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Grade 8Math

Oak Meadow

Coursebook

Oak Meadow, Inc.Post Office Box 1346

Brattleboro, Vermont 05302-1346oakmeadow.com

Item #b084010

iii

Grade

8 Contents

Introduction ..................................................................... vii

Lesson 1: Using a Calculator .......................................... 1Using a Calculator to Perform Basic Operations With DecimalsConverting Common Fractions To Decimals With a Calculator

Lesson 2: Converting Decimals to Percents ................ 13Finding a Percent of a Number Using a CalculatorFinding Percents in Word Problems

Lesson 3: Squares and Exponents ................................ 23Square Roots

Lesson 4: Negative Numbers ......................................... 33Directions and the Number LineAdding and Subtracting Signed NumbersAdding Signed Numbers

Lesson 5: Multiplying Signed Numbers........................ 43Dividing Signed Numbers

Lesson 6: Order of Operations ..................................... 51Addition and SubtractionParentheses in the Order of OperationsOrder of Operations with Multiplication

Lesson 7: Order of Operations with Division .............. 63Order of Operations with ExponentsPEMDAS—The Order of OperationsFractions in the Order of Operations

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Contents Grade 8 English

Lesson 8: Equations ....................................................... 77Addition Rule of EquationsThe Subtraction Rule of Equations

Lesson 9: Division Rule For Equations ......................... 85The Multiplication Rule For Equations

Lesson 10: Using Two Rules to Solve Equations ......... 93Variables, Terms, and Coefficients

Lesson 11: Combining Like Terms .............................. 103Negative CoefficientsTwo-step Evaluation Problems

Lesson 12: Using a Compass ...................................... 113Drawing an Equilateral TriangleConstructing a Perpendicular BisectorDrawing a Geometric Design

Lesson 13: Angles ......................................................... 125Right AnglesTypes of AnglesMeasuring AnglesCopying and Bisecting Angles by ConstructionBisecting an Angle

Lesson 14: Ratios ......................................................... 137Using Ratios to Compare PricesProportions

Lesson 15: Using Proportions in Word Problems .... 145Converting Units in Proportions

Lesson 16: Polygons ..................................................... 153TrianglesClassifying by AnglesClassifying by SidesSum of the AnglesCongruent and Similar TrianglesConstructing Triangles

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Grade 8 English Contents

Lesson 17: Formulas .................................................... 165Area of a RectangleDistance, Rate, and TimeTransforming Formulas

Lesson 18: First Semester Exam .................................. 173

Lesson 19: Creating Equations from Word Problems ........................................................ 181More Equations From Word Problems

Lesson 20: Equations for Parts of Numbers ............. 193Word Problems For Parts of Numbers

Lesson 21: Symbols of Inclusion ................................. 201Fractions in Brackets

Lesson 22: Factors of Whole Numbers ...................... 209Prime NumbersThird and Fourth Roots of NumbersGraphing Inequalities

Lesson 23: Evaluating Variables With Exponents ..... 219Multiplying Exponents

Lesson 24: Equations With Exponents ...................... 227Multiple-Term EquationsCombining Terms on Both Sides

Lesson 25: Areas of Triangles ...................................... 235The Pythagorean Theorem

Lesson 26: Pi and the Measures of a Circle ............... 245Pi and the Area of a Circle

Lesson 27: Geometric Solids ....................................... 255Volume of Solids

Lesson 28: Interest and Principal ............................... 265Compound Interest

Lesson 29: Finding the Mean and the Median .......... 273Advanced Ratio Problems

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Lesson 30: Fractions with Exponents ........................ 283Roots of Fractions

Lesson 31: Exponents with Negative Bases ............... 289Roots of Negative Numbers

Lesson 32: Scientific Notation .................................... 299Multiplying with Scientific Notation

Lesson 33: Functions ................................................... 307Finding Functions

Lesson 34: Recangular Coordinates ........................... 321Graphing a Line for an Equation

Lesson 35: Base 2 Numbers ........................................ 333Writing a Base 2 Number

Lesson 36: Second Semester Exam ............................. 343

Appendix ....................................................................... 353Answer Keys: Skill Practice and Application Practice ProblemsB-Tests For Enrolled Students

Contents Grade 8 English

23

Squares and Exponents

Grade 8

3When we multiply one number by the same number, we call this a square. We can find the square of any number by multiplying that number by it-self. So the square of 3 is 9, because 3 x 3 = 9, and the square of 5 is 25, because 5 x 5 = 25.

