Rangkuman Smp kelas 1: Rangkuman Matematika kelas 1 smp

SUMMARY MATH CLASS 7 junior

Chapter 1

Number

1. The integers consist of a negative integer, zero, and positive integers.

2. The properties of the sum of the integers.

a. The nature of the closed

For any integers a and b, apply: a + b = c where c is also an integer.

b. The nature of the commutative

For any integers a and b, always apply: a + b = b + a

c. The nature of the associative

For any integers a, b, and c always applies: (a + b) + c = a + (b + c)

d. Having identity element

For any integers a, always apply: a + 0 = 0 + a .

The number zero (0) is the identity element in the summation.

e. Having inverse

For any integers a, always apply: a + (-a) = (-a) + a = 0 .

The inverse of a is -a, whereas the inverse of -a is a.

3. If a and b are integers then applies: a - b = a + (-b).

4. Operations on integers reduction applies closed nature.

5. If n is any positive integer then applies

6. If p and q are integers then

a. pxq = pq c. px (q) = - (pxq) = -pq

b. (-p) xq = - (pxq) = -pq d. (p) x (q) = pxq = pq

7. For each p, q, and r integers apply properties

a. closed under multiplication operation;

b. commutative: pxq = qxp

c. associative: (pxq) xr = px (QXR)

d. distributive multiplication of the sum of: px (q + r) = (pxq) + (PXR)

e. distributive multiplication of the reduction: px (q - r) = (pxq) - (PXR)

8. The element of the identity of the multiplication is 1, so that for every integer p applies: px 1 = 1 xp = p

9. The division is the inverse operation of multiplication.

10. In the integer division operation is not closed.

11. a ² = b synonymous with:

12. A ³ = b synonymous with:

13. If in a mixture of integer arithmetic operations there are no parentheses, the process is based on the properties of the following arithmetic operations.

a. The additions (+) and subtraction (-) as strong, it means that the operation is located on the left side done first.

b. The operation of multiplication (x) and division (:) as strong, it means that the operation is located on the left side done first.

c. The operation of multiplication (x) and division (:) is stronger than the sum operation (+) and subtraction (-), meaning that the operation of multiplication (x) and division (:) is done in advance rather than the operations of addition (+) and subtraction (- ).

Choose one right answer!

1. The temperature of a piece of ice initially 5 ^° C. Two hours later the temperature dropped 7 ^° C. The temperature of the ice now is ....

a. -12 ^° C c. 2 ^o C

b. -2 ^° C d. -12 ^° C

DISCUSSION: 1.

The final temperature = 5 ° - 7 °

= -2 °

So, it's now the ice temperature is -2 °

2. If x is greater than 1 and less than 4 then the appropriate writing is ....

a. x> 1> 4 c. 1> x> 4

b. x <1 <4 d. 1 <x <4

3. The following statement is true ....

a. 17 - (-13) - 4 = 0 c. -18 + (-2) + 13 = 7

b. -25 - (-8) - 17 = -34 d. 12 + (-7) - 6 = 1

DISCUSSION: 3.

a. 17 - (-13) - 4 = 0

17 + 13 - 4 = 0

26 ≠ 0

b. -25 - (-8) - 17 = -34

- 25 + 8 - 17 = - 34

- 34 = - 34 ® Answers

c. -18 + (-2) + 13 = 7

- 7 ≠ 7

D.12 + (-7) - 6 = 1

- 1 ≠ 1

4. If p = 1, q = -4, and r = 2, the value of is ....

a. -1 c. 1

b. -2 d. 2

DISCUSSION: 4.

5. The value of (6: 3) ² x 2 ³ is ....

a. 22 c. 32

b. 23 d. 33

DISCUSSION: 5.

