Lecture 1

Question 1

What is a variable?

Answer 1

A symbol or letter that represents an unknown or changing
quantity in a mathematical expression or equation: e.g. x, y, p, θ, k

Question 2

What is a coefficient?

Answer 2

A numerical or constant factor that multiplies a variable in an algebraic expression or equation: e.g. 4𝑥 where 4 is the coefficient and 𝑥 is the variable.

Question 3

What is a reciprocal?

Answer 3

The multiplicative inverse of a number or variable: e.g. The reciprocal of 8 is 1/8

Question 4

What is a modulus?

Answer 4

The absolute (non-negative) value of a real number or
variable. For positive numbers, the modulus is the number itself. For
negative numbers, it’s the number without its negative sign.

Question 5

How is the modulus represented?

Answer 5

By a value or variable sandwiched between two
vertical parallel lines: |17| is 17, but the |−9.5| is 9.5

Question 6

What are factorials?

Answer 6

A number that is the product of all positive integers from n down, is denoted by an exclamation mark (e.g. 3!)

e.g. 4! = 4 x 3 x 2 x 1 =24
or
3! = 3 x 2 x 1 =6

Question 7

Where are factorials used?

Answer 7

• Calculus
• Probability
• Combinations
• Permutations

Question 8

What can factorials not be calculated by?

Answer 8

Negative numbers and fractions

Question 9

What is the factorial of 1 and 0?

Answer 9

1

Question 10

What is the top part of a fraction?

Answer 10

Numerator

Question 11

What is the bottom part of a fraction?

Answer 11

Denominator

Question 12

How does the law of indices simplify algebraic fractions?

Answer 12

pq² / rq⁵ becomes pq / rq³

Question 13

How are algebraic fractions multiplied?

Answer 13

The numerator terms are multiplied
together, and the denominator terms are multiplied together

Question 14

How are algebraic fractions divided?

Answer 14

By inverting the second fraction and then multiplying the fractions
(p/q) / (r/s) = ps/qr

Question 15

How are algebraic fractions added/ subtracted?

Answer 15

The opposite denominator joins the opposite numerators and the denominators are combined
e.g. 𝑎/𝑏 + 𝑐/𝑑 = 𝑎𝑑+𝑐𝑏/𝑏𝑑
or
6𝑚/𝑘𝑝 − 𝑞𝑟/𝑡 = 6𝑚𝑡−𝑘𝑝𝑞𝑟/𝑘𝑝𝑡