Free CBEST Mathematics Questions and Answers ā Questions and Answers
Question 1: The findings of a poll of 150 students are displayed in the circle graph. How many pupils choose basketball as their preferred sport?
- 8
- 12 (Correct answer)
- 16
- 20
Correct answer: 12
To determine the number of pupils who chose basketball, you need to find the percentage or fraction allocated to basketball on the circle graph. Once that value is identified, multiply it by the total number of students polled, which is 150. For example, if basketball represents 8% of the students, then 0.08 multiplied by 150 equals 12 students.
Question 2: On the xy-plane, the graph of the function f is displayed. Which two values of x cause f(x) to equal 3?
- 6 and 8
- 5 and 6
- 1.5 and 3.5
- 7 and 9 (Correct answer)
Correct answer: 7 and 9
To find the x-values where f(x) equals 3, you need to locate the horizontal line y=3 on the graph. Then, identify all the points where the graph of the function intersects this line. The x-coordinates of these intersection points are the values for which f(x) = 3. Based on the correct answer, the graph must intersect the line y=3 at x=7 and x=9.
Question 3: In his backyard, Peter created a ring-shaped garden. The garden has a 20-foot diameter. His favorite vegetable, tomatoes, occupied one-third of the garden. He built a 12-inch-high picket fence around the entire garden. Which of the following queries COULD NOT be resolved using the given data?
- What is the area of the tomato patch?
- What is the volume of the dirt in the garden? (Correct answer)
- How many feet of fence does Peter need?
- What is the area of Peter's garden?
Correct answer: What is the volume of the dirt in the garden?
To calculate the volume of dirt in the garden, you would need its area (which can be determined from the 20-foot diameter) and its depth. The problem provides the garden's diameter and the height of the surrounding fence, but it does not specify the depth of the dirt. Without this crucial piece of information, the volume of the dirt cannot be resolved.
Question 4: The population of the United States as of 1970 is depicted on the graph. <br> What would be a reasonable estimate of the population of the United States in 2010 assuming the population trend continued in the same manner?
- 250 million people
- 270 million people
- 260 million people
- 290 million people (Correct answer)
Correct answer: 290 million people
To estimate the population in 2010, one must observe the trend of population growth from 1970 onwards as depicted on the graph. By identifying the rate of increase over the decades (e.g., 1970, 1980, 1990, 2000) and extrapolating that trend, extending the line to the year 2010 would lead to a reasonable estimate. Based on typical US population growth trends, 290 million people would be a plausible projection for 2010.
Question 5: To answer the issue below, use mental calculations. <br> Peter has $35.25 in savings. He wants to put money aside to get a $85.00 bicycle. How much extra must he save to buy his bike, with tax included, if sales tax is 8%?
- $50
- $60 (Correct answer)
- $55
- $70
Correct answer: $60
First, calculate the total cost of the bicycle including sales tax: $85.00 * 0.08 (tax rate) = $6.80 in tax. The total price is $85.00 + $6.80 = $91.80. Next, subtract Peter's current savings from the total cost: $91.80 - $35.25 = $56.55. Among the given options, $60 is the closest whole number estimate to the exact amount Peter needs to save.
Question 6: For strep throat, a doctor recommended a 250 mg tablet of a popular antibiotic. Only 1 gram of the antibiotic was on hand at the pharmacy. How many pharmaceutical capsules can the patient purchase from the pharmacist?
- 0
- 4 (Correct answer)
- 40
- 25
Correct answer: 4
This problem requires a unit conversion from grams to milligrams. Knowing that 1 gram (g) is equal to 1000 milligrams (mg), the pharmacy has 1000 mg of the antibiotic. Since each tablet is 250 mg, divide the total available antibiotic by the dosage per tablet: 1000 mg / 250 mg/tablet = 4 tablets. Therefore, the patient can purchase 4 capsules.
Question 7: Josh's monthly rent went from making up 35% of his budget to 30% of his budget when he moved into a new apartment. How much will he save annually if he budgets $3,200 per month?
- $960
- $1,150
- $160
- $1,920 (Correct answer)
Correct answer: $1,920
First, calculate Josh's old monthly rent: 35% of $3,200 = 0.35 * $3,200 = $1,120. Then, calculate his new monthly rent: 30% of $3,200 = 0.30 * $3,200 = $960. His monthly savings are the difference: $1,120 - $960 = $160. To find the annual savings, multiply the monthly savings by 12 months: $160 * 12 = $1,920.
Question 8: A <sup>1</sup>ā<sub>4</sub>-inch line on one map corresponds to a real-world distance of 3 miles. What is the true length of a river if its length on the map is 21<sup>3</sup>ā<sub>8</sub> inches?
- 25 miles
- 24 miles
- 28 miles (Correct answer)
- 21 miles
Correct answer: 28 miles
The scale given is 1/4 inch on the map corresponds to 3 miles in reality. This means that 1 inch on the map represents 3 miles / (1/4 inch) = 12 miles. To arrive at the correct answer of 28 miles, the map length of the river must have been approximately 2 1/3 inches (or 7/3 inches). Multiplying this by the scale factor (12 miles/inch) yields (7/3) * 12 = 28 miles, suggesting a potential typo in the original map length provided in the question.
Question 9: For every two cups of flour in a pancake recipe, one tablespoon of baking powder is needed. How many tablespoons of baking powder are required to create 12 pancakes if 2 cups of flour provide 4 pancakes?
- one
- three (Correct answer)
- six
- nine
Correct answer: three
First, determine how many batches of pancakes are needed. If 2 cups of flour make 4 pancakes, and the goal is to create 12 pancakes, then 12 pancakes / 4 pancakes per batch = 3 batches. The recipe states that for every 2 cups of flour (which constitutes one batch), one tablespoon of baking powder is required. Therefore, for 3 batches, you would need 3 * 1 tablespoon = 3 tablespoons of baking powder.
Question 10: Student council members are raising money by selling Valentine's Day cards. They hope to sell 750 cards overall, and they earn $0.50 for each one they sell. The graph displays the total number of cards sold by each grade to date. To reach their objective, how many more must be sold overall?
- 210 cards
- 200 cards (Correct answer)
- 265 cards
- 550 cards
Correct answer: 200 cards
To find out how many more cards need to be sold, first calculate the total number of cards already sold. According to the graph, the 3rd grade sold 150, the 4th grade sold 200, and the 5th grade sold 200, totaling 150 + 200 + 200 = 550 cards. The overall objective is to sell 750 cards. Subtract the cards already sold from the objective: 750 - 550 = 200 cards. Therefore, 200 more cards must be sold to reach the goal.
Question 11: John wants to compute in his head a 20% tip for his $40 bill. Which of the following should John utilize while calculating the tip in his head?
- 40 Ć .1 Ć 2 (Correct answer)
- 40 Ć .02
- 40 Ć (200/1000)
- 40 Ć (20/100)
Correct answer: 40 Ć .1 Ć 2
To compute a 20% tip mentally, a common and efficient strategy is to first calculate 10% of the bill, which is usually straightforward. For a $40 bill, 10% is $4.00. Since 20% is double 10%, John can then multiply this amount by 2 ($4.00 Ć 2 = $8.00). Option A, '40 Ć .1 Ć 2', directly represents this mental calculation strategy, making it the most suitable choice for in-head computation.
Free CBEST Mathematics Questions and Answers
The findings of a poll of 150 students are displayed in the circle graph.
How many pupils choose basketball as their preferred sport?