We call these numbers squares because this is how they are derived. For ex-ample, we can show 3 times 3 like this:

Each smaller square is 1 unit, so each side is 3 units long. When we count all the smaller squares within the figure we find there are 9 squares in all. So we can say that 3 times 3 equals 9, or the square of 3 is 9.

When we want to indicate repeated multiplication of any number, we do this with an exponent. We indicate the square of 3 by writing

23 . The small

2 that is at the upper right of the 3 is called an exponent, and the 3 is called the base. The exponent indicates how many times the number is to be used in the repeated multiplication. If we write this out in a horizontal format, we can see clearly what this means:

32 = 3 × 3 = 9We read numbers with exponents in the following way:

We read 32 as “3 to the second power,” or “3 squared.”

We read 53 as “5 to the third power,” or “5 cubed.”

We read 64 as “6 to the fourth power.”

We read 25 as “2 to the fifth power.”

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(continued)

Lesson 3 Grade 8 Math

Example 1: What is the value of 43?

43 means 4 × 4 × 4. We can write this out by hand like this:

4× 4

1 6× 4

6 4So we can say that 43 = 64. We can do this on a calculator as follows:

Step 1: Clear the calculator to make sure no previous numbers are entered.

Step 2: Enter 4.

Step 3: Press the × key to indicate multiplication.

Step 4: Enter 4.


Step 6: Enter 4.

Step 7: Press the = key to display the answer, which is 64.

We can also use exponents with decimal fractions, as follows:

Example 2: What is the value of 3.22?


Step 2: Enter 3.2.


Step 4: Enter 3.2.

Step 5: Press the = key to display the answer, which is 10.24.

If the base is larger, even a small exponent can cause the value of a number to increase very quickly, as in the following example:

Example 3: What is the value of 564?

If we look at the sequence of this at each stage of multiplication, we can see how quickly the size of the number increases:

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(continued)

Grade 8 Math Lesson 3

56 × 56 = 3,1363,136 × 56 = 175,616

175,616 × 56 = 9,834,496When a value increases quickly by means of an exponent, we say that the increase in the value is exponential, or that the value is increasing exponentially.

Square Roots

When we square a number, we multiply it by itself. To find a square root of a number, we find a number which, when multiplied by itself, equals the original number. Thus, the square root of 9 is 3, because 3 x 3 = 9. To indicate the square root of a number, we use a square root symbol, which looks like this:

Using this symbol, we read 25 as “the square root of 25.” We can write the solution to the problem like this:

25 5=

This means that when we multiply 5 times itself, we get 25.

Example 1: What is the square root of 49?

To solve this, we have to ask ourselves, “What number multiplied by itself equals 49?” We know that 7 x 7 = 49, so we can say that the square root of 49 is 7.

Example 2: What is the value of 64 ?

Since 8 x 8 = 64, the square root of 64 is 8.

Finding square roots for familiar numbers in the multiplication table is not difficult, but when we encounter other numbers we can use the square root key on a calculator. Look at the following example:

Example 3: What is the value of 729 ?


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(continued)


Step 2: Enter 729.

Step 3: Press the key to indicate the square root.

Step 4: The calculator displays the square root, which is 27.

You can also use your calculator to find the square root of a decimal number, as follows:

Example 4: What is the value of 32.64 ?


Step 2: Enter 32.64.

Step 3: Press the key.

Step 4: The calculator displays the square root, which is 5.7131427. Since square roots of decimal fractions will often be large decimal fractions themselves, we usually round them off to two decimal places. Using the basic rule of rounding, we get 5.71.

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Skill Practice A

Use your calculator to determine the value of the following terms. Do not round off decimal answers.

1. What is the value of 152?


3. What is the value of 6.34?




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Skill Practice A continued







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Skill Practice B

Use your calculator to determine the value of the following terms. Round off decimal fractions to two decimal places.

1. What is the square root of 169?

2. What is the value of 640 ?

3. What is the the value of 1,024 ?

4. What is the square root of 14.44?


6. What is the square root of 10,000?

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Skill Practice B continued



9. What is the value of 92.16 ?

10. What is the square root of 625?



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Grade 8 Math Lesson 3Math 8 Lesson 3 - 11

REVIEW 2

Use a calculator to solve decimal problems, and solve common fraction problems by hand. Round off longer answers to two decimal places.

