Mathematics 3

Question 1

what is the formula for the axis of symmetry of a parabola?

Answer 1

x = -b/2a

Question 2

What is step one of solving a quadratic equation by completing the square?

Answer 2

express as x squared + px = q

Question 3

What is step two of solving a quadratic equation by completing the square?

Answer 3

Add the square of half the coefficient of x to both sides

Question 4

What is step three of solving a quadratic equation by completing the square?

Answer 4

Replace the perfect trinomial square by its binomial squared

Question 5

What is step four of solving a quadratic equation by completing the square?

Answer 5

Take the square root of both sides

Don’t forget square roots can usually be positive or negative

Question 6

What is the quadratic formula?

Answer 6

x = -b +- sqroot of b2 - 4ac all over 2a

Question 7

Every quadratic equation has two roots.

Answer 7

If the product of two factors is zero, then one or the other factors or both must equal zero.

Question 8

What is a reciprocal of a number?

Answer 8

1 divided by the number

Question 9

Rule 1 of Reciprocals

Answer 9

The fractions a/b and b/a are reciprocals of each other, that is, the reciprocal of a fraction is the fraction inverted

Question 10

Rule 2 of Reciprocals

Answer 10

The product of two reciprocals is 1

Question 11

Rule 3 of reciprocals

Answer 11

To divide by a number or a fraction, multiply by it’s reciprocal

Question 12

Rule 4 of Reciprocals

Answer 12

To solve an equation for an unknown having a fractional coefficient, multiply both members by the reciprocal fraction.

Thus if 2/3x = 10 multiply both sides by 3/2. x = 30/2 x = 15

Question 13

If a fraction means division, what does 3/4 mean?

Answer 13

3 divided by 4

The numerator is the dividend and the denominator is the divisor.

Question 14

If x and y vary inversely as each other, and a value of either x or y is multiplied by a number, then the corresponding value of the other is ________ by the same number.

Answer 14

Divided

Question 15

If the length of a rectangle is doubled and the width is halved, its area _______.

Answer 15

Remains constant

Question 16

What is the formula for an inverse variation with a constant?

Answer 16

xy = k

Question 17

What follows from xy = k?

Answer 17

X and y vary inversely as each other

x and y are inversely proportional to each other, that is x2/x1 = y1/y2

Question 18

what follows from y = kx

Answer 18

x and y var directly as each other

x and y are directly proportional to each other, that is x2/x1 = y2/y1

Question 19

A variable in algebra is a letter which may represent

Answer 19

any number of a set of numbers under discussion when the set contains more than one number

Question 20

In algebra, a constant is any letter or number which

Answer 20

has a fixed value that does not change under discussion. The letter k is used to represent a constant while the letters x, y, and z represent variables.

Question 21

What is an adjacent angle?

Answer 21

Angles sharing the same vertex and a common side between them

Question 22

What are complementary angles

Answer 22

Two angles the sum of whose measures equals 90 degrees

Question 23

supplementary angles

Answer 23

two angles the sum of whose measure equals 180 or a straight angle

Question 24

What is a proportion?

Answer 24

An equality of two ratios

2:5 = 4:10 or 2/5 = 4/10

Question 25

The fourth term of a proportion is the ____________

Answer 25

fourth proportional to the other three taken in order

Question 26

The means of a proportion are its

Answer 26

middle terms, that is, its second and third terms

Question 27

The extremes of a proportion are its ____________.

Answer 27

outside terms, that is, its first and fourth terms

Question 28

If a:b = c:d, what follows?

Answer 28

ad = bc

Question 29

In any proportion, the ________ are equal

Answer 29

cross products

Question 30

In any proportion, the product of the __________ the product of the extremes.

Answer 30

means equals