Chapter 4: Algebra

Question 1

What do you do when multiplying terms with the same base?

Answer 1

You add the terms together.

Question 2

What do you do when dividing terms with the same base?

Answer 2

You subtract the terms.

Question 3

What do you do when a power is being raised to another power?

Answer 3

You multiply the terms together.

Question 4

What do you do when a product of terms is being raised to a power?

Answer 4

Both products are raised to that power.

Question 5

What do you do when a fraction is being rased to a power?

Answer 5

Both the numerator and denominator are raised to that power.

Question 6

What do you do when a number is raised to the power of zero?

Answer 6

The answer becomes 1.

Question 7

What happens when a number is raised to a negative power?

Answer 7

A fraction is created (with a numerator of 1).

Question 8

What happens when a fraction is raised to the power of -1?

Answer 8

The fraction is flipped, with the denominator becoming the new numerator and the numerator becoming the new denominator.

Question 9

How do you add/subtract a fraction?

Answer 9

1. Find the lowest common denominator.
2. Multiply the top by each respective multiplication.
3. Add/subtract the fractions.
4. Simplify if necessary.

Question 10

How do you multiply a fraction?

Answer 10

1. Cancel any common factors.
2. Multiply the fractions.
3. Simplify if necessary.

Question 11

How do you divide a fraction?

Answer 11

1. Flip the second fraction so the denominator is on top and the numerator is on the bottom.
2. Multiply the two fractions.
3. Simplify if necessary.

Question 12

How do you expand an expression (e.g 2(a + b))?

Answer 12

1. Multiply the outside number by the inside numbers
2. Simplify where necessary.
   e. g 2(a + b) = 2a + 2b

Question 13

How do you factorise an expression (e.g 25a^2 - 20ab)?

Answer 13

1. Identify the highest common factor
2. Divide each term into the HCF
3. Place the answers inside brackets.
   e. g 25a^2 - 20ab = 5a(5a - 4b)

Question 14

How do you expand a binomial product (the 2 x 2 table)?

Answer 14

Multiply each term in the first binomial by each term in the second binomial.

Question 15

What is a quadratic expression?

Answer 15

An equation with a variable higher than 2.

Question 16

How do you factorise using the form x^2 + bx + c.

Answer 16

1. Find two numbers with a sum of b and a product of c.

2. Use the two numbers to write a binomial product in the form of (x _), (x _)