1. 62.4 18.29− 2. 12.45

9.2× 3. 3 57 73 4÷

4. 0.63 3.49+ 5. 313 42 5+ 6. 7.9 0.65−

7. 9.76 14× 8. .7 32.1 9. 157 2×

10. 42 3.6÷ 11. 1 45 57 4− 12. 12.4 7.7+

Lesson 3 Review


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Lesson 3 Review continued

Use your calculator to solve the following problems.

Math 8 Lesson 3 - 12

Use your calculator to solve the following problems. 13. 576 14. 38.7

15. 415 16. 475.24 17. 25% of the people at Becky's church are under 18 years old. If there are

320 people in the church, how many are under 18? 18. Dennis loves to cook, and he has 60 recipes in his collection. 8 of his

recipes are for cookies. What percent of his total collection are cookie recipes? Round off the answer to a whole number.

19. Ricky bought a pair of pants for $29.95, and the clerk added sales tax of

6%. If he gave the clerk $40, how much change should he have received? (Round off the sales tax to the nearest cent)

20. Craig's cat Amadeus gave birth to 7 kittens. 5 of the kittens are female

and 2 are male. What percent of Amadeus's kittens are female? (Round off your answer to the nearest one percent)

17. 25% of the people at Becky’s church are under 18 years old. If there are 320 people in the church, how many are under 18?

18. Dennis loves to cook, and he has 60 recipes in his collection. 8 of his recipes are for cookies. What percent of his total collection are cookie recipes? Round off the answer to a whole number.

19. Ricky bought a pair of pants for $29.95, and the clerk added sales tax of 6%. If he gave the clerk $40, how much change should he have received? (Round off the sales tax to the nearest cent)

20. Craig’s cat Amadeus gave birth to 7 kittens. 5 of the kittens are female and 2 are male. What percent of Amadeus’s kittens are female? (Round off your answer to the nearest one percent)

33

Negative Numbers

Grade 8

4We can show a sequence of numbers using a number line like the one be-low. The arrows on each end of the number line show that the line contin-ues without end in both directions. The numbers that are marked on the number line are called whole numbers, and they include the number zero.

The whole numbers to the right of zero on the number line are known as positive numbers. To the left of zero are negative numbers. We can show them on the number line as follows:

Negative numbers are all the numbers less than zero, and they always have a minus sign in front of them. Each positive number has an opposite neg-ative number. The opposite of 5 is -5, and the opposite of 38 is - 38. Zero is between the positive and the negative numbers, so it is neither positive nor negative. All of the whole numbers on the number line (the positive whole numbers, the negative whole numbers, and zero) are called integers. Between the integers are all of the fractional numbers, both common and decimal fractions. We can call all of these numbers (except zero) signed numbers, because they have a sign, either positive or negative.

Positive numbers can be written with or without a plus sign. If there is no sign before a number, then it is a positive number.

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Negative Numbers

(continued)


Directions and the Number Line

When we move to the right on the number line, we are moving in a positive direction. When we move to the left on the number line, we’re moving in a negative direction. A positive direction is indicated by a plus sign, and a negative direction is indicated by a minus sign. For example, if we start with a +2 and move 3 units in a negative direction, the operation looks like this:

We could write this as 2 - 3, and we would say that 2 - 3 = -1.

If we start at +2 and move 3 units in a positive direction, the operation looks like this:

We could write this as 2 + 3, and we would say that 2 + 3 = 5.

Adding and Subtracting Signed Numbers

As we mentioned in the previous section, signed numbers include all positive and negative numbers. When we add or subtract signed numbers, we not only have to consider the operation itself (whether it’s addition or subtrac-tion), but we also have to consider the signs of the numbers themselves. To complete these operations correctly, mathematicians have developed certain rules and definitions. Let’s first look at a definition:

Absolute Value—The value of an integer without its sign.

The absolute value of -3 and +3 is 3

The absolute value of -12 and +12 is 12

Now that we know the meaning of absolute value, let’s look at the rules and some examples of adding signed numbers.

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Negative Numbers

(continued)


Adding Signed Numbers

Rule 1: If two numbers have the same sign, add their absolute values and give the sum the sign of the original numbers.

