NCE PRACTICE EXAM

-3ab + 4ac - 2ad = -(3ab - 4ac + 2ad)

-3ab + 4ac - 2ad = -3ab + 4ac - 2ad

If X represents the amount given to one son, $500 - X represents the amount given to the other son.

5X = 20

X = 20 ÷ 5

X = 4

X - 5 = 15

X = 15 + 5

X = 20

3X + 7 - 2 = 8

3X + 5 = 8

3X = 3

X = 3 ÷ 3

X = 1

If Irene is N years old and Tom is twice as old as Irene, the algebraic formula to show how old Tom is would be 2 x N or 2N.

If John starts with B bats and buys C more bats, the total number of bats John has would be represented by the formula B + C.  

When John gives D bats away, the sum of B + C would subtract D bats to determine how many he has left. 

So, the formula is B + C - D.
 

There are a variety of ways to show multiplication, L x Y.

LY
L · Y
(L)(Y)

 

3x + 6x = 9x

5a + 2b - b + 4a =

5a + 4a + 2b - b =

9a + b
 

If a = 2, b = 3 and c = 4,

3abc =

3(2)(3)(4) =

6 x 12 = 72

 

8 + 3(8) = 32

9 + 3(9) = 36

10 + 3(10) = 40

11 + 3(11) = 44


 

i = l x r x t

l = $500, r = 6% and t = 4 years

l = $500 x .06 x 4

i = $30 x 4

i = $120

 

A dependent variable is a variable that depends on one or more other variables. In this equation, V depends on the value of m.

An independent variable is a variable that can have its value chosen without considering the values of other variables.  In this equation, m is an independent variable.

A constant is a value that does not change. In this equation, 3 is a fixed number that will not change.

A coefficient is a number used to multiple a variable.  In this equation, 4 is a coefficient of the independent variable w.

v = bdt

v   = d
bt
 

B = 1hm
        2

2B = 1hm

2B = h
m

The absolute value of a number, even a negative number, is a positive number.

- 3 + (-14) =

- 3 - 14 = - 17

20 - (-6) =

20 + 6 = 26

3x - 2y + 2y + 3z + 2z - 4x - 5y = 

 3x - 4x - 2y - 5y + 2y + 3z + 2z =

-x - 5y + 5z

6x - 10 = 4(x + 3)

6x - 10 = 4x + 12

6x = 4x + 22

2x = 22

x = 11

x - 6 = 17

x = 17 + 6

x = 23

Grouping symbols such as parentheses, brackets and braces in math will contain numbers, variables and operations. The grouping symbol tells you to do the operation first. An arrow, on the other hand, is an implicaiton notation to show that both sides of an notation are equal.

If a minus sign appears outside of a parentheses, the minus sign changes the terms within the parentheses when the parentheses is removed. For example,

- (2x - 4y)

-2x + 4y

If x = 5,

6x + 2x - x =

6(5) + 2(5) - 5 =

30 + 10 - 5 = 35

If 10 is separated into two parts, one of which is y, the second part will be 10 - y.

x = 1st number

x + 1 = 2nd number

x + 2 = 3rd number

3x = x + 1 + x + 2 + 8

3x = 2x + 11

x = 11

7/5 = 210/x

7x = 1,050

x = 150

When factoring, look to see what you can take out of a parentheses to put out front of it.  It is the opposite of distributing in polynomial expressions.  

The first term 5x can be factored (5)(x).

The second term 15 can be factored (5)(3).

5 is the only factor common to both terms.  Divide out the 5 from the terms and move the common factor to the front of the parentheses.

Remember, when dividing 15 by 5, a 3 is left over.

5x/5 - 15/5 = x - 3

Move the common factor to the front.

5(x - 3)