latihan soal

Ryan Okitavina 26 Oktober jam 17:31

Uji Kompetensi 1
1. Tentukan koefisien-koefisien dari setiap variabel pada bentuk aljabar berikut ini !
a. 2 x² – 3y d. 4x – 7
b. a2 – 3ab – b2 + 5 e. p3 – pq + 3pq² – 5q³ + 8
c. 4x + 2xy + y2
Jawab: a).x²=+2 ,y=-3 b).a=+2, ab=-3 ,b=-2 , 5 c).x=+4 ,xy=+2 ,y:+2 d).x=+4 ,-7 e).p=+3 ,pq²=+3 ,q³=-5 ,8

2. Tentukan konstanta pada setiap bentuk aljabar berikut
a. 2x2 – 4y + 8 = 8 d. (x - 3)2 =-3 dan 2
b. xy – 2x + y2 – 1 =-1 e. 2 + 3x + 5x2 =2
c. 3x + 9 = 9

3. Manakah dari bentuk-bentuk aljabar berikut yang merupakan suku satu, suku dua, dan suku tiga ?
a. 2x + 5 = √
b. 4x dengan x ≠ 0 = √
c. x3 – x2 = √
d. a2 - b2 + (3a2 + 3b + 5) = √
e. 1 + 3y – x + 3x2 – 6xy =x

4. Termasuk suku berapakah bentuk aljabar berikut ini !
a. 2 + 3x – ax2 + 5x3 + 7x4 =suku 4
b. pqr + 3 =suku 1
c. ( a + b) + ( a - b) + (3a – 2b) + (a + 2b) =suku 4
d. 3a x 2b + c ( dengan c = ab) =suku 2
e. 5p : q ( dengan q = dan p ≠ 0 ) =suku 2

5. Tulislah setiap kalimat berikut dengan menggunakan variabel x
a. Umur Ratna dan umur Intan berselisih 5 tahun dan berjumlah tiga belas tahun =5x + 8x
b. Suatu bilangan jika dikalikan dua kemudian ditambah tiga, dan dikuadratkanmenghasilkan bilangan 225. = 6x
c. Sepuluh kurangnya dari luas suatu persegi adalah 111 cm2 =101x
d. Sebuah pecahan jika penyebutnya di tambah tiga dan pembilangnya di kurangi empat sama dengan=
e. Umur Endang tiga puluh tahun yang lalu adalah umurnya sekarang =30x

Nama : Ryan Okitavina
Kelas :8e
No : 32

FRACTIONS

1. Multiply each the following numbers by 10 and 1000 !
a. 4.7
b. 8.62
c. 0.072
d. 0.00008
2. Do the following multiplications !
a. 8.9 x 7.6
b. 0.5 x 0.017
c. 4.05 x 3.17
d. 1.05 x 0.0046
e. 425 x 0.0648
f. 24.3 x 1.82
3. Do the following multiplications !
a. 6.9 x 400
b. 0.075 x 60,000
4. Find the area of a square whose side length is 8.7 cm !
5. Find the area of a rectangle whose length is 9.6 cm and width is 6.4 cm !
6. A number of coins are piled such as the figure at the left. If the thickness of each coin is 0.35 cm, find the height of the entire stack !
7. Divide each of the following decimals by 10 and 1.000 !
a. 4.326
b. 38.42
c. 0.83
d. 0.007
8. Divide each of the following decimals by 8 and 80 !
a. 25.6
b. 5.44
9. Divide :
a. 0.414 dengan 0.9
b. 4.32 dengan 0.18
10. Do the following divisions ?
a. 37.6 : 80
b. 27.6 : 400
11. The area of a rectangle is 29.24 cm2 and its length is 6.8 cm. Find is width !
12. The product of two numbers is 18.204. If one of the numbers is 2.46, what is the other number ?
13. Round the following decimals to two decimal place !
a. 1.2436
b. 9.0683
c. 0.08653
d. 15.0097
14. Round 0.20463 to:
a. four decimal places,
b. three decimal places,
c. two decimal places,
15. Round the following decimals to the nearest integers !
a. 3.7
b. 12.56
c. 27.129
d. 125.55
e. 1,250.9
f. 4,375.753
g. 10,015.15
h. 19,299.975

