Convert the number 0.00045 to scientific notation.
A) 4.5×10^−4
B) 45×10^−5
C) 4.5×10^−5
D) 45×10^−6
Correct Answer: C) 4.5×10^−5
Explanation: In scientific notation, 0.00045 is written as 4.54 times 10 raised to the power of −5 to represent the decimal moving five places to the right.
If the slope of a line is 22, which of the following could be the coordinates of two points on the line?
A) (1,2)(1,2) and (3,8)(3,8)
B) (0,0)(0,0) and (2,4)(2,4)
C) (2,3)(2,3) and (4,7)(4,7)
D) (1,1)(1,1) and (2,3)(2,3)
Correct Answer: B) (0,0)(0,0) and (2,4)(2,4)
Explanation: The slope formula is (y2−y1)/(x2−x1). For option B, the slope between the points is (4−0)/(2−0)=2, matching the given slope..
How is the Pythagorean Theorem used to find the distance between two points on a coordinate plane?
A) By calculating the hypotenuse of a right triangle formed by the points
B) By adding the x-coordinates and y-coordinates of the points
C) By multiplying the x-coordinate of one point by the y-coordinate of the other
D) By subtracting the coordinates of one point from the coordinates of the other
Correct Answer: A) By calculating the hypotenuse of a right triangle formed by the points
Explanation: The distance between two points forms the hypotenuse of a right triangle, and the Pythagorean Theorem is used to calculate it.
What does the slope of a line represent in a proportional relationship shown in a graph?
A) The x-intercept of the graph
B) The y-intercept of the graph
C) The rate of change between the variables
D) The maximum value of the dependent variable
Correct Answer: C) The rate of change between the variables
Explanation: In a graph of a proportional relationship, the slope represents the unit rate or the rate of change between the two variables.
What is the slope of the line that passes through the points (2, 4) and (6, 16)?
A) 2
B) 3
C) 4
D) 5
Correct Answer: B) 3
Explanation: The slope (m) is calculated by the formula m = (y 2 −y 1 )/(x 2 −x 1 ). Substituting the given points gives m =(16−4)/(6−2)=12/4=3m=(16−4)/(6−2)=12/4=3.
A cylinder has a base area of 28 square centimeters and a height of 10 centimeters. What is its volume?
A) 280 cm^3
B) 38 cm^3
C) 18 cm^3
D) 140 cm^3
Correct Answer: A) 280 cm^3
Explanation: The volume of a cylinder is calculated as V=Bh where B is the area of the base and ℎh is the height. Therefore, V=28×10=280V=28×10=280 cm^3.
Which equation represents a linear relationship that can be graphed to pass through the origin?
A) y = 5x+2
B) y=4x
C) y=x−3
D) y=2x+5
Correct Answer: B) y=4x
Explanation: A linear equation that passes through the origin is of the form y=mx, where m is the slope and there is no y-intercept.y=4x meets this criterion.
What is the value of 3.2×10^3 in standard form?
A) 320
B) 3200
C) 32000
D) 3.2
Correct Answer: B) 3200
Explanation: 3.2×1033.2×103 means 3.2 multiplied by 1000, which equals 3200.
Which of the following is a correct representation of the Pythagorean Theorem?
A) a^2 + b^2 = c^2
B) a^2 - b^2 = c^2
C) ab = c^2
D) a/b = c^2
Correct Answer: A) a^2 + b^2 = c^2
Explanation: The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
If the scale factor of a dilation is 1/2, what happens to the area of a two-dimensional figure after the dilation?
A) It doubles.
B) It remains the same.
C) It is halved.
D) It is quartered.
Correct Answer: D) It is quartered.
Explanation: When a two-dimensional figure is dilated by a scale factor of 1/2, its area becomes 1/4 of the original area, because area scales by the square of the scale factor.
