Algebra

Question 1

Answer 1

Question 2

What does it mean when a problem says “express y in terms of x”

Answer 2

Question 3

Simply the following :

Answer 3

Question 4

What does it suggest when you see :

A x B = 0 Or x(x + 100) = 0

Answer 4

Question 5

What must you do to a quadratic equation before you factorise and solve it?

Answer 5

Quadratic equations should be set equal to zero and should be in the form below :

Question 6

Answer 6

Question 7

Answer 7

Question 8

Answer 8

Question 9

Answer 9

Question 10

Answer 10

Question 11

Answer 11

Question 12

What are the six testing cases, for unknown numbers, algebraic inequalities, integers

Answer 12

Question 13

Answer 13

Question 14

Answer 14

Question 15

A. When can you add inequalities

B. When can you subtract inequalities

Answer 15

A. You can add inequalities when they are facing same direction and are the same sign

B. You can subtract inequalities when they are facing opposite direction.

Question 16

Explain the following terms below :

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

Translate the following words into math operations like (x, - , /, +) and inequalities.

Answer 19

Question 20

1. In order to combine inequalities between a common term and two other terms, the common term must have what relation to the other inequalities ?
2. If R < S and S < T, show the inequality S combined ?
3. If A < C and T < C, the show the inequality?

Answer 20

1. For combining to work, the common term must be greater than one term and less than another term, see question 2.
2. R < S < T
3. You cannot combine the inequality as both terms are less than C, one has to bigger and one has to be smaller than C for combination to work

Question 21

If all variables are positive integers where A > B and C > D, then which one is true?

1. ( A + C ) > ( B + D )
2. ( A + C ) < ( B + D )
3. ( B + C ) > ( D + A )
4. Cannot work out with the information provided

Answer 21

1. ( A + C ) > ( B + D ) = Correct, we can add inequalities in same direction, they must be always in same direction to add them, for example plug in numbers where :

A = 5, C = 2, B = 11 , D = 8

( 5 + 11 ) > ( 2 + 8 )

Question 22

If all variables are positive integers where A > B and D < C, then which one is true?

1. ( A - C ) < ( B - D )
2. ( A - D ) > ( B - C )
3. ( B - C ) > ( D - A )
4. Cannot work out with the information provided

Answer 22

2. ( A - D ) > ( B - C ), we can subtract inequalities that are facing opposite directions.

Suppose A = 20, B = 15, C = 12 , d = 10

Clearly 20 > 15 and 10 < 12, so :

(20 > 15) —(10 < 12) —————-
  10 > 3

Question 23

1. Which one of these must be greater than number x :
2. X + 2
3. 2x
4. X*2
5. Which one of these must be less than Number B :
6. B - 3
7. B*2
8. 3B
9. 1 & 3
10. All of them

Answer 23

1. X + 2 is greater than x, adding any positive integer to any “number” makes it bigger
2. One is the correct answer, subtracting any integer from negative or even positive number will make it smaller, it may be tempting to choose answer choice 4 but consider if B was to 0.

Question 24

1. Express 5 < X < 17 as an absolute value inequality.

Answer 24

Answer = Find average between two (5+17/2 = 11), so both 5 and 17 are a distance of 6 from 11. Now you can set up equation

Answer = [ x - 11 ] < 6

Question 25

Answer 25

Question 26

Answer 26

Answer = 21

Question 27

Answer 27

Question 28

What does defined mean? And what does it mean in a fraction

Answer 28

Defined means a certain problem is solvable, like in a calculator a problem which is unsolvable will give undefined. Such as 0 in denominator.

When you have defined in a question it means you cannot have a zero in the denominator.