FRACTIONS

1. Multiply each the following numbers by 10 and 1000 !
a. 4.7
b. 8.62
c. 0.072
d. 0.00008
2. Do the following multiplications !
a. 8.9 x 7.6
b. 0.5 x 0.017
c. 4.05 x 3.17
d. 1.05 x 0.0046
e. 425 x 0.0648
f. 24.3 x 1.82
3. Do the following multiplications !
a. 6.9 x 400
b. 0.075 x 60,000
4. Find the area of a square whose side length is 8.7 cm !
5. Find the area of a rectangle whose length is 9.6 cm and width is 6.4 cm !
6. A number of coins are piled such as the figure at the left. If the thickness of each coin is 0.35 cm, find the height of the entire stack !
7. Divide each of the following decimals by 10 and 1.000 !
a. 4.326
b. 38.42
c. 0.83
d. 0.007
8. Divide each of the following decimals by 8 and 80 !
a. 25.6
b. 5.44
9. Divide :
a. 0.414 dengan 0.9
b. 4.32 dengan 0.18
10. Do the following divisions ?
a. 37.6 : 80
b. 27.6 : 400
11. The area of a rectangle is 29.24 cm2 and its length is 6.8 cm. Find is width !
12. The product of two numbers is 18.204. If one of the numbers is 2.46, what is the other number ?
13. Round the following decimals to two decimal place !
a. 1.2436
b. 9.0683
c. 0.08653
d. 15.0097
14. Round 0.20463 to:
a. four decimal places,
b. three decimal places,
c. two decimal places,
15. Round the following decimals to the nearest integers !
a. 3.7
b. 12.56
c. 27.129
d. 125.55
e. 1,250.9
f. 4,375.753
g. 10,015.15
h. 19,299.975

COMPETENCY TEST CHAPTER 3

I. For each problem numbered 1 to 20 choose the right answer!
1. Among the following statements
(1) x + 7 = 9
(2) 5 + 6 = 11
(3) 3y + 4 = 2y – 3
(4) g is an odd number those which are open sentence are …
a. 1, 2, and 3
b. 1, 2, and 4
c. 1, 3, and 4
d. 2, 3, and 4
2. For y = 5, 10, 15 and 20, the solutions of y + 4  19 are …
a. 5 and 10
b. 5 and 15
c. 5, 10, and 15
d. 5, 10, and 20
3. The solution of 6 + 3x = 18 is …
a. 4
b. 6
c. 8
d. 12
4. The solution of 2x + 3 = 3x + 7 is …
a. -5
b. -4
c. 4
d. 5
5. The solution of 7c – 4 = 4x + 20 is …
a. 4
b. 5
c. 6
d. 8
6. The solution of 3 (2y – 2) + 4y = 2 is …
a. 4
b. 5
c. 6
d. 8
7. The solution of is …
a.
b.
c.
d.
8. The solution is …
a. -2
b.
c.
d.
9. The numbers 0.4444 … expressed as a proper fraction is …
a.
b.
c.
d.
10. The numbers 0.272727 … expressed as a proper fraction is …
a.
b.
c.
d.
11. The solution of (4x + 5) (x – 2) = 4x (x – 2) is …
a. -2
b.
c.
d. 2
12. The solution of (y + 8) (y – 12) = (y + 4) is …
a. -14
b.
c.
d. 14
13. The solution of 8x + 2 > 3x + 3 is …
a. x >
b. x >
c. x >
d. x >
14. The solution of 4 (2 – x) < x + 5 is …
a. x <
b. x >
c. x <
d. x >
15. The solution of 2 (3x + 1)  5 (x – 6) is …
a. x  -28
b. x ≥ -28
c. x  -32
d. x ≥ -32
16. The solution of is …
a. x 
b. x ≥
c. x 
d. x ≥
17. The solution of  is is …
a. x 
b. x ≥
c. x 
d. x ≥
18. The perimeter of a rectangle is 90 cm long. If length is 5 cm more than is width, then the width of the rectangle is …
a. 20
b. 25
c. 30
d. 35
19. The graph of the solutions of 2x – 1  3x + 2 for x = -5, -4, -3, -2, -1, 0, 1 and 2 is …
a.

