Real Number and Pic
TUTORIAL: NUMBER SYSTEM
1. Determine whether each statement is true or false a) Every counting number is an integer b) Zero is a counting number c) Negative six is greater than negative three d) Some of the integers is natural numbers
2. List the number describe and graph them on the number line a) The counting number smaller than 6 b) The integer between -3 and 3
3. Given S = {-3, 0,[pic], [pic], e, , 4, 8…}, identify the set of (a) natural numbers (b) whole numbers (c) integers (d) rational numbers (e) irrational numbers (f) real numbers
4. Express each of the numbers as a quotient [pic] (a) 0.7777…… (b) 2.7181818….
5. Write each of the following inequalities in interval notation and show them on the real number line. (a) 2 < x < 6 (b) (5 < x < (1 (c) (3 ( x ( 7 (d) (2 < x ( 0 (e) x < 3 (f) x ( (1 (g) x ( (2 (h) (3 ( x < 2
6. Show each of the following intervals on the real number line. (a) [(2, 3] (b) ((4, 4) (c) (((, 5] (d) [(1, () (e) ((3, 6] (f) [(2, 3) (g) ((2, 0) ( (3, 6) (h) [(6, 2) ( [(3, 7)
2 Evaluate
(a) [pic] (b) 27[pic] (c) [pic] (d) [pic] (e) (0.36)[pic] (f) (2.56)[pic] (g) [pic] (h) [pic]
7. Simplify the following expressions: (a) 3[pic] (b) 4[pic] (c) 9[pic][pic] (d) 5[pic]
8. Solve the following equations:
(a) 9[pic]= 27 (b) 3[pic]= 243 (c) 2[pic] = [pic]
(d) 4[pic] (e) x[pic] (f) 4x[pic]
(g) 7[pic]- 49[pic]= 0 (h) (4[pic]= 4[pic]
9. Solve the equations:
(a) [pic] (b) [pic]
(b) [pic] (d) [pic]
10. Express in terms of the simplest possible surds:
(a) [pic] (b) [pic]
(c) [pic] (d) [pic]
11. Simplify:
(a) [pic] (b) ([pic]
(c) [pic] (d) [pic]
12. Rationalise the denominators and simplify
1. Determine whether each statement is true or false a) Every counting number is an integer b) Zero is a counting number c) Negative six is greater than negative three d) Some of the integers is natural numbers
2. List the number describe and graph them on the number line a) The counting number smaller than 6 b) The integer between -3 and 3
3. Given S = {-3, 0,[pic], [pic], e, , 4, 8…}, identify the set of (a) natural numbers (b) whole numbers (c) integers (d) rational numbers (e) irrational numbers (f) real numbers
4. Express each of the numbers as a quotient [pic] (a) 0.7777…… (b) 2.7181818….
5. Write each of the following inequalities in interval notation and show them on the real number line. (a) 2 < x < 6 (b) (5 < x < (1 (c) (3 ( x ( 7 (d) (2 < x ( 0 (e) x < 3 (f) x ( (1 (g) x ( (2 (h) (3 ( x < 2
6. Show each of the following intervals on the real number line. (a) [(2, 3] (b) ((4, 4) (c) (((, 5] (d) [(1, () (e) ((3, 6] (f) [(2, 3) (g) ((2, 0) ( (3, 6) (h) [(6, 2) ( [(3, 7)
2 Evaluate
(a) [pic] (b) 27[pic] (c) [pic] (d) [pic] (e) (0.36)[pic] (f) (2.56)[pic] (g) [pic] (h) [pic]
7. Simplify the following expressions: (a) 3[pic] (b) 4[pic] (c) 9[pic][pic] (d) 5[pic]
8. Solve the following equations:
(a) 9[pic]= 27 (b) 3[pic]= 243 (c) 2[pic] = [pic]
(d) 4[pic] (e) x[pic] (f) 4x[pic]
(g) 7[pic]- 49[pic]= 0 (h) (4[pic]= 4[pic]
9. Solve the equations:
(a) [pic] (b) [pic]
(b) [pic] (d) [pic]
10. Express in terms of the simplest possible surds:
(a) [pic] (b) [pic]
(c) [pic] (d) [pic]
11. Simplify:
(a) [pic] (b) ([pic]
(c) [pic] (d) [pic]
12. Rationalise the denominators and simplify