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Interactives for grades 6-8

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Practice Tests - Council on Competiveness

Council on Competiveness presents a truly rigorous exam - select 8th Grade and then Math [timed exam] :
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Practice Tests- Brainchild Testing

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Practice Tests - Math 8

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Science Essay Competition for South African School Pupils Prizewinners: 2004
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Thuật Ngữ Hình Học

CLICK vao LINK tren de tai file pdf, Anh Viet

Cong thuc tinh: chu vi, dien tich, the tich cac hinh

1. Hinh chu nhat (Rectangle)

Chu vi hinhchu nhat: P=(a+b)*2 -----(dai + rong)*2 Perimeter: P = 2l + 2w or P = 2(l+w)

Dien tich hinh chu nhat: S=a*b------(dai* rong) Area: A=lw or A=bh (A=area, l=length, w=width, b=base, h=hight)

2. Hinh vuong (Square)

Chu vi hinh vuong: P=a*4 ..............(canh*4) Perimeter: P = 4s

Dien tich hinh vuong: S= a*a ..........(canh*canh) Area: A= s² (s = side= cạnh)

3.Hinh tam giac (triangle)

Dien tich hinh tam giac: S = (a*h)/2 ..............(day * chieu cao)/2

A= ½ bh, or A = bh/2

Dien tich hinh tam giac vuong: S= ( a* b)/2--------( hai canh hinh vuong nhan voi nhau)/2

4. Hinh thang (trapezoid)

Dien tich hinh thang: S= (( a+b)* h)/2------( tong hai day* chieu cao)/2

A= ½ (b1+b2)h or A = (b1+b2)h/2

Chu vi hinh thang: Tong hai canh day cong voi hai canh ben

5. Hinh tron (circle) ∏ ≈ 3.14 or ∏ ≈ 22/7

. Dien tich hinh tron: S= r*r* 3,14---------( ban kinh* ban kinh* 3,14) A=∏r² (r = radius= bán kính)

. Chu vi hinh tron: C = d* 3,14----------( chu vi = duong kinh * 3,14)

Circumferance: C = 2 ∏ r or C= ∏ d (d=diameter= đường kính )

6. Hinh hop chu nhat (rectangular parallelepiped)

Dien tich xung quanh : Sxq= (a+b) *2* c------(( dai+ rong) *2* chieu cao)

Dien tich day : Sd= a* b---------( S day= dai* rong)

Dien tich toan phan : Stp = Sxq + Sd * 2 hay Stp= ( a+b) *2 *c + a*b*2

The tich hinh hop chu nhat: V= a* b* c hay V= Sd * c ---------( dai* rong* cao)

7. Hinh lap phuong (cube)

-Dien tich 1 mat: Sm= a*a -------(canh * canh)

-Dien tich xung quanh: Sxq= Sm* 4 hay Sxq= a*a*4------ ( canh* canh * 4)

-Dien tich toan phan: Stp= Sxq+ Sd* 2 hay Sxq = a*a * 6 -------( canh *canh *6)

Surface area: S= 6 s² (S = Surface area, s= side)

-The tich hinh lap phuong: V= a*a*a------ ( canh* canh* canh)

8. Hinh tru (cylinder)

-Dien tich day hinh tru: S= r * r * 3,14 -------(ban kinh*ban kinh* 3,14)

-Chu vi day hinh tru : Cd= r *2 *3,14 ----- ( chu vi day= ban kinh* 2* 3,14)

-Dien tich xung quanh: Sxq= Cd * h -------( chu vi day* chieu cao hinh tru)

Lateral surface area: S = 2∏rh

-Dien tich toan phan: Stp= Sxq+ Sd *2 hay Stp = (r * 2 *3,14) *h + (r * r * 3,14) *2

Total surface area: S = 2∏rh + 2∏r² or S = 2 ∏r (h+r)

-The tich hinh tru: V= Sd * h ------ ( dien tich day * chieu cao) hay V= (r *r * 3,14) *h

Volume: V= bh (b = the area of the Base of a solid figure)

9. Hinh non (cone)

- Lateral surface area: S= ∏rl

- Total surface area: S = ∏rl + ∏r² or S = ∏r (l + r)

- Volume: V = 1/3 bh (b = the area of the Base of a solid figure)

10. Hinh cau (sphere)

- Surface area: S= 4 ∏r²

- Volume: V= 4/3 ∏r³

11. Hinh lang tru (prism)

-Volume: V =bh (b = the area of the Base of a solid figure)

