Grade 10 Mathematics CB-RAT 2024

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Questions and Answers

What is the key difference between permutation and combination?

Permutation considers order, combination does not (correct)
Combination involves probability, permutation does not
Combination deals with arrangement, permutation with selection
Order is important in both

How many ways can Sir Jayson choose 6 individuals from the 15 players who applied for the team?

5, 005 (correct)
12, 376
8, 910, 700
3, 603, 600

What is the correct description of the intersection of events in drawing cards?

Drawing a face card and a red card (correct)
Drawing a face card and a club card
Drawing a face card or a king card
Drawing a king card or a diamond card

What does the shaded portion in the figure represent?

Intersection of events (D) Signup and view all the answers

What is the key difference between permutation and arrangement?

Permutation considers order, arrangement does not (C) Signup and view all the answers

If 17 players applied for the team, how many ways can Sir Jayson choose 6 individuals?

18, 150 (A) Signup and view all the answers

What is the correct statement about the relationship between permutation and combination?

Combination is a type of permutation (B) Signup and view all the answers

What does the union of events represent in drawing cards?

Drawing a face card or a red card (D) Signup and view all the answers

What is the sample space in the context of drawing cards?

The set of all possible outcomes (C) Signup and view all the answers

What is the correct description of the complement of events in drawing cards?

Not drawing a face card or a red card (D) Signup and view all the answers

Flashcards

Permutation vs. Combination

Permutation considers the order of items, while combination does not consider order.

Choosing individuals (15 from 6)

The number of ways to choose 6 individuals from 15 players is 5,005.

Intersection of Events (Cards)

The intersection of events involves outcomes that satisfy both events. E.g., Drawing a card that is both a face card and red.

Relationship: Permutation & Combination

Combination is a selection of items where order does not matter.

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Union of events (cards)

The union of events includes outcomes that satisfy either event. E.g., Drawing a card that is either a face card or a red card.

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Sample Space

The set of all possible outcomes of an experiment.

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Complement of Events (Cards)

The complement of an event includes all outcomes NOT in the event. E.g., Not drawing a face card or a red card.

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Study Notes

Mathematics Review for Grade 10

Sequences and Series

Identify the next number in the sequence 7, 15, 24, 34, ___: A. 43, B. 44, C. 45, D. 46
Formula for permutation of non-distinct objects: P(n, r) = n! / (n-r)!
Arithmetic mean of 3 and 15: A. 10, B. 9

Probability

Sample space: all possible outcomes of an experiment
Event: a set of outcomes of an experiment
Probability of an event: number of favorable outcomes / total number of possible outcomes

Circles

Center and radius of a circle: C (0, 0); r = 4, or C (1, 1); r = 4
Equation of a circle: (x - 5)² + (y - 0)² = 25
Area of a circle: πr²

Combinatorics

Permutation: arrangement of objects in a specific order
Combination: selection of objects without regard to order
Formula for permutation: P(n, r) = n! / (n-r)!
Formula for combination: C(n, r) = n! / (r!(n-r)!)
Example: number of ways to choose 6 individuals from 15 players: A. 5, 005, B. 12, 376, C. 3, 603, 600, D. 8, 910, 700

Polynomials

Factoring polynomials: finding the linear factors of a quadratic expression
Example: x² + 5x - 6 = (x + 6)(x - 1)

Geometry

Semicircle arch: diameter = 4 meters, length of iron before bending = π meters
Circle inside a square: radius = 4 inches, area = 16π sq.in.

Sets

Union of sets: all elements in either set A or set B
Intersection of sets: all elements common to both sets A and B
Example: A = {1, 2, 3, 4}, B = {4, 5, 6, 7}, A ∪ B = {1, 2, 3, 4, 5, 6, 7}, A ∩ B = {4}