📚 • Module 1 : Foundations of Math

Question 1

What are prime numbers?

Answer 1

Numbers with exactly 2 factors: 1 and itself. Examples: 2, 3, 5, 7, 11.

Question 2

What is the difference between a multiple and a factor?

Answer 2

Multiples : product of a number, so (4, 8, 12) for 4.
Factors : numbers that divide into another, so (1, 2, 4) for 4.

Question 3

How to find the Highest Common Factor (HCF)?

Answer 3

Find the largest shared factor of two numbers.

Example : HCF of 12 and 18:
Factors of 12 = 1, 2, 3, 4, 6, 12
Factors of 18 = 1, 2, 3, 6, 9, 18
Common factors = 1, 2, 3, 6
HCF = 6 (longest shared factor)

Question 4

How are directed numbers used in mathematics?

Answer 4

Directed numbers (positive and negative) are used to represent values with direction, such as temperature, and altitude.
Example :
+5°C — (above freezing)
-5°C — (below freezing)

Question 5

What does substitution mean in algebra?

Answer 5

Substitution means replacing a variable with a number.

Example : if 𝑥=3, substitute 3 for 𝑥 in 2𝑥+4.
Answer: 2(3)+4=6+4=10

Question 6

Simplify 3𝑥+4𝑥-2

Answer 6

7𝑥-2

Because… 3+4=7.

Question 7

Sum of angles on a straight line?

Answer 7

180°

Question 8

Sum of interior angles in a triangle?

Answer 8

180°

Question 9

Formula for the sum of interior angles of a polygon?

Answer 9

(n-2)x180°

Example :
For a hexagon, it has 6 sides, so (n = 6)
(6-2)x180°=4x180°=720°

Question 10

What is prime factorization?

Answer 10

Breaking a number into its prime factors.

Example : 12 = 2 x 2 x 3

Question 11

How do you find the LCM using prime factorization?

Answer 11

Take all prime factors, use the highest powers.

Example : LCM of 12 and 15 = 2² x 3 x 5 = 60

Question 12

How do you find the HCF using prime factorization?

Answer 12

Take the lowest powers of common prime factors.

Example : HCF of 12 and 15 = 3

Question 13

Simplify 3𝑥 x 4𝑦

Answer 13

12𝑥𝑦

Question 14

What is the sum of angles around a point?

Answer 14

360°

Question 15

What are alternate angles between parallel lines?

Answer 15

They are equal.

Question 16

What are the properties of an isosceles triangle?

Answer 16

Two sides are equal, two angles are equal.

Question 17

What is the sum of exterior angles of any polygon?

Answer 17

360°

Question 18

What is the place value of 5 in 3,524?

Answer 18

500 (hundreds place).

Question 19

Write an algebraic expression for “5 more than twice a number 𝑥.”

Answer 19

2𝑥+5

Question 20

What is an acute angle?

Answer 20

An angle less than 90°.

Question 21

What tool do you use to measure angles?

Answer 21

A protractor.

Question 22

What is the difference between discrete and continuous data?

Answer 22

Discrete data : Specific, separate values (example : number of students).

Continuous data : Any value within a range (example : height, weight).

Question 23

What are whole numbers?

Answer 23

Whole numbers are non-negative numbers without fractions or decimals.

Example : 0, 1, 2, 3…

Question 24

What is a right-angled triangle?

Answer 24

A triangle with one 90° angle.

Question 25

What are the properties of a rectangle?

Answer 25

Opposite sides are equal, and all angles are 90°.

Question 26

What is sampling in data collection?

Answer 26

Selecting a small group to represent the whole population.

Question 27

What is a frequency table?

Answer 27

A table that shows how often each value occurs in a dataset.

Question 28

What do line graphs represent?

Answer 28

They show trends in data over time using connected data points.

Question 29

What is the measure of each exterior angles in a regular polygon?

Answer 29

360°/n when n is the number of sides.

Question 30

What is the difference between qualitative and quantitative data?

Answer 30

Qualitative : Descriptive data (example : colors, names). Quantitative : Numerical data (example : height, age).

Question 31

What is special about an equilateral triangle?

Answer 31

All sides and angles are equal; each angle is 60°

Question 32

If two angles are supplementary and one is 110°, what is the other angle?

Answer 32

180°-110°=70°

Question 33

What is random sampling?

Answer 33

Every member of the population has an equal chance of being selected.

Question 34

What is the relationship between an exterior angle of a triangle and its interior opposite angles?

Answer 34

The exterior angle is equal to the sum of the two opposite interior angles.

Question 35

What is an obtuse triangle?

Answer 35

A triangle where one of the angles is greater than 90°. Example : A triangle with angles of 120°, 30°, and 30° is obtuse.