12. Hinh chop (pyramid)

-Volume: V = 1/3bh (b = the area of the Base of a solid figure)

ISAT Mathematics Grade 8 Sample Items

http://web.archive.org/web/20040409094807/http://electron-net.eztest.eppg.com/ISBE/2003/grade8math/

ISAT Mathematics Grade 8 Sample Items

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Reporting Sets of Illinois Standards for Mathematics
1. Estimation/Number Sense/Computation Illinois Learning Standards 6A, 6B, 6C, 6D, 8C 2. Algebraic Patterns and Variables Illinois Learning Standards 8A, 8D 3. Algebraic Relationships/Representations Illinois Learning Standard 8B 4. Geometric Concepts Illinois Learning Standard 9A	5. Geometric Relationships Illinois Learning Standards 9B, 9D 6. Measurement Illinois Learning Standards 7A, 7B, 7C 7. Data Organization and Analysis Illinois Learning Standards 10A, 10B 8. Probability Illinois Learning Standard 10C

All questions have only one correct answer. Click the button at the bottom of this page to have your responses scored.

There are 55 sample items.

1. A square garden measuring 8 feet on a side is surrounded by a 1-foot-wide path.

What is the area of the path?

Reporting Sets - 1, 6

8 square feet
9 square feet
28 square feet
36 square feet
64 square feet

2. Michael has a bag of 300 marbles. He randomly pulls out 15 marbles and finds that 4 are purple.

Of the original 300 marbles, about how many should Michael expect to be purple?

Reporting Sets - 1, 2, 8

20
40
60
80
120

3. Which shows the number 34,600,000 written in scientific notation?

Reporting Set - 1

346 x 10⁵
34.6 x 10⁶
3.46 x 10⁷
3.46 x 10^-7
0.346 x 10^-8

4. The Burger Shop offers hamburgers fixed 5 different ways. They also offer French fries, tater tots, onion rings, and fried mushrooms as side orders.

How many different combinations of one hamburger and one side could be offered?

Reporting Sets - 1, 8

2 combinations
6 combinations
9 combinations
20 combinations
25 combinations

5. What is the approximate length of the hypotenuse of an isosceles right triangle where side x = 12 centimeters?

Reporting Sets - 1, 4

About 9 centimeters
About 12 centimeters
About 17 centimeters
About 24 centimeters
About 30 centimeters

6. Misty is working in a store. A customer gives her $22.00 to pay for $21.55 worth of groceries.

What is the correct change she should give the customer using the fewest coins possible?

Reporting Sets - 1, 6

1 nickel, 1 quarter
2 nickels, 1 quarter
1 dime, 1 quarter
2 dimes, 1 quarter
4 nickels, 1 quarter

7. On the number line below, where is - located?

Reporting Set - 3

Between A and B
Between B and C
Between C and D
Between D and E
Between E and F

8. Find the measure of X.

Reporting Sets - 1, 4, 5

36°
45°
72°
81°
97°

9. HIJ is similar to STR.

What is the perimeter of STR?

Reporting Sets - 2, 5, 6

32
37
40
42
120

10. A bag contains 3 red marbles, 4 blue marbles, and 2 green marbles.

If John picks a marble from the bag without looking, what is the probability it will be red or blue?

Reporting Set - 8

11. Below are Matt's test scores for 1st and 2nd quarters.

Which statement is true about the data?

Reporting Sets - 1, 7

The 1st quarter mean score is higher than the 2nd.
The 1st quarter mode score is higher than the 2nd.
The modes of each quarter's scores are equal.
The means of each quarter's scores are equal.
The 2nd quarter mean score is higher than the 1st.

12. Which describes the statement, "two dollars is at least enough to buy 3 stamps and a $0.50 postcard"?

Reporting Set - 3

2 ≤ 3s - .50
2 ≥ 3s + .50
3s = 2 + .50
3s + .50 > 2
3s < .50

13. Carmen has a custard recipe that requires 6 eggs, 1 cup of sugar, 3 cups of milk, and 1 teaspoon of vanilla. However, she has only 4 eggs. She decides to adjust the recipe accordingly.

How much milk will she need?

Reporting Sets - 1, 2

1 cup
1 cups
2 cups
3 cups
4 cups

14.

What is the measure of ∠SRT?

Reporting Sets - 1, 4, 5

148°
140°
135°
90°
45°

15. Which figure below will result if triangle FHI is reflected across the y-axis?

Reporting Set - 5

16. How many different ways are there to travel from Mason to Jackson if travel is allowed only in the direction of the arrows shown in the drawing?