(6: 3) ² x 2 ³ = (2) ² x 2 ³

= 2 ^{2 + 3}

= 2 ⁵

= 2x2x2x2x2

= 32

6. A simple form of (3 x 4) ³ x (2 x 5 x 7) ² : (2 x 5 x 6) ² is ...

a. 2 ² x 3 x 7 ² c. 2 x 3 ² x 7 ³

DISCUSSION: 6.

(3 x 4) ³ x (2 x 5 x 7) ² : (2 x 5 x 6) ² =

= 2 ⁸^{- 4} x 3 ³^{- 2} x 5 ²^{- 2} x 7 ²

= 2 ⁴ x 3 x 7 ²

b. 2 x 3 ² x 7 ² d. 2 ⁴ x 3 x 7 ²

7. The value of is ....

a. 6 c. 15

b. 12 d. 20

DISCUSSION: 7.

= 12

8. KPK and FPB of 72 and 120 respectively are ....

a. 40 and 24 c. 360 and 40

b. 360 and 24 d. 240 and 360

DISCUSSION: 8.

Factorization of 72 = 2 ³ × 3 ²

Factorization of 120 = 2 ³ × 3 × 5

KPK = 2 ³ × 3 ² × 5

= 8 × 9 × 5

= 360

FPB = 2 ³ × 3

= 8 × 3

= 24

9. The value of 35 + 14 x 8-34: 17 is ....

a. 145 c. 246

DISCUSSION: 9.

35 + 14 x 8-34: 17 = 35 + (14 x 8) - (34: 17)

= 35 + 112 - 2

= 145

b. 245 d. 345

10. The value of -3 x (15 + (-52)) = ...

a. 97 c. 111

b. -111 d. -201

DISCUSSION: 10.

-3 x (15 + (-52)) = - 3 × (15 - 52)

= - 3 × - 37

= 111

CHAPTER 2

FRACTIONS

1. Fractions are numbers that describe the part of keseluruhan.Pecahan is a number that can be expressed as; with p, q integers and q ≠ 0. Number p is called the numerator and denominator q is called.

2. Fractions are valued at the fragments of equal value. Fractions worth obtained by multiplying or dividing the numerator and denominator with sama.Suatu fractional numbers, , q ≠ 0 can be simplified by dividing the numerator and denominator of the fraction with the factors of greatest.

3. If the denominator of the two different fractions, fractions to compare the state into fractions were worth, and then compare the numerator.

4. On the number line, a larger fraction on the right, while the smaller denominations are on the left.

5. In between the two different fractions can always be found fragments whose value is in between the two fractions.

6. Each integer p, q can be expressed in bits, where p is a multiple of q, q ≠ 0.

10. Form the mixture fraction with r ≠ 0 can be expressed in the form of ordinary fractions:

11. To change a fraction to a percentage of the forms can be done by changing the original fractions into fractions with denominators worth 100. If it is difficult to do, it can be done by multiplying the fraction by 100%.

12. To determine the result of addition or subtraction of two fractions, the denominator equate the two fractions, that is by looking for the Commission of the denominator-the denominator, then newly added or subtracted numerator.

13. To determine the result of multiplying two fractions is done by multiplying the numerator by numerator and denominator by the denominator.

14. The inverse of multiplication of fractions is or multiplicative inverse of is

15. A number when multiplied by the inverse perkaliannya result is equal to 1.

16. For any fractions and with q ≠ 0, r ≠ 0, s ≠ 0 applies:

17. For any integer p and p, q ≠ 0 and m are positive integers apply:

Fractions called a prime number.

18. For any integers p, q with q ≠ 0 and m, n are positive integers apply the following properties:

19. Addition and subtraction of decimal fractions performed at each value of a tiered manner. Sort figures hundreds, tens, units, tenth, hundredth, and so on in a single column.

20. Results of times a decimal number with a decimal number obtained by multiplying the numbers like multiplying integers. Many times the result decimal decimal numbers obtained by summing many decimal places of multiplier-pengalinya.