Example 1: 5 + 3 = 8

We add the absolute value of 5 and 3 and get 8. Since neither number has a sign, that means they are both positive, so the answer is also positive. (We could add the sign and make it +8, but since the original numbers didn’t have a sign, we leave it off the answer also).

Example 2: -5 + (-3) = -8

We add the absolute value of 5 and 3 to get 8. Since both signs are neg-ative, we give the answer a negative sign. We put the -3 in parentheses to show the difference between the addition sign and the sign of the number.

Rule 2: If two numbers have different signs, subtract the smaller absolute value from the larger and give the result the sign of the number with the larger absolute value.

Example 3: -4 + 2 = -2

The first number is negative and the second has no sign, so it’s positive. We subtract the absolute value of the smaller number from the absolute value of the larger number to get 2. Since the sign of the larger number is negative, then we make the answer negative also.

Example 4: 4 + (-2) = +2

The first number has no sign, so it’s positive, while the second number is negative. We subtract the absolute value of 2 from 4 and get 2. The larger number is positive, so the answer is positive.

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Negative Numbers

(continued)


Subtracting Signed Numbers

To subtract signed numbers, we must remember that subtraction is the inverse operation to addition. This means that we can use signed numbers to make any subtraction problem into an addition problem. We can use a number line to demonstrate this principle:

Example 1: 1 - 3

When we subtract 3 from 1, this gives the same result as if we started at 1 and added -3, because we are still moving from 1 in a negative direction on the number line. So we can say that 1 - 3 = 1 + (-3), and the answer is -2. Using this principle, there is only one rule for subtracting signed numbers:

Rule 1: To subtract signed numbers, add the first number and the oppo-site of the number being subtracted.

Example 2: 5 - 2

We can use the subtraction rule to add 5 and the opposite of 2, which is -2. (Since 2 doesn’t have a sign, it’s positive, so the opposite of positive 2 is negative 2).

5 - 2 = 5 + (-2)Then we can solve it using the same rules for adding signed numbers that we have just practiced:

5 - 2 = 5 + (-2) = 3Example 3: 2 - 7

Once again, the 7 doesn’t have a sign, so when we rewrite it as an addition problem we change the 7 to its opposite, which is -7.

2 - 7 = 2 + (-7)Then we solve it, using the rule of addition:

2 - 7 = 2 + (-7) = -5

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Negative Numbers

(continued)


Example 4: -8 - 3

-8 - 3 = -8 + (-3) = -11Example 5: -5 - (-6)

The sign of the second number is given, so we change the problem to addition and reverse the sign of the 6, as follows:

-5 - (-6) = -5 + (+6) = +1Example 6: 8 - (-4)

8 - (-4) = 8 + 4 = 12

For Enrolled StudentsBefore you continue with Lesson 5, send the Review and Test for lessons 3 and 4 to your teacher.

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Notes

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Skill Practice A

Solve the following expressions.

1. 10+(−4)=

2. −15+12=

3. −11+3=

4. 8+(−8)=

5. −9+(−3)=

6. 12+4=

7. 14+(−6)=

8. −7+(−12)=

9. 5+(−6)=

10. −4+(−3)=

11. 7+(−2)=

12. 3+(−4)=

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Skill Practice B

Solve the following expressions.

1. −2−(+3)=

2. 3−(+9)=

3. −11−(−4)=

4. 12−(+8)=

5. 15−(+7)=

6. −4−(−9)=

7. 10−(+10)=

8. 8−(+2)=

9. 3−(+6)=

10. −7−(−3)=

11. 9−(−2)=

12. 5−(+6)=

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Math 8 Lesson 4 - 9

TEST 2


1. ( )2 5− + − 2. 13.6 8.9+ 3. ( )14 9− +

4. ( )3 7− − − 5. 155 2÷ 6. .409 .8×

7. 1 13 22 × 8. 0.3 24.9 9. ( )4 6+ −

10. 14 2.3÷ 11. 8.1 0.42− 12. 28.735.4×

Lesson 4 Test


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Lesson 4 Test

13. Write 352 as a decimal.

14. Write 23 as a decimal rounded off to hundredths

15. What is 38% of 1,200?

16. What percent is 47 out of 50?

219

Evaluating Variables with Exponents

Grade 8

23We have learned how to evaluate an algebraic expression by substituting numerical values for the variables, as in the following example:

Example 1: Evaluate 3x if x = 2

We substitute the given value into the expression and simplify:

3x=3(2)=6If one of the variables is the base of an exponential expression, we can evaluate it the same way, by substituting the given value for the variable.