b.


c.


d.


20. A rectangle has a length of (x – 3) cm and a width of 6 cm. if the area of the rectangle is less than 48 cm2, the value of x is ….
a. x < 5
b. x < 11
c. 3 < x < 5
d. 3 < x < 11

II. Do the following problems in detail!
1. Find the solution of each of the following equations!
a. 3x + 2 = 6x – 1
b. 3 (2p – 2) = 5p + 3
c. (2x + 5) + (3x – 7) = 11
d.

2. Find the solution of each of the following inewualities!
a. 9x + 5 > 2x + 7
b. 6x  2 (2x + 3)
c. (x + 8) > 2x + 1
d.
3. The price of a polo shirt is the same as the price of two T-shirts is Rp420,000. If the price a polo shirt is x rupiah, then :
a. form an equations in x,
b. find the value of x!
4. The perimeter of a rectangle is not more than 90 cm long. If its length is x and its width is (x – 5) cm, find :
a. The inequality that gives the perimeter of the rectangle
b. The length and width of the rectangle,
c. The area of the rectangle!
5. Uncle Sam has 24 coins consisting of two-hundred denominations and five hundred denominations. If the amount of his money is Rp9,000, find the number of each coin!

LINEAR EQUATIONS

1. The price of a printing machine is 5 times the price of a computer. The total price of 5 computers and 2 printing machines is Rp 48,000,000. What is the price of a printing machine?
2. A rectangle is (2a + 5) meters long and (2a – 1) meters wide. If its perimeter is 32 meters long, then:
a. Form an equation in a and then solve it,
b. Find its length and width!
3. Anggi is 30 years old younger than his father. Five years later, the sum of their ages is 46 years. How old are Anggi and her father now? (Suppose that her father’s age is x ?
4. Fatia has 18 coins consisting of two hundred denominations and five – hundred denominations. If the amount of her money is Rp 5,400, find the number of each coin!
5. In along holiday, Joni traveled out of the city. At first the took a bus for ½ hours at a speed of (2x – 10) km/hour, and then he continued the trip by a train for 2 hours at a speed of (2x + 10) km/hour.
a. Express the entire distance traveled by Joni in terms of x !
b. If the distance traveled was 140 km, then form an equation in x and solve it!
c. Find the seed of each vehicle!