Reporting Sets - 7, 8

3 ways
5 ways
12 ways
13 ways
21 ways

17. For her school newspaper, the editor has a photo that has a height of 4" and a width of 6". She needs to enlarge the picture proportionally to fit a space with a height of 7".

What will the new width be?

Reporting Sets - 1, 2

17"
14"
11"
10"
4"

18. Jill plans to put ribbon around the rim of a pot and attach a bow onto the ribbon. The bow itself will take 18 inches of the ribbon.

What is the least amount of ribbon needed for one pot if the pot is 8 inches in diameter?

Reporting Sets - 1, 6

About 18 inches
About 44 inches
About 56 inches
About 96 inches
About 144 inches

19. Jessie runs at a constant rate of 7 meters per second. At the beginning of a race, she is 350 meters from the finish line.

How long will it take Jessie to reach the finish line?

Reporting Set - 1

40 seconds
50 seconds
60 seconds
100 seconds
400 seconds

20. The perimeter of a square is 60 cm.

How long is one side of the square?

Reporting Sets - 1, 4, 6

20 cm
15 cm
12 cm
10 cm
6 cm

21. Mr. Jordan has 36 feet of fencing to make an exercise area for his dog.

What should the dimensions of the rectangular region be in order to produce the largest possible area for the dog?

Reporting Sets - 1, 6

5 feet by 13 feet
6 feet by 12 feet
7 feet by 11 feet
8 feet by 10 feet
9 feet by 9 feet

22. The average life span of a person is 72 years.

If about 9 of these years are spent eating, approximately how many years has a 16-year-old person spent eating already?

Reporting Sets - 1, 2

6 years
5 years
4 years
3 years
2 years

23. An airplane flying at an altitude of 32,000 feet descends at a rate of 1,300 feet per minute.

If the plane descends for 15 minutes, what would its altitude be in feet?

Reporting Sets - 1, 2

10,000 feet
12,500 feet
19,000 feet
19,500 feet
30,200 feet

24. During what 10-year period did automobile sales increase the most?

Reporting Set - 7

1940-1950
1950-1960
1960-1970
1970-1980
1980-1990

25. Determine the measure of angle G.

Reporting Sets - 1, 2, 4

10°
40°
50°
60°
70°

26. A bag contains 50 cards numbered from 1 to 50.

Without looking, what is the probability of drawing a card that is numbered with a multiple of 5?

Reporting Sets - 1, 8

27. A training ring for horses is an oval that is made from a rectangle with 2 semi-circles on each end.

If the entire ring is to be fenced in, what is the minimum amount of fencing needed?
(Round your answer to the nearest foot.)

Reporting Sets - 1, 2, 6

77 feet
90 feet
138 feet
154 feet
191 feet

28. Which graph represents the solution to the following inequality? (x is a real number.)

x + 3 ≤ 7

Reporting Sets - 2, 3

29. The shaded surface of this access ramp will be covered with all-weather carpet.

Find the area of the carpet needed.

Reporting Sets - 2, 4, 6

12 sq ft of carpet
32 sq ft of carpet
40 sq ft of carpet
48 sq ft of carpet
96 sq ft of carpet

30. A parking garage charges $1.50 for the first hour and $0.75 for each additional hour or part of an hour.

How much will it cost to park in the garage for 6 hours?

Reporting Sets - 1, 2

$ 5.63
$ 6.00
$ 6.38
$14.63
$15.75

31. Mr. Brown makes $350 a week.

How Mr. Brown Spends His Money Each Week

How much money does he spend on entertainment each week?

Reporting Sets - 1, 2, 7

$13.00
$42.00
$45.50
$87.50
$98.00

32. The table shows the results of the Spirit Week Survey.

Estimate the probability of an 8th-grade student voting yes.

Reporting Sets - 1, 7, 8

About .53
About .45
About .36
About .21
About .11

33. The measures of the angles of a triangle are 3x, 2x - 10, and 3x + 30 degrees.

What is the difference between the measures of the largest and the smallest angles of the triangle?

Reporting Sets - 1, 2, 4

25°
30°
60°
90°
120°

34. The chart lists exam scores for five students. All exam scores have a possible 100 points.

What score does Cathy need on a fifth exam to have an average score of exactly 90?

Reporting Sets - 1, 2, 7

90
92
94
96
98

35. If the first coordinate of an ordered pair is zero, such as (0, 4), (0, 6), and (0, 8), then the line connecting two such points is ____________________.