21. The shape of the raw numbers of more than 10 is expressed by: ax 10 ⁿ with 1 ≤ a <10 and n natural numbers.

22. The shape of the raw number between 0 and 1 is expressed by: ax 10 ⁿ with 1 ≤ a <10 and n natural numbers.

Choose one right answer!

1. 0.49 + (0.72: 0.8) - 0.5 = ...

DISCUSSION: 1.

0.49 + (0.72: 0.8) - 0.5 = 0.49 + from 0.9 to 0.5

= 0.89

A. 0.89 B. 8.68 C. 9.84 D. 10.68

2. The shape is 0.78 percent of the number ...

A. 7.8% B. 78% C. 0.78% D. 0.078%

DISCUSSION: 2.

3. The shape of the decimal number:

A. 253 B. 25.3 C. 2.53 D. 0.253

DISCUSSION: 3.

= 0.253

4. The name decimal fractions

are

A. 0.25 B. 0.50 C. 0.75 D. 1.25

if converted to decimal fraction is

A. 0.875 B. 0.1875 C. 1.175 D. 1.875

DISCUSSION: 5.

6. The shape of the decimal fraction

DISCUSSION: 6.

A. 0.2 B. 0.3 C. 0.4 D. 0.5

7. Coat cent for

A. 0.4125% B. 4.125% C. 41.25% D. 412.5%

DISCUSSION: 7.

8. Results of 0.36 × 2.43 is ...

A. 0.7538 B. 0.7738 C 0.8548 D. 0.8748

DISCUSSION: 8.

0.36 × 2.43 = 0.8748

9. 28.45 × 9.52 = ...

A. 175.644 B. 270.844 C. 174.644 D. 174.544

DISCUSSION: 9.

28.45 × 9.52 = 270.844

10. 3.25 × 1.12 = ...

A. 3.53 B. 3.63 C. 3.64 D. 3.74

DISCUSSION: 10.

3.25 × 1.12 = 3.64

11. The result is a time of 3.18 to 1.15 ...

DISCUSSION: 11.

3.18 × 1.15 = 3.6570

A. 3657.0 B. 365.70 C. 36.570 D. 3.6570

14. , n = ........

A. 15 B. 25 C. 35 D. 45

15. 185% + 2 to 1.25 = ........

A. 19.60 B. 4.36 C. 2.6 D. 22.10

DISCUSSION: 15.

185% + 2 to 1.25 =

= 2.6

Chapter 3

Algebra

1. Variables, constants, factors, and the rate was similar and similar.

a. The variable is a symbol substitutes a number of unknown value clearly.

b. The constant is the rate of a form of algebra that is a number and not a variable load.

c. The tribes are the kind that has a variable rate and rank of each of the same variable.

d. Tribe is not a type that has a variable rate and rank of each variable are not the same.

2. In the algebra, addition and subtraction operations can only be performed on similar tribes.

3. The multiplication of a constant number k the algebraic form of the tribes and the two tribes expressed as follows:

a. k (ax) = KAX b. k (ax + b) = KAX + kb

4. The product of the two forms of algebra is expressed as follows:

a. (ax + b) (cx + d) = acx ² + (ad + bc) x + bd

b. (ax + b) (cx ² + dx + e) = acx ³ + (ad + bc) x ² + (ae + bd) x + Be

c. (x + a) (x - a) = x ² - a ²

5. On the powers of the algebra of two tribes, sukusukunya coefficients determined with Pascal's triangle.

a. (a + b) ¹ = a + b , for rank 1 does not need to be written.

b. (a + b) ² = a ² + 2ab + b ²

c. (a + b) ³ = a ³ + 3a ² b + 3AB ² + b ³ and so on

6. The value of the algebra can be determined by any number menyubstitusikan on variables form the algebra.

7. A fraction of the simplest forms of algebra is said if the numerator and denominator have no fellowship factors except 1 and the denominator is not zero.

