Learning Resources
Activity
Section 01 Rational Algebraic Expressions
For each of the exercises 1 - 12, perform the indicated operations and express the answer in simplest terms. Also state which values must be excluded from the replacement set.
1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
Solve the equations in exercises 13 - 14. State which values must be excluded from the replacement set.
13. 
14. 
Section 02 Rearranging Formulas
Solve each of the formulas in exercises 1 - 5 for the variable indicated:
1. 
for u
2. 
for F
3. 
for x
4. 
for a
5. 
for V
6. (a) Solve the formula 
for d,
(b) Use the answer to part (a) to find d if S = 65 , n = 5 , a = 7.
7. The shaded area in the diagram below is obtained by removing a semicircular area from both ends of the rectangle ABCD.
(a) Express the shaded area, SA , as a function of x and y.
(b) If y = 2x + 5, express SA as a function of x only.
(c) Use the formula in part (b) to find SA if x = 
8. A rectangle is drawn in a coordinate system with vertices on line L as shown on the diagram below:
(a) Express the area of the rectangle, A , as a function of x and y.
(b) If the slope of the line L is -
, express A as a function of x only.
(c) If the area of the rectangle is 20 square units, what is the value of x?
Test Yourself
For each of the exercises 1 - 5 , perform the indicated operations and express the answer in simplest terms. Also state which values must be excluded from the replacement set.
1. 
2. 
3. 
4. 
5. 
6. Solve 
for y. State the values must be excluded from the replacement set.
7. Solve 
for t1
8. The shaded area in the diagram below is obtained by cutting an equilateral triangle out of the rectangle ABCD.
(a) Express the area, A , of the shaded region as a function of x and y.
(b) If y = 2x, express A as a function of x only.
(c) If the area in part (b) is 12 square units , find (i) the exact value of x, (ii) the approximate value of x rounded to the tenth's place.