Reporting Sets - 3, 4

a vertical line
a horizontal line
a diagonal line
a curved line
a pair of intersecting lines

36. Clifton runs 100 meters in 30 seconds at track practice.

If he maintains this constant rate, how long will it take him to run 1 kilometer?

Reporting Sets - 1, 6

3 minutes
5 minutes
10 minutes
30 minutes
300 minutes

37. Which table satisfies the following equation?

y = 3 - x

Reporting Sets - 1, 3

38. Which path describes Celia's bike trip if Celia rode slowly at first and gradually increased her speed?

Reporting Set - 3

39. Find the value of x.

Reporting Sets - 1, 2, 4

83
59
54
14
10

40. A coat that regularly costs $152.98 is on sale for 25% off. The sales tax is 8%.

What is the total cost of the coat?
(Round your answer to the nearest dollar.)

Reporting Sets - 1, 2

About $ 40
About $115
About $120
About $124
About $140

41. Josh's baseball card collection went up in value by approximately 50%. It is now worth about $225.

Determine the approximate value of his card collection before this increase.

Reporting Sets - 1, 2

$100
$110
$150
$400
$450

42. The Washington Monument is 555 feet tall. For a class project, Tom is making a scale model of the monument to place in the front hall display case. The display case is 24 inches tall.

Which scale allows him to make the tallest model that will fit in the display case?

Reporting Sets - 1, 6

1 inch = 10 feet
1 inch = 15 feet
1 inch = 17 feet
1 inch = 20 feet
1 inch = 25 feet

43. Determine the measure of angle x.

Reporting Sets - 1, 2, 4

10°
35°
55°
145°
155°

44. Luke wants to buy a CD player that costs $56 including tax. He gets $10 a week for his allowance. He spends $3.50 a week and saves the rest.

What is the fewest number of weeks it will take him to save enough money to buy the CD player?

Reporting Sets - 1, 2

6 weeks
7 weeks
8 weeks
9 weeks
10 weeks

45. Calculate the surface area of the cube below.

Reporting Sets - 1, 4, 6

3.375 cm²
4.5 cm²
6.75 cm²
9 cm²
13.5 cm²

46. Mark plans to put a circular garden in front of the school. The garden has a diameter of 18 feet. He needs to cover the garden with peat moss. Each bag of peat moss can cover 150 square feet.

How many bags does he need?

Reporting Sets - 1, 6

1 bag
2 bags
3 bags
4 bags
5 bags

47. The volume of this box is 288 cubic cm, and the height is 4 cm. The length is triple the height.

Find the width (w).

Reporting Sets - 1, 2, 6

6 cm
8 cm
10 cm
12 cm
24 cm

48. XYZ is similar to RST.

What is the length of ?

Reporting Sets - 1, 2, 5

5 cm
7.5 cm
8 cm
9 cm
10 cm

49. Which would result in the largest number?

Reporting Set - 1

10² + 30²
10⁴
19 x 21 + 29 x 31
25 x 36
40²

50. Estimate the area of the shaded region.

Reporting Sets - 1, 4, 6

About 84 m²
About 78 m²
About 31 m²
About 21 m²
About 9 m²

51. Lines m and n are parallel.

Which angles are all congruent to angle 1?

Reporting Sets - 4, 5

2, 4, 6
3, 5, 7
4, 5, 6
6, 7, 8
8, 4, 1

52. As Stephen walks home he walks by an empty rectangular field. He can either walk across the field diagonally or walk the length and width.

About how much shorter is the walk diagonally through the lot?

Reporting Sets - 1, 4

About 141 feet
About 200 feet
About 279 feet
About 420 feet
About 721 feet

53. What is the median low temperature for these cities?

Temperature Ranges
City	High	Low
Chicago	84°	63°
Cincinnati	88°	67°
Denver	89°	58°
Philadelphia	93°	75°
Tuscon	106°	77°

Reporting Set - 7

58°
67°
75°
89°
92°

54. The circle graph represents the car sales of five different people.

Which person accounted for about 25% of the sales?

Reporting Set - 7

Kim
Lee
Max
Sue
Tony

55. Assuming all sections are equal in size, what is the probability of the spinner stopping on a blue section?

Reporting Set - 8

1 out of 3
2 out of 8
3 out of 5
3 out of 8
5 out of 8

Prepared by: McGraw-Hill for ISBE

Illinois State Board of Education