Algebra Worksheet

USEFUL FORMULAS:

Laws of exponents

Arithmetic formulas
(a−b)(a+b) = a²−b²,

(a+b)² = a²+2ab+b²,

(a−b)² = a²−2ab+b².

Rules concerning logarithms

Rules about solving equations
• Whenever you divide by some number make sure it is not 0!

• If a fraction is 0 then this means its numerator is 0, i.e.

• If a product is equal to 0 than one of its parts is zero, so check
all of them, i.e.
f(x) · g(x) = 0 => solve f(x) = 0 and g(x) = 0.

• Know the quadratic formula and remember that if x²+bx+c = 0
has roots and then x² + bx + c = (x − ) · (x −β ).

1. Decide if the following are TRUE or FALSE.

2. Solve for t: (t − 5)(t + 1) = 11

3. Solve for θ:

4. Solve for y in terms of x : x² + 3y = −7xy + 11.

5. Does the following equation determine y as a function of x: y² −
x³ = αx.

6. Solve for T and simplify as much as possible:

7. The following sequence of exercises is meant to review basic identities
that you should know.
Start with (x + 2)² and do the multiplication, you should get x² +
4x + 4.
Now do the same for (x + 3)², (2 + x)² and (x + y)².
At this point you should see that there is an actual formula that one
can use in for each of these . The formula is

(A + B)² = A² + 2AB + B².

Next, start with (x − 2)² and do the multiplication, you should get
x² − 4x + 4.
Now do the same for (x − 3)², (2 − x)² and (x − y)².
Again you should see that there is a convenient formula

(A − B)² = A² − 2AB + B².

The two formulas above are the basic tools for completing the square.
There is one more formula that is important. Here is a way to get it.
Multiply (x − 1)(x + 1), what do you get?
Now do the same for (x+2)(x−2), (x−7)(x+7), and (x−y)(x+y).
Do you see a formula?
You always have

(A − B)(A + B) = A² − B².

Now that you know the basic formulas let’s do some exercises with
them. The next exercise aims to do exactly this.

8. Simplify