8. The results of the operations of addition and subtraction on algebraic fractions obtained by equating the denominator, then add or subtract the numerator.

Choose one right answer!

1. The coefficient of x in the algebra 2x ² - 24x + 7adalah ....

a. 2 c. 24

b. -7 d. -24

2. The form of the following algebra consisting of three tribes is ....

a. abc + PQR c. ab - pq

b. ab + ac - bc d. 3AB - 3cd

3. The simplest form of 2 (3x + 2y) - 4 (x - 5y) is ....

a. 10x - 10y c. 2x - y

DISCUSSION: 3.

2 (3x + 2y) - 4 (x - 5y) = 6x + 4y - 4x + 20y

= 2x + 24y

b. 2x + 24y d. 2x - 3y

4. The simple form of 8x - 4 - 6x + 7 is ....

a. 2x + 3 c. 2x - 3

b. -2x + 3 d. -2x - 3

5. If p = 2, q = -3, and r = 5, the value of 2p ² r - pq is ....

a. 74 c. 96

DISCUSSION: 5.

2p ² r - pq = (2 × ( - 3) ² × 5) - (2 × ( - 3))

= (2 × 9 × 5) - ( - 6)

= 90 + 6

= 96

b. 46 d. 34

6. The results of the translation of (2x - 3) ² is ....

a. 4x ² + 6x + 9 c. 2x ² + 12x + 3

b. 4x ² - 12x + 9 d. 2x ² + 6x + 3

DISCUSSION: 6.

(2x - 3) ² = (2x - 3) (2x - 3)

= 4x ² - 6x - 6x + 9

= 4x ² - 12x + 9

7. Results of

is ....

DISCUSSION: 7.

8. The value of

is ....

DISCUSSION: 8.

9. The length of the sides of a triangle are known respectively p cm, 2p cm, and (p + 4) cm. Circumference of the triangle is ....

a. (4p + 4) cm c. (2p + 6) cm

b. (3p + 4) cm d. (2p + 2) cm

DISCUSSION: 9.

CHAPTER 4

LINEAR EQUATIONS AND INEQUALITIES OF VARIABLE

1. The statement is a sentence which can be determined truth value (true value or is false). Open sentence is a sentence that contains a variable and unknown truth value. The set of the completion of the open sentence is the set of all the replacement of variables in an open sentence that the sentence is true. The equation is open sentences connected by an equal sign (=).

2. The equation of linear one variable is an open sentence that is connected by an equal sign (=) and only has one rank one variable. The general form of the variables is linear equations ax + b = 0 and a ≠ 0.

3. Completion of linear equations is a replacement variable x is causing the equation is true.

4. The two equations equivalent or better to say if it has the same set of settlement and is denoted with a " ↔ ".

5. An equation can be expressed in a manner equivalent to the equation:

a. increase or decrease both sides with the same number;

b. multiply or divide both sides by the same number.

6. An inequality is always marked with one of the following hyphen.

" < " to declare less than.

" > " to declare more than.

" ≥ " to express no more than or less than or equal to.

" ≥ " to express not less than or more than or equal to.

10. Inequality is open sentence that states the relationship inequality ( > , < , ≥ , or ≥ ).

11. To determine the completion of one variable linear inequalities, can be done in two ways as follows.

a. Looking ahead completion of the inequality equation obtained by replacing the inequality sign with the sign " = ".

b. Declare to the equivalent inequality

Choose one right answer!

1. Completion of equation 6 - 2x = 5x + 20 with the x variable on the set of integers is ....

a. x = 1 c. x = -2

b. x = 2 d. x = -1

DISCUSSION: 1.

6 - 2x = 5x + 20

x =

x = -2

2. The length of the sides of a triangle are known 2x cm, (2x + 2) cm, and (3x + 1) cm. If the circumference of 24 cm, the length of the longest side is ....

a. 6 cm c. 10 cm

DISCUSSION: 2.

the length of the hypotenuse = (3x + 1)