Mathematics Quiz for Grade 10

Which of the following illustrates the number of ways 5 boys seated arranged in a row?

• 5 • 4 • 3

• 5 • 4 • 3 • 2 • 1

• r!

• n!

Answer explanation

The number of ways to arrange 5 boys in a row is calculated using factorial notation, which is 5! = 5 • 4 • 3 • 2 • 1. This represents all possible permutations of the boys.

What is the value of 8 P 5?

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Answer explanation

The value of 8 P 5 (permutations of 8 items taken 5 at a time) is calculated as 8! / (8-5)! = 8! / 3! = 8 × 7 × 6 × 5 × 4 = 6720.

If (5) means that there are 5 elements in the set P ∩ Q, how many elements are there in P ∪ Q?

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Answer explanation

To find the number of elements in P ∪ Q, we use the formula |P ∪ Q| = |P| + |Q| - |P ∩ Q|. Since |P ∩ Q| = 5, we need the sizes of P and Q to calculate |P ∪ Q|. Without those, we can't determine the exact number.

The probability that a visit to the school clinic is neither due to dental reasons nor medical reasons is 35%. Of those coming to the clinic, 30% are due to medical reasons and 40% are due to dental reasons. What is the probability that a visit to the school clinic is due to both dental and medical reasons?

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Answer explanation

Let P(M) = 0.30, P(D) = 0.40, and P(N) = 0.35. Using the formula P(M or D) = 1 - P(N), we find P(M or D) = 0.65. Then, P(M and D) = P(M) + P(D) - P(M or D) = 0.30 + 0.40 - 0.65 = 0.05. Thus, the probability is 5%.

What do you call the different arrangements of objects of a group?

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Answer explanation

The different arrangements of objects of a group are called permutations. Permutations consider the order of arrangement, distinguishing them from combinations, which do not.

Which of the following illustrates permutation?

• selecting fruits to make a salad

• assigning telephone numbers to homes

• choosing household chores to do after classes

• selecting posters to hang in the walls of your room

Answer explanation

Assigning telephone numbers to homes is a permutation because the order of assignment matters; each number is unique to a specific home. The other options do not involve unique arrangements where order is significant.

The two events, A and B, are not mutually exclusive, which of the following shows the probability that either A or B occur?

• P(A) + P(B)

• P(A) – P(B)

• P(A) + P(B) – P(A and B)

• P(A) – P(B) + P(A and B)

Answer explanation

For non-mutually exclusive events A and B, the probability of either A or B occurring is given by P(A) + P(B) - P(A and B). This accounts for the overlap of A and B, ensuring we don't double-count.

How many different 4-digit even numbers can be formed from the digits 1, 3, 5, 6, 8, and 9 if no repetition of digits is allowed?

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Answer explanation

To form a 4-digit even number, the last digit must be 6 or 8. If 6 is last, we have 4 choices for the first digit (1, 3, 5, 8) and 3 choices for the second and third digits. If 8 is last, we have 4 choices for the first digit (1, 3, 5, 6) and 3 choices for the second and third digits. Thus, total = 4*3*2 + 4*3*2 = 48.

A card is selected from a pack of 52 cards. Find the probability that the card is red and a heart.

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Answer explanation

There are 26 red cards in a deck (13 hearts and 13 diamonds). The probability of drawing a heart (which is red) is 13/52. Thus, the probability that the card is red and a heart is 1/4.

Which of the following does NOT illustrate combination?

• Selecting 3 songs from 7 choices for a singing audition

• Fixing schedule of tourist for 3 days in Underground River

• enumerating 2 seats of meals out of 5

• listing the first 5 players out of 12 for a basketball match

Answer explanation

Selecting 3 songs from 7 choices is a combination, but it does not illustrate a unique arrangement or order, unlike listing players or fixing schedules, which involve specific sequences.