 𝑥 = 12.

25
Q

What are the steps to calculate compound interest?

A

Use the formula 𝐴 = 𝑃(1 + 𝑟/𝑛)^𝑛𝑡, where
𝐴 is the amount of money accumulated after n years, including interest. 𝑃 is the principal amount, 𝑟 is the annual interest rate, 𝑛 is the number of times that interest is compounded per year, and 𝑡 is the time the money is invested or borrowed for.

26
Q

How do you calculate the surface area of a sphere?

A

Use the formula 4πr^2, where 𝑟 is the radius of the sphere.

27
Q

What is a composite number?

A

A composite number is a positive integer that has at least one positive divisor other than one or itself.

28
Q

How do you find the common denominator of fractions like 1/4 and 1/6 ?

A

The common denominator would be 12, the least common multiple of 4 and 6.

29
Q

What is Euler’s Formula related to polyhedra?

A

V−E+F=2, where 𝑉 is the number of vertices,
𝐸 is the number of edges, and 𝐹 is the number of faces in the polyhedron.

30
Q

How do you determine if a set of points are collinear?

A

Points are collinear if the slope between any two pairs of points is the same.

31
Q

What is the formula for calculating the area of a circle?

A

Area = πr², where r is the radius of the circle.

32
Q

How do you solve the proportion 3/4 = x/12 ?

A

Cross-multiply to get 3 × 12 = 4x, then divide by 4 to solve for x:𝑥 = 9.

33
Q

What does it mean for two sets to be disjoint?

A

Two sets are disjoint if they have no elements in common.

34
Q

How do you convert a percentage to a fraction?

A

Divide the percentage by 100 and simplify the fraction if possible.

35
Q

How do you calculate the sum of the interior angles of a polygon?

A

The sum of the interior angles of a polygon with n sides is (𝑛 − 2) × 180 degrees.

36
Q

What is the difference between direct and inverse variation?

A

In direct variation, the variables change in the same way (as one increases, so does the other). In inverse variation, the variables change in opposite ways (as one increases, the other decreases).

37
Q

How do you calculate the diagonal of a cube with side length s?

A

Use the formula 𝑠√3, where s is the side length of the cube.

38
Q

What is a binomial, and how is it different from a trinomial?

A

A binomial is a polynomial with two terms. A trinomial has three terms.

39
Q

How do you graph the equation
𝑦 = −2𝑥 + 3 using the slope-intercept method?

A

Plot the y-intercept (3) on the y-axis, then from this point, use the slope (-2) to find another point (down 2 units, right 1 unit), and draw the line.

40
Q

How do you simplify the expression
4𝑥 − 3𝑦 + 2𝑥 + 5𝑦 ?

A

Combine like terms: 6𝑥 + 2𝑦.

41
Q

What are coprime numbers?

A

Coprime numbers are two or more numbers whose greatest common divisor is 1; they have no other common factors besides 1.

42
Q

How do you find the greatest common divisor (GCD) of two numbers?

A

The GCD of two numbers can be found using the Euclidean algorithm, which involves repeated division.

43
Q

What does the term ‘rationalize the denominator’ mean?

A

To rationalize the denominator means to eliminate any radicals (like square roots) from the denominator of a fraction by multiplying both the numerator and the denominator by an appropriate value.

44
Q

What is an asymptote in graphing?

A

An asymptote is a line that a graph approaches but never touches. Horizontal and vertical asymptotes occur in rational functions and some algebraic expressions.

45
Q

What is the Binomial Theorem and how is it used?

A

The Binomial Theorem provides a formula for expanding powers of binomials,
(𝑎 + 𝑏)^𝑛, involving binomial coefficients.

46
Q

How do you determine if a number is a perfect square?

A

A number is a perfect square if its square root is an integer.

47
Q

What is the difference between an arithmetic and a geometric sequence?

A

In an arithmetic sequence, the difference between consecutive terms is constant. In a geometric sequence, the ratio between consecutive terms is constant.

48
Q

How do you find the probability of a single event occurring?

A

Probability =
Number of favorable outcomes /
Total number of possible outcomes.

49
Q

How do you simplify the expression √12?

A

Simplify by factoring:
√12 = √4 × 3 = 2√3.

50
Q

What is the angle sum property of a triangle?

A

The sum of the interior angles of any triangle is always 180 degrees.

ATI TEAS 7. (4 decks)

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