COLEGIO SAN PATRICIOMath Practice for 3rd Period Exam

School Year 2010 – 2011

Binary System I. Convert each decimal number to the binary number it represents.

48 = 110000 104 = 1101000

II. Convert each binary number to the decimal number it represents.

1110010 = 114 10101 = 21

The Number Line

III. Write the missing numbers.

IV. Order the next numbers in the number line.

0 0.50 1 1½ 1.25 2

Verbal Phrases and Algebraic Expressions.

V. Answer the next problems.

Is it correct?

1. 2x + 6 = 12 CORRECT Two times a number, plus six is twelve.

2. (5) (6) − x = 25 INCORRECT5(6−x)=25

Five times the difference of six and a number is twenty five.

3. 8(4 + 9) = 104 CORRECT Eight times the sum of four and nine is one hundred four.

VI. Write each as an algebraic expression.

1. The difference of 10 and 5 10−5

2. The quotient of 14 and 7 14÷7

3. u decreased by 17 u − 17

4. The product of x and 7 7x

5. Twice q 2q

Problem Solving Using Algebraic Equations.

VII. Solve.

1. If 2/3 of the pizza is left, what part will you and your two friends get?

A: for each. (You divide 2/3 by the 3 friends)

2. My brother will be forty years old in four years (I wrote forty instead of four). Let b be the age of my brother now:

A: b) b+4 = 40, then you need to solve the equation. Do as follows: Checking Processb + 4 = 40 b + 4 = 40 b = 40 – 4 36 + 4 = 40 b = 36 40 = 40

3. Donna got 84 in a quiz, which includes 5-point bonus. Let x be the grade she would have had without the bonus.

A: c) x + 5 = 84, then you need to solve the equation. Do as follows: Checking Processx + 5 = 84 x+ 5 = 84 x = 84 – 5 79 + 5 = 84 x = 79 84 = 84

VIII. Write an equation.

1. I have to check 90 exams. I have checked 35. How many exams am I missing?

A: Possible equation: x + 35 = 90 I am missing 55 exams x = 90 – 35 x = 55

Checking Process: x + 35 = 9055 + 35 = 90

90 90

4. One trip is ¾ kms. If we decide to take 6 trips, how many kilometers are we going to travel?

A: 4 ½ kms. (You multiply ¾ by the 6 trips)

Distributive Property.

1. Apply the Distributive Property. 1. −6(a+8) 2. 6(−5n+7) 3. (1+9x)(-4x) 4. 7m(m-9)

-6a – 48 - 30n + 42 -4x – 36x² 7m² - 63m

Combining Like Terms

2. Simplify the expression. (Order it, then combine like terms, and simplify).

1. -5c + 3c + 9 – 2 -2c + 7 (this is the answer)

2. -4u² - u² + 10+8 -5u²+18 (this is the answer)

3.7x + (8 – 4x)7x + 8 – 4x7x – 4x + 8 3x+8 (this is the answer)

Equations

3. Find the value of the variable.

1. 2. 3. 4. 40 - 30 = 10x a = 33/3 n = 0 + 5 p = 20 + 20 10 = 10x a = 11 n = 5 p = 40 10/10 = x 1 = x x = 1Checking Process Checking Process Checking Process Checking Process 40 = 10x + 30 3a = 33 -5 + n = 0 p – 20 = 2040 = 10 (1) + 30 3(11) = 33 -5 + (5) = 0 40 – 20 = 2040 = 10 + 30 33 = 33 -5 + 5 = 0 20 = 2040 = 40 0 = 0

1. 20 5. 7. 8. x/2 = 20 – 10 k = 10 (2) 2x – 4 = 6 x = 60/3x/2 = 10 k = 20 2x = 6 + 4 x =20x= 10(2) 2x = 10 x = 20 x= 10/2 x= 5

Checking Process Checking Process Checking Process Checking Process x/2 + 10 = 20 k/2 = 10 3x – x - 4 = 6 3x =6020/2 = 10 20/2 = 10 3(5) – 5 – 4 = 6 3(20) = 60 10 = 10 10 = 10 15 – 5 – 4 = 6 60 = 60 10 – 4 = 6 6 = 6

4. Solve using the integers rules.

1. 7- (+8) – 5 2. 45 (-5) + |6| 3. 4 + (-5) 4. 5 – (-5+8) 7 – 8 – 5 -225 + 6 4 – 5 5 + 5 – 8 -1 – 5 - 219 -1 10 – 8 -6 + 2