Example 2: Evaluate x2 if x = 3We substitute the given value into the expression and simplify:

x2=32=3⋅3=9This same process applies if the variable is the exponent itself, rather than the base, as in the following example.

Example 3: Evaluate 5x if x = 2We substitute the given value into the expression and simplify:

5x=52=5∙5=25This same process also applies when we are evaluating roots. Look at the following examples:

Example 4: Evaluate 4 n if n = 81We substitute the given value into the expression and simplify:

4 4n 81 3= =

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Evaluating Variables with

Exponents

(continued)


We can also substitute for the power of the root, as follows:

Example 5: Evaluate n 125 if n = 3We substitute the given value into the expression and simplify:

3n 125 125 5= =

Multiplying Exponents

We have learned that an exponential expression indicates a process of multiplication. For example, the expression 43 means 3∙3∙3∙3, and the product is 81.

If we multiply two exponential expressions, one solution is to simplify each term and add the results, like this:

22∙24=(2∙2)(2∙2∙2∙2)=(4)(16)=64Notice that in this process, the base (2) is multiplied by itself 6 times. This is the same value as the total of the exponents of the two original expres-sions (2 + 4 = 6). This leads us to a rule for multiplying exponents:

To multiply exponential terms with the same base, add the exponents.

Example 1: 42∙43

Since both expressions have the same base (4), we add the exponents. 2 + 3 = 5, so the result is 54 .

Example 2: a4∙a6

Since variables take the place of numbers, we can apply the same rule with variables that have exponents. Both expressions have the same base, so we add the exponents. 4 + 6 = 10, so

a4∙a6=a10

Example 3: 34∙46

The rule for multiplying exponents only applies when both terms have the same base. These terms have different bases. One base is 3 and the other is 4. We can’t add the exponents, so we leave it as is: 34∙46.

Example 4: a4∙b6

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Evaluating Variables with Exponents

(continued)


Although both terms contain variables, the variables are different, so the terms have different bases. We can’t add the exponents, so we put the two terms together as a4b6, to indicate multiplication.

Example 5: x2∙xThe bases are the same, so we can add the exponents. The first term has an exponent of 2. The second term doesn’t have an exponent. When a vari-able doesn’t have an exponent, we treat it as if it has an exponent of 1.

When we add the exponents, 2 + 1 = 3, so the value is 3x .

If the multiplication of two numbers results in a very large exponent, we generally don’t simplify it completely; we just leave it in exponential form. To multiply it would result in a very large number that would be more sub-ject to error than just leaving it as the base and the exponent alone. For example, if we are mulitplying 812∙815, we leave the answer as 827.

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Notes

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Skill Practice A

Evaluate the following expressions for the given values:

1. 2a if a = 4

2. x6 if x = 3

3. 3 d if d = 343

4. n 256 if n = 4

5. 3p if p = 8

6. w3 if w = 4

7. 4 c if c = 1,296

8. e 729 if e = 3

9. 4g if g = 8

10. m18 if m = 3

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Skill Practice B

Solve the following using the rule for multilication of exponents. In this practice, you only need to indicate the correct base and exponent. For example, the correct answer for 44∙43 would be 47.

1. 23∙25

2. b5∙b9

3. 52∙63

4. c2∙d2

5. y3∙y

6. 47∙48

7. e3∙e9

8. 92∙75

9. x12∙y10

10. g3∙g4∙g

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Lesson 23 Review

1. Is 31 a prime number?

2. 4 times a number is 17 less than 29. What is the number?

3. If 3x 8 2+ = , what is the value of 12 x 12+ ?

4. If an airplane is flying at the rate of 25 miles in 3 minutes, how long will it take it to travel 1,500 miles?

5. What is the root of 3 1,331?

6. Simplify: 2[8(5)+5(7−3)]+3[(6−3)+2(4)]

7. Evaluate 12x if x = 3

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Lesson 23 Review continued

8. Evaluate 3b−2bc+13 for b = 8 and c = 3.

9. The sum of twice a number and 16 is 84. What is the number?

10. The ratio of nuts to bolts in the box is 3:2. If there are 60 nuts in the box, how many bolts are there?

11. a4∙a6

12. 18 c=−4

13. 2 13 z+18=6

14. 25 = 45

w

15. 512∙518

16. 38 +6d=−2 1

4

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Equations with Exponents

Grade 8

24We have learned how to solve equations with single variables, such as the following:

x+2=8 3x=12 4x+3=11In all of these equations, the variable does not have an exponent. In this lesson, we will explore equations in which the variable has an exponent. Look at the following example:

Example 1: Solve this equation for x: x2=9In this equation, we know the value of x2, but we need to find the value of x. To reduce x2 to x and solve the equation, we have to use the basic rule of equations: whatever we do to one side of the equation, we must do to the other side. To reduce x2 to x, we take the square root of x2, which is x. So if we take the square root of x2, then we have to take the square root of 9, which is 3. This seems simple enough, but when we consider negative numbers, there are actually two solutions to the problem:

√9=3 because (3)(3)=9 √9=−3 because (−3)(−3)=9For this reason, when we solve an equation that contains an exponent that is a square, the answer is given as “plus or minus” the value. This is written as follows:

x2 =9x =±3

The answer is read as “plus or minus 3.”

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(continued)


Example 2: Solve this equation for y: y2=119The square root of 119 is not an even value. Round off the answer to two decimal places and put the ± symbol in front of it, as follows:

y2=119y=±10.91

Example 3: Solve this equation for d: d2+6=22First, we use the subtraction rule for equations:

d2+ 6 = 22− 6 = −6

d2= 16Then we take the square root of both sides:

d2=16d=±4

Multiple-Term Equations

When an equation has more than one term on either side, we must first combine the like terms and then solve it using one or more of the rules for equations.

Example 1: 3x−4−x+6=42Step 1: We combine all the like terms:

3x−4−x+6=4 2x+2=42Step 2: We use the necessary rules for equations to separate the variable and find the answer:

2x + 2=42− 2=−2

2x=40y=6

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(continued)


Example 2: 2y−8+y+17=27 2y−8+y+17=27 3y+9=27 −9=−9 3y=18 y=6

Combining Terms on Both Sides

To solve some equations, you have to combine like terms on both sides, as in the following examples:

Example 1: 4x−2+x+6=3x+6In these kinds of equations, the object is to get the variables on one side of the equation and the numbers on the other side. If we follow a consis-tent process, the equation is not difficult to solve:

Step 1: Combine the like terms on both sides.

4x−2+x+6=3x+6 5x+4=3x+6Step 2: Using rules for equations, move the variables to one side of the

equation.

5 x + 4 = 3 x + 6− 3 x =− 3 x

2 x + 4 = 6Step 3: Using rules for equations, move the numbers to the other side of

the equation and solve

2 x + 4 = 6− 4 =− 42 x = 2

x = 1

For Enrolled StudentsBefore you continue with Lesson 25, send the Review and Test for lessons 23 and 24 to your teacher.

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Skill Practice A

Solve the following equations for the variable without the exponent.

1. 2x 25=

2. 2d 106=

3. 2y 6 42+ =

4. 2b 9 47+ =

5. p2−14=43

6. a2−12=37

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Skill Practice B

1. 4b+6−14+2b=46

2. 7x−9−3x+5=28

3. 18−2a−12+9a=27

4. 5g−2g+15−9=45

5. 2c+6−c+8=42

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Skill Practice C

1. 2x+6=x+4

2. −3y−2+7y+7=2y+23

3. 4b+6−2b=23+3b−7

4. −d+2+3d−7=18−d+7

5. 2w+6=−5w−16+w+20+4w

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Lesson 24 Test

Use a calculator to solve decimal problems. Round off longer answers to two decimal places. Reduce common fractions to lowest terms.

1. 2e+ 14 =−3 1

2

2. x2+3=19

3. 39∙313

4. 5[2(3)+4(6−1)]−6(17−13)

5. 38 =

27a

6. Evaluate 9x if x = 4

7. 1 12 d−5=10

8. 5 times a number is 25 less than 110. What is the number?

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Lesson 24 Test continued

9. What is the root of 3 2,197 ?

10. 5w+7−w=14+3w−8

11. If 2x+ 12 =4, what is the value of 4x−8?

12. 16 p=−2 1

3

13. Is 43 a prime number?

14. Evaluate a2−3a+6 for a = 4.

15. The sum of twice a number and 19 is 47. What is the number?

16. n3∙n5

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