PERT Math Practice Quiz 2 — Questions and Answers
Question 1: One third of the candidates for a job were 25 years old or younger. Two sevenths of the candidates were at least 50 years old. If 84 people applied for the job, how many were between 25 and 50?
- 32 (Correct answer)
- 28
- 24
- 33
Correct answer: 32
Calculate the number of candidates 25 or younger: (1/3) * 84 = 28 people. Then, calculate the number of candidates at least 50 years old: (2/7) * 84 = 24 people. The total number of candidates in these two age groups is 28 + 24 = 52. Subtract this sum from the total number of applicants to find those between 25 and 50: 84 - 52 = 32 people.
Question 2: Which of the following is a factor of 450 and multiple of 25?
- 30
- 75 (Correct answer)
- 90
- 100
Correct answer: 75
A factor of 450 means 450 is perfectly divisible by that number, and a multiple of 25 means the number can be expressed as 25 multiplied by an integer. Checking the options, 75 is a multiple of 25 (75 = 3 * 25). Also, 450 is divisible by 75 (450 / 75 = 6), making 75 a factor of 450. Thus, 75 satisfies both conditions.
Question 3: The formula h - 15 = 3.2t gives the height h in inches of a plant t weeks after planting. Which is the rate at which the plant's height is increasing?
- 15 inches per week
- 18.2 inches per week
- 3.2 inches per week (Correct answer)
- 48 inches per week
Correct answer: 3.2 inches per week
The formula h - 15 = 3.2t can be rewritten as h = 3.2t + 15. This equation is in the slope-intercept form (y = mx + b), where 'm' represents the rate of change. Here, 'h' is the height and 't' is time in weeks, so the coefficient of 't', which is 3.2, represents the rate at which the plant's height is increasing in inches per week.
Question 4: The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. How high was the initial height of the shrub?
- 15 inches (Correct answer)
- 3.2 inches
- 18.2 inches
- 11.8 inches
Correct answer: 15 inches
The initial height of the plant occurs at time t = 0, before any growth has taken place. Substitute t = 0 into the given formula: h - 15 = 3.2 * (0). This simplifies to h - 15 = 0, which means h = 15. Therefore, the initial height of the shrub was 15 inches.
Question 5: The formula h -15 = 3.2t gives the height h in inches of a plant t weeks after planting. When was the height 31 inches?
- Some time between 11 and 18 weeks
- Some time between 7 and 12 weeks
- Some time between 6 and 10 weeks
- Some time between 3 and 7 weeks (Correct answer)
Correct answer: Some time between 3 and 7 weeks
To find when the height was 31 inches, substitute h = 31 into the formula: 31 - 15 = 3.2t. This simplifies to 16 = 3.2t. Dividing both sides by 3.2 gives t = 16 / 3.2 = 5. So, the height was 31 inches after 5 weeks, which falls within the range of 'Some time between 3 and 7 weeks'.
Question 6: A graph of the temperature T (degrees Fahrenheit) in a refrigerator t hours after midday. What is the equation of the axis of symmetry of this graph?
- T = 9
- t = 3
- T = 0
- t = 0 (Correct answer)
Correct answer: t = 0
Without the specific graph or function, we assume a common parabolic temperature model, such as T = 9 - t^2 (as implied by Q12). For such a function, the axis of symmetry is the vertical line that passes through the vertex. In this case, the vertex is at t=0, so the equation of the axis of symmetry is t = 0, representing midday.
Question 7: It is necessary to find the times when the temperature is 8o F. Which of the following is the correct equation to do this.
- 9 - t = 8
- 9 + t2 = 8
- 9 - t2 = 8 (Correct answer)
- 9t - t2 = 8
Correct answer: 9 - t2 = 8
To find the times when the temperature T is 8°F, we need an equation that models the temperature as a function of time t and sets it equal to 8. Option C, 9 - t^2 = 8, represents a plausible quadratic function for temperature (T = 9 - t^2) set to the desired temperature. This form suggests a temperature that peaks at t=0 and decreases quadratically.
Question 8: Which of the following is the equation of the straight line joining the points on the graph corresponding to t = 2 and t = 1?
- T + 3t = 11 (Correct answer)
- T - 3t = 11
- T + 11t = 3
- T + 3t = 1
Correct answer: T + 3t = 11
Using the temperature function T = 9 - t^2 (inferred from Q12), find the points: for t=1, T = 9 - 1^2 = 8 (point (1, 8)); for t=2, T = 9 - 2^2 = 5 (point (2, 5)). The slope of the line is (5-8)/(2-1) = -3. Using the point-slope form T - T1 = m(t - t1) with (1, 8): T - 8 = -3(t - 1), which simplifies to T - 8 = -3t + 3, or T + 3t = 11.
Question 9: If the radius of the sphere were doubled by what factor would the surface area be enlarged?
Correct answer: 4
The surface area of a sphere is given by the formula A = 4πr^2. If the radius 'r' is doubled to '2r', the new surface area A' becomes A' = 4π(2r)^2. This simplifies to A' = 4π(4r^2) = 4 * (4πr^2). Thus, the new surface area is 4 times the original surface area, meaning it's enlarged by a factor of 4.
Question 10: Which of the following is the same as (√3 + √2)2 ?
- (A) 5 + 2√6 (Correct answer)
- (B) 5
- (C) 6
- (D)5 + 2√5
Correct answer: (A) 5 + 2√6
To expand (√3 + √2)^2, use the algebraic identity (a + b)^2 = a^2 + 2ab + b^2. Here, a = √3 and b = √2. So, (√3)^2 + 2(√3)(√2) + (√2)^2. This simplifies to 3 + 2√(3*2) + 2, which further combines to 3 + 2√6 + 2, resulting in 5 + 2√6.
