Algebra

Question 1

Algebraic Identities

a^2 - b^2 =

Algebra

Answer 1

(a+b)(a-b)

Question 2

Algebraic Identities

a^2 + b^2 + 2ab =

Algebra

Answer 2

(a+b)^2

Question 3

Algebraic Identities

a^2 + b^2 - 2ab =

Algebra

Answer 3

(a-b)^2

Question 4

Algebraic Identities

(a+b)^2

Algebra

Answer 4

(a-b)^2 + 4ab

Question 5

Algebraic Identities

(a-b)^2

Algebra

Answer 5

(a+b)^2 - 4ab

Question 6

(sqrt(x^2)) / x = ?

Answer 6

¦x¦ / x

Question 7

What are the steps to solving quadratic inequalities?

Answer 7

1. Factor the quadratic
2. Map the points where x = 0 on quadratic curve
3. If inequality is >0 take area above curve, if inequality is <0 take the area below the curve

Question 8

How do you know is linear inequalities have unique solutions?

Answer 8

Coefficients are not in proportion
a1/a2 =/= b1/b2

Question 9

How do you know is linear inequalities have infinit solutions?

Answer 9

Coefficients are in proportion
a1/a2 = b1/b2

Question 10

How do you know is linear inequalities have no solutions?

Answer 10

Coefficients are in proportion BUT not with the constants
a1/a2 = b1/b2 =/= c1/c2

Question 11

How do you solve inequalities with absolute values?

Answer 11

1. Use the corollary method

Question 12

How do you solve:
¦ax + b¦ + ¦cx + d¦ = e?

Also applies to subtraction

Answer 12

1. Use the corollary method

Question 13

When multiplying an inequality by -1 you must remember to do what?

Answer 13

Flip the inequality sign

Question 14

What are the three methods of solving linear inequalities?

Answer 14

1. Visualisation
2. Adding
3. Substitution

Question 15

How do you solve rational inequalities?

Answer 15

1. Multiply both sides of the inequality by the (denominator)^2

Question 16

What are the formulae for a geometric progression?

Answer 16

1. a = a1(r^(n-1))
2. S = (a1(1-(r^n)))/(1-r)

Question 17

A function range is what?

Answer 17

A set of output values obtained by the function

Question 18

A function domain is what?

Answer 18

A set of input values for which the output is defined

Question 19

What is the basic job of a function equation?

Answer 19

To find if the equation is solvable

Question 20

1. f(x) x g(x) =
2. f(x) / g(x) =

Answer 20

1. fg(x)
2. (f/g)(x)

Question 21

1. f(x) + g(x) =
2. f(x) - g(x) =

Answer 21

1. (f+g)(x)
2. (f-g)(x)

Question 22

What are the formulae for arithmetic progression?

Answer 22

an = a1 + (n-1)d
Sn = (n/2) (2a + (n-1) d)

Question 23

What is the process to solve equations using the corollary?

Answer 23

1. Find the break points
2. Find the constraints
3. Solve
4. Check the solution is in range
5. Check the inequalitz holds at the break point (if ineq qn)
6. Determine final solution

Question 24

What is the process to solve:
|x + a | = b OR | x + a |= bx

Answer 24

1. Translate into linear equations
2. Solve
3. Check against constraints

Question 25

How do higher powers >1 affect the wavy line method of solving inequalities?

Answer 25

• Odd powers >1 = 1
• Even powers > 1 you can’t include in the breakpoint but may be included in the solution

Question 26

What is the process to use the wavy line method?

Answer 26

1. Find the breakpoints where QE = 0
2. Draw line through the breakpoints top right down
3. Find range based on inequality

Question 27

To solve linear inequalities you must:

Answer 27

• Have inequalities with the same sign
• Align like terms by adding two inequalities

Question 28

If p, q are the two solutions to a quadratic formula then:
1. p + q =?
2. pq =?

Answer 28

1. p + q = -b/a
2. pq = c/a