Grade 10 Mathematics CB-RAT 2024

10 Questions

What is the key difference between permutation and combination?

Permutation considers order, combination does not

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

5, 005

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

Drawing a face card and a red card

What does the shaded portion in the figure represent?

Intersection of events

What is the key difference between permutation and arrangement?

Permutation considers order, arrangement does not

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

18, 150

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

Combination is a type of permutation

What does the union of events represent in drawing cards?

Drawing a face card or a red card

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

The set of all possible outcomes

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

Not drawing a face card or a red card

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}