LINEAR INEQUALITIES IN ONE VARIABLE

1. Insert one of the signs >, = or < between the following pairs of number to form true sentences!
a. 14 ….. – 27
b. – 13 …. 17
c. – 34 …. – 81
d.
2. Express the following sentences in the form of mathematical sentences!
a. p lies in between – 3 and 7
b. q is not less than 18
c. y is not greater than 27
3. Combine each the following pairs of inequalities into a single inequality!
a. 5 < 8 and 8 < 10
b. 4 > 2 and 2 > - 3
c. – 2 < 5 and 14 > 5
4. Which of the following inequalities is a linear inequality?
a. 4 (x – 2)  12
b. X (6 + x) > 27
c.
d. y (4 – y) ≥ 9
5. Find the simplest equivalent inequality to each of the following inequalities. Write the answer in the form of, for example “x < 3” or “x ≥ 5”.
a. x – 5 > 8
b. x + 9 < 6
c. y + 4  -7
d. y – 11 ≥ - 1
e. 7 + z ≥ -3
f. 11  5 – p
6. Find the solution of each of the following inequalities !
a. 4x ≥ 3x + 7
b. 5x – 4  4x + 4
c. 2 < x + 4 < 9
d.
e. -3  y – 7  5
f. 2 (m – 3) < 3 – 8
g.
7. Find the solution of each of the following inequalities!
a. 2x < 10
b. 3x > -21
c.
d. -4y ≥ 24
8. Find the solutions of each of the following inequalities!
a. -5y ≥ y – 30
b. 2y – 8 < - 14
c. -3y + 15 > 9
d. 3 – 2y < 15
e. 16 + < 7
f. 7k < 15 + 2k
g. 3p > 8p – 10
h. 3p – 5 ≥ 4p
9. Find the solution of each of the following inequalities!
a. 2m + 6 < 4m – 2
b. 5m – 4 > 7m – 11
c. -6 < 2p < 16
d. -8  -4p  7m – 11
e. 2 (p + 1) >1
f. 5 (p – 4) > 7p – 11
g. 2 (2n – 1) < 3 (2x + 3)
h. 2 (4 – 3n)  4 (n – 5)
10. Find the solution of each of the following inequalities !
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.

ALGEBRAIC

1. Simplify each of the following algebraic fractions !
a.
b.
c.
d.
2. By finding the common denominator, simplify the following algebraic expressions !
a.
b.
c.
d.
e.
f.
g.
h.
3. By finding the common denominator, simplify the following algebraic expressions !
a.
b.
4. Find the LCM of the denominators of the following algebraic fractions, and then simplify !
a.
b.
c.
d.


5. Simplify the following algebraic fractions !
a.
b.
c.
d.
e.
f.
g.
h.
6. Simplify the following algebraic fractions !
a.
b.
c.
d.
e.
f.
g.
h.
7. Find the power of each of the following algebraic exponentiations !
a.
b.
c.
d.
e.
f.
8. Find the product quotient of each of the following algebraic multiplications divisions !
a.
b.
c.
d.
e.
9. Expand the following algebraic expressions !
a. x(2x + 5
b. 3x(x – 2)
c. -3x2(6x + 5xy)
d. 5p(2p – 3q + 4)
e. 4p2(3p2 – 5pq + 6q2)
10. Expand by means of the distributive law !
a. (x + 3) (x + 4)
b. (x + 2) (x – 5)
c. (3x + 2y) (x – 5y)
d. (3x – 4y) (2x + 7y)
e. (4x – 3y) (5x – 4y)
11. Expand the following algebraic expressions using schemes !
a. (a + 3) (a + 5)
b. (3a + 4) (3a – 2)
c. (4x – 2y) (4x – 5y)
d. (1 – 4y) (1 + 4y)
e. (9 + 12y) (9 – 12y)
f. (x2 + y2) (x2 – y2)
g. (x2 + 5x) (x2 – 10x)
h. (p + 3) (p2 – 2p + 1)
i. (p – 4) (p2 + 4p + 16)
j. (3p + 2q) (9p2 – 6pq + 4q2)
12. Expand the following squared binomials !
a. (m + n)2
b. (a – 10)2
c. (4p + 15)2
d. (3p – 10)2
13. Copy and then fill in the blanks !
a. (x + …)2 = … + … + 16
b. (3x - … )2 = … - … + 25
c. (3y + … )2 = … + 24y + …
d. (4y - ….)2 = … - 40y + …
14. Expand the following algebraic expressions and simplify the results !
a.
b.
c.
d.
e.
f.
g.
h.
15. By using identity a(b ++c) or (x +a) (x – a), do the following multiplications !
a. 9  76
b. 7  89
c. 6  94
d. 4  236
e. 7  324
f. 5  468
g. 32  28
h. 75  85
i. 43  37
j. 38  32
k. 76  74
l. 91  109