Free MAP 8th Grade Math Questions and Answers 1 — Questions and Answers
Question 1: When a figure is transformed using one of the following methods on a coordinate grid, which one does not preserve congruency?
- A reflection across the x-axis
- A rotation of 320° clockwise
- A translation of 38 units left
- A dilation by a scale factor of 0.5 (Correct answer)
Correct answer: A dilation by a scale factor of 0.5
Congruency means that two figures have the same size and shape. Reflections, rotations, and translations are isometric transformations, meaning they preserve both the size and shape of a figure, thus maintaining congruency. A dilation, however, changes the size of a figure by a given scale factor, either enlarging or shrinking it. Therefore, a dilation does not preserve congruency because the transformed figure will be a different size than the original.
Question 2: An engineer determined the length of a square cardboard diagonal in centimeters by solving the equation x2 = 140. Which of the following sums up the square's diagonal's approximate length in centimeters?
- 35
- 70
- 12 (Correct answer)
- 28
Correct answer: 12
To find the length of the diagonal, we need to solve the equation x² = 140 by taking the square root of both sides, so x = √140. We know that 11² = 121 and 12² = 144. Since 140 is between 121 and 144, the square root of 140 will be between 11 and 12. As 140 is much closer to 144 than to 121, the approximate length of the diagonal is 12 centimeters.
Question 3: Jos puts $2,350 into two bank accounts for savings. <br> <br> Every year, Account X offers 3.25% simple interest. <br> 3.75% interest is compounded annually on Account Y. <br> <br> Which amount, if Jos made no more deposits or withdrawals, would be closest to the difference between the interest Jos will receive in Account X and Account Y after three years?
- $503.53
- $45.28 (Correct answer)
- $229.13
- $274.40
Correct answer: $45.28
For Account X, simple interest is calculated as Principal × Rate × Time, so $2,350 × 0.0325 × 3 = $229.13. For Account Y, compound interest is calculated using the formula A = P(1+r)^t, which yields $2,350(1+0.0375)³ ≈ $2,624.40, meaning the interest earned is $2,624.40 - $2,350 = $274.40. The difference between the interest from Account Y and Account X is $274.40 - $229.13 = $45.27, which is closest to $45.28.
Question 4: On a coordinate grid, parallelogram XVUW was translated six units to the right and seven units down to produce parallelogram X'V'U'W. Which of the following rules best sums up this change?
- (x,y) → (x + 6,y – 7) (Correct answer)
- (x,y) → (x + 6,y + 7)
- (x,y) → (x – 6,y + 7)
- (x,y) → (x – 6,y – 7)
Correct answer: (x,y) → (x + 6,y – 7)
A translation moves every point of a figure the same distance in the same direction. Moving a figure 'six units to the right' means adding 6 to the x-coordinate of each point. Moving a figure 'seven units down' means subtracting 7 from the y-coordinate of each point. Therefore, the rule that best describes this transformation is (x,y) → (x + 6, y – 7).
Question 5: A client requests a $15,000 loan so that he can remodel his house. Which of the following loan choices enables the borrower to make the lowest possible interest payment?
- A 6-year loan with an 7.8% annual simple interest rate
- A 5-year loan with a 4.8% annual simple interest rate
- A 4-year loan with a 4.5% annual simple interest rate
- A 3-year loan with a 5.6% annual simple interest rate (Correct answer)
Correct answer: A 3-year loan with a 5.6% annual simple interest rate
To find the lowest possible interest payment, we calculate the simple interest for each loan option using the formula Interest = Principal × Rate × Time. For option A, the interest is $15,000 × 0.078 × 6 = $7,020. For option B, it's $15,000 × 0.048 × 5 = $3,600. For option C, it's $15,000 × 0.045 × 4 = $2,700. Finally, for option D, the interest is $15,000 × 0.056 × 3 = $2,520, which is the lowest among all choices.
Question 6: Examine the following diagram, which illustrates a conical birthday cap's height. <br> <br> The cone is 675π cubic centimeters in volume. What is the cone's approximate radius in centimeters?
- 12.5
- 9 (Correct answer)
- 18
- 16
Correct answer: 9
The volume of a cone is given by the formula V = (1/3)πr²h. We are given the volume V = 675π cubic centimeters and, assuming the diagram indicates a height (h) of 25 cm, we can substitute these values into the formula. This gives us 675π = (1/3)πr²(25). Dividing both sides by π and simplifying, we get 675 = (25/3)r². Multiplying by 3/25 yields r² = 675 * (3/25) = 81, so the radius r = √81 = 9 centimeters.
Question 7: Examine the following graph of a linear function:
- -5
- -10
- 10 (Correct answer)
- 5
Correct answer: 10
The question asks to examine the graph of a linear function, and the correct answer is 10. Without the actual graph, it is implied that the question is asking for a specific feature of the graph, most likely the y-intercept. The y-intercept is the point where the line crosses the y-axis, and if the line intersects the y-axis at (0, 10), then 10 is the correct value.
Question 8: Alan put $9,000 into a business savings account with an annual simple interest rate of 5.75%. No more money will be deposited or taken out. <br> <br> What is the closest estimate of the interest that will be deposited into the account after a period of 12 years?
- $15,210
- $6,210 (Correct answer)
- $8,625
- $4,312.50
Correct answer: $6,210
To calculate the simple interest deposited into the account, use the formula Interest = Principal × Rate × Time. Given a principal of $9,000, an annual simple interest rate of 5.75% (or 0.0575 as a decimal), and a period of 12 years, the calculation is $9,000 × 0.0575 × 12. This multiplication results in an interest amount of $6,210.
Question 9: A tank has a volume of 5,991,000 square millimeters. How should this square centimeter amount be expressed in scientific notation?
- 5,991 × 10⁻³
- 5.991 × 10⁶ (Correct answer)
- 5.991 × 10⁻⁶
- 5,991 × 10³
Correct answer: 5.991 × 10⁶
To express a number in scientific notation, you need to write it as a product of a number between 1 and 10 (inclusive of 1, exclusive of 10) and a power of 10. For 5,991,000, move the decimal point from its implied position at the end of the number six places to the left to get 5.991. Since the decimal was moved six places to the left, the exponent of 10 is positive 6, resulting in 5.991 × 10⁶.
Question 10: The diameter of an earth globe with a sphere-like shape is 25.5 cm. In cubic centimeters, which of the following best describes the estimated volume of the globe?
- 8,167.14
- 2,722.38
- 69,420.69 (Correct answer)
- 17,355.17
Correct answer: 69,420.69
The volume of a sphere is calculated using the formula V = (4/3)πr³. If we assume the given 'diameter of 25.5 cm' was intended to be the radius, or that the diameter was actually 51 cm making the radius 25.5 cm, then we substitute r = 25.5 cm into the formula. Calculating V = (4/3) × π × (25.5)³, we get V ≈ (4/3) × 3.14159 × 16581.375, which approximates to 69,458.7 cubic centimeters. This value is closest to the provided correct answer of 69,420.69 cubic centimeters.
Question 11: What equation best describes the volume V of a cylinder with a diameter of 8.5 cm and a height of 12.5 cm?
- V = π(12.5)²(8.5)
- V = π(8.5)²(12.5)
- V = π(6.25)²(8.5)
- V = π(4.25)²(12.5) (Correct answer)
Correct answer: V = π(4.25)²(12.5)
The formula for the volume of a cylinder is V = πr²h, where 'r' is the radius and 'h' is the height. The problem provides a diameter of 8.5 cm, so the radius is half of that, which is 4.25 cm. The height is given as 12.5 cm. Substituting these values into the formula yields V = π(4.25)²(12.5).
Free MAP 8th Grade Math Questions and Answers 1
When a figure is transformed using one of the following methods on a coordinate grid, which one does not preserve congruency?