CHAPTER Number Systems Solutions Practice Questions 1 6

CHAPTER Number Systems Solutions: Practice Questions 1. 6 01

01 1. Practice Questions 1. 6 Which of the following numbers are rational and which are irrational? (i) Rational because it can be expressed in the form . (iii) Rational because it can be expressed in the form . (iv) Irational because it can’t be expressed in the form (v) Rational because it can be expressed in the form . .

01 2. (i) (iii) (iv) (v) Practice Questions 1. 6 Simplify the following without using a calculator:

01 2. (vi) (viii) Practice Questions 1. 6 Simplify the following without using a calculator:

Practice Questions 1. 6 01 3. (i) Express, in simplest form, and .

01 3. Practice Questions 1. 6 (ii) Hence, or otherwise simplify .

01 4. (i) Practice Questions 1. 6 Simplify the following: (ii)

01 4. (iii) Practice Questions 1. 6 Simplify the following: (iv)

01 5. Practice Questions 1. 6 Calculate the area of the triangle, giving your answer as an integer. All sides’ lengths are in metres. Area = = 6 m 2.

01 6. Practice Questions 1. 6 A rectangular garden has length and width