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Math Assessment

UT Austin 8th Grade Math CBE: Obj 2 & 3 Comprehensive

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Objectives 2 & 3: Interactive Review - UT Austin CBE

8th Grade Math CBE Practice Examination

Objectives 2 & 3: Number Operations & Proportionality

Directions: Select the BEST response for each question. Click "Submit Quiz" at the bottom to check your score.

Objective 2: Real Number System & Classification

1. Which of the following lists all the subsets of the real number system to which the number \(-8\) belongs?

2. Which of the following values is classified as an irrational number?

3. If you were to place the number \(0\) into a Venn diagram of the Real Number System, what is the most specific subset it belongs to?

4. Which of the following statements is ALWAYS true regarding the real number system?

5. The repeating decimal \(0.333...\) belongs to which subset of real numbers?

Objective 2: Irrational Approximations

6. The value of \( \sqrt{85} \) lies between which two consecutive integers?

7. Which integer is the closest approximation to the value of \( \sqrt{40} \)?

8. Point A is located on a number line between 7 and 8, but it is much closer to 8. Which of the following could be the value of Point A?

9. Estimate the sum of \( \sqrt{10} + \sqrt{50} \) to the nearest whole number.

10. Which value is the greatest?

Objective 2: Scientific Notation

11. How is the number \( 4,500,000 \) correctly written in scientific notation?

12. Convert \( 0.00072 \) into scientific notation.

13. What is \( 2.1 \times 10^{-3} \) in standard decimal form?

14. In the expression \( 3.4 \times 10^{-5} \), what does the exponent \(-5\) indicate about the standard form of the number?

15. Which of the following represents the largest number?

Objective 2: Ordering Sets of Real Numbers

16. Order the following numbers from least to greatest: \( \frac{1}{3}, 0.3, 33\%, \sqrt{0.09} \).

17. Arrange the following in descending order (greatest to least): \( \pi, 3.1, \frac{22}{7}, \sqrt{10} \).

18. Which number correctly fits between \( \frac{1}{2} \) and \( \frac{3}{4} \) on a number line?

19. Order the following from least to greatest: \( -3.5, -\sqrt{10}, -3, -\frac{11}{3} \).

20. Which value in this set is the greatest? \( \{4.1, \quad 4\frac{1}{8}, \quad 415\%, \quad \sqrt{17}\} \)

Objective 3: Dilation & Similarity

21. A figure is dilated by a scale factor of 4 with the origin as the center of dilation. Which algebraic rule represents this transformation?

22. Point \( B(6, -2) \) is dilated by a scale factor of \( \frac{1}{2} \) centered at the origin. What are the coordinates of \( B' \)?

23. A square with a perimeter of 20 cm is dilated by a scale factor of 3. What is the perimeter of the new square?

24. If a rectangle is dilated by a scale factor of 2, how does its new area compare to the original area?

25. Two similar triangles have corresponding side lengths of 4 cm and 10 cm. What is the scale factor used to dilate the first triangle to the second?

26. Which of the following attributes is preserved during a dilation?

Objective 3: Slope & Rate of Change

27. Calculate the slope of the line passing through points \( (2, 3) \) and \( (4, 11) \).

28. What is the rate of change for the linear function \( y = -0.5x + 7 \)?

29. A table shows \( x = 1, 2, 3 \) and \( y = 8, 13, 18 \). What is the rate of change?

30. A car travels 150 miles in 3 hours. Assuming a constant speed, what is the slope (unit rate) of the line representing distance as a function of time?

31. Which concept explains why the slope is identical between *any* two points on a straight line?

32. What is the slope of a perfectly horizontal line?

Objective 3: Proportional vs. Non-Proportional

33. Which of the following equations models a proportional relationship?

34. Visually, what must be true for a graphed line to represent a proportional relationship?

35. A mechanic charges a $40 diagnostic fee plus $60 per hour of labor. Why is this relationship non-proportional?

36. The formula \( y = kx \) represents direct variation. What does \( k \) stand for?

37. Which table represents a proportional relationship?

38. If \( y \) varies directly with \( x \), and \( y = 12 \) when \( x = 3 \), what is the correct equation?

Objective 3: Multiple Representations

39. A gym charges a $20 sign-up fee and $10 per month. Which equation represents the total cost \( y \) for \( x \) months?

40. Given the equation \( y = 2x - 5 \), which table of \((x, y)\) values is correct?

41. A line intersects the y-axis at \(-3\) and has a slope of \(2\). What is its equation?

42. What is the equation of the line that passes through the points \((1, 4), (2, 7),\) and \((3, 10)\)?

43. The total cost to rent equipment is \( C = 25h + 50 \), where \( h \) is the hours rented. If you rent the equipment for 3 hours, what is the total cost?

44. For the linear equation \( y = 3x - 12 \), what is the x-intercept?

Objective 3: Bivariate Data (Scatterplots)

45. A scatterplot shows the relationship between hours spent studying and grades on a test. As hours increase, grades tend to increase. This represents a:

46. What is the primary purpose of drawing a Trend Line (Line of Best Fit) on a scatterplot?

47. A trend line equation on a scatterplot is \( y = -2x + 100 \). What is the predicted \( y \)-value when \( x = 10 \)?

48. In a bivariate data set, how is an "outlier" defined?

49. A scatterplot shows data points that form a distinct U-shape (a curve). What type of association is this?

50. If a student uses a trend line to estimate a value that falls far outside the range of the originally collected data points, this process is called:

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