BASMATH REVIEWER
1 EQUATIONS AND INEQUALITIES IN ONE VARIABLE
a. Linear Equations
b. Quadratic and Rational Equations
c. Linear, Quadratic and Rational Inequalities
d. Equations and Inequalities Involving Absolute Values
Solve for the unknown variable.
1. 14 − 2𝑥2=(5− 𝑥)(2𝑥 + 1);
2. √2𝑦 − 1 − √𝑦 + 1 = 0;
3. 6𝑎𝑥 −𝑎𝑏 =𝑎𝑥 + 9𝑎𝑏, where a and b are constants;
4. 9
𝑥+1 −2𝑥+3
𝑥−2 =7𝑥−2𝑥2
𝑥2−𝑥−2;
5. √5𝑥 + 6 = 𝑥 + 2;
6. √𝑥 + 2√2𝑥 + 3 − 3 = 0;
7. |2𝑥 − 1|=|4𝑥 + 9|;
8. |𝑎 − 2|= 3𝑎 + 1;
9. |𝑥2− 2𝑥 − 16|= 8;
10. 2𝑥 − 3 ≥ 3;
11. −2 < 3𝑎
5< 7;
12. |𝑏−4|
6≤ 3;
13. 6𝑥2−13𝑥 − 28 ≤ 0;
14. |𝑥2+ 1|> 5;
15. √2𝑥 + 6 + 3 ≤ 9;
16. √𝑥2− 2𝑥 − 8 > 𝑥 + 2;
17. The sum of three consecutive multiples of 4 is 444. Find these multiples.
18. The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find the two
numbers.
19. The difference between two numbers is 48. The ratio of the two numbers is 7:3. What are
the two numbers?
20. Aaron is 5 years younger that Ron. Four years later, Ron will be twice as old as Aaron.
Find their present ages.
21. The cost of two tables and three chairs is ₱705.00. If the table costs ₱40 more than the
chair, find the cost of the table and the chair.
2 FUNCTIONS AND THEIR GRAPHS
a. Functions (Domain, range, graph, vertical line test, increasing/decreasing functions)
b. Evaluating Functions
c. Types of Functions (Linear and constant, absolute value, quadratic, polynomial, rational)
d. Operations on Functions
e. Piecewise-defined Functions
f. One to one Functions and the Horizontal Line Test
g. Inverse Functions
Graph the following functions and determine its domain and range.
1. 𝑓(𝑥) = √𝑥 + 1 + 4
2. 𝑓(𝑥) = 𝑥2− 8𝑥 + 16
3. 𝑓(𝑥) = 3𝑥2
