BECE Math 1 — Questions and Answers

Question 1: Which of the following represents a finite set?

{... 2,3,5,7}
{3,6,9,12} (Correct answer)
{2,4,6,8 ...}
{1,2,3,4, ...}

Correct answer: {3,6,9,12}

A finite set is a set that has a countable number of elements, meaning its elements can be listed and the list will eventually end. The set {3, 6, 9, 12} contains exactly four elements, making it a finite set. Options A, C, and D all use '...' to indicate that the sequence of elements continues indefinitely, representing infinite sets.

Question 2: Which one of the following is not a prime number?

5
3
9 (Correct answer)
7

Correct answer: 9

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Looking at the options, 5, 3, and 7 are all prime numbers as they are only divisible by 1 and themselves. However, 9 is not a prime number because it is divisible by 1, 3, and 9, meaning it has a divisor other than 1 and itself.

Question 3: An instrument retailer offers all students a 10% discount off the original price of an instrument. During a back-to-school sale, an additional 15% is deducted from the reduced price. Sophia, a local high school student, buys a flute for $306. How much did it cost originally?

400 (Correct answer)
410
330
378

Correct answer: 400

Let the original price of the flute be P. After a 10% discount, the price becomes P * (1 - 0.10) = 0.90P. An additional 15% discount is then applied to this reduced price, making the final price 0.90P * (1 - 0.15) = 0.90P * 0.85 = 0.765P. Since Sophia paid $306, we have 0.765P = 306. Solving for P, we get P = 306 / 0.765 = $400. Therefore, the flute originally cost $400.

Question 4: Which of the following numbers is not equivalent to 34(58+9).

58(34+9) (Correct answer)
1,972 + 306
34 * 67
34 * 58 + 34 * 9

Correct answer: 58(34+9)

The original expression 34(58+9) simplifies to 34 * 67 = 2278. We need to find the option that does not equal this value. Option A, 58(34+9), simplifies to 58 * 43 = 2494, which is not equal to 2278. Options B, C, and D all correctly represent or simplify to 2278, either through direct calculation or by applying the distributive property.

Question 5: How many 3 inch cubed pieces of fudge can fit into a Christmas tin that is 9 inches deep, 12 inches wide, and 9 inches high while still allowing the top to close?

24
15
36 (Correct answer)
30

Correct answer: 36

To find how many fudge pieces fit, we can calculate how many fit along each dimension. The tin is 9 inches deep, 12 inches wide, and 9 inches high, and each fudge cube is 3 inches on a side. So, 9/3 = 3 pieces fit along the depth, 12/3 = 4 pieces fit along the width, and 9/3 = 3 pieces fit along the height. Multiplying these values gives the total number of pieces: 3 * 4 * 3 = 36 pieces.

Question 6: How much will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile costs $8.91 per square yard?

236.55
275.18
224.51
237.6 (Correct answer)

Correct answer: 237.6

First, calculate the area of the kitchen floor: 12 feet * 20 feet = 240 square feet. Since the tile cost is given per square yard, convert the area to square yards. There are 3 feet in a yard, so 1 square yard = 3 feet * 3 feet = 9 square feet. Thus, 240 square feet / 9 square feet/square yard = 26.666... square yards. Finally, multiply the area in square yards by the cost per square yard: 26.666... * $8.91 = $237.60. The total cost to tile the floor is $237.60.

Question 7: If 3x = 6x-15, then x + 8=

12
13 (Correct answer)
11
10

Correct answer: 13

First, solve the equation 3x = 6x - 15 for x. Subtract 6x from both sides to get -3x = -15. Then, divide both sides by -3, which yields x = 5. The question asks for the value of x + 8. Substituting x = 5 into the expression gives 5 + 8 = 13.

Question 8: Riding on a ferry costs $5.00 for car and driver, and an extra 50 cents per passenger. If the ferry ticket costs $6.50, how many persons were in the vehicle?

4 (Correct answer)
3
2
5

Correct answer: 4

The ferry costs $5.00 for the car and driver. The total cost was $6.50, so the amount spent on extra passengers is $6.50 - $5.00 = $1.50. Since each extra passenger costs 50 cents ($0.50), the number of extra passengers is $1.50 / $0.50 = 3. Including the driver, the total number of persons in the vehicle is 1 (driver) + 3 (extra passengers) = 4 persons.

Question 9: A boy's pocket contains three red marbles, four blue marbles, and four green marbles. How many will he need to pull from his pocket to make sure he has at least one of each color?

8
9 (Correct answer)
3
5

Correct answer: 9

To guarantee at least one of each color, you must consider the worst-case scenario. This means drawing all marbles of the two most numerous colors first. There are 4 blue and 4 green marbles, so you could draw all 4 blue and all 4 green marbles (a total of 8 marbles) without getting any red. The very next marble drawn (the 9th one) would then guarantee that you have at least one red marble, thus ensuring you have at least one of each color.

Question 10: Find the missing term from the following sequence: 4, 9, 19, __, 79.

38
36
39 (Correct answer)
36

Correct answer: 39

To find the missing term, analyze the pattern of differences between consecutive numbers. The difference between 9 and 4 is 5. The difference between 19 and 9 is 10. This suggests a pattern where each difference is double the previous one. Following this pattern, the next difference should be 10 * 2 = 20. Adding this to 19 gives the missing term: 19 + 20 = 39. To verify, the next difference should be 20 * 2 = 40, and 39 + 40 = 79, which matches the last number in the sequence.

Question 11: How much money did Nicole save if she just spent 20% of her food budget in May 2001, rather than the full 25%?

$150.12
$131.10 (Correct answer)
$140.30
$165.22

Correct answer: $131.10

Nicole saved the difference between 25% and 20% of her food budget, which is 5% of her food budget. The question implies that the correct answer option represents this 5% saving. If the saving was $131.10, then 5% of her food budget is $131.10. This means her total food budget was $131.10 / 0.05 = $2622. Spending 20% ($524.40) instead of 25% ($655.50) of this budget results in a saving of $131.10.

BECE Math 1

Which of the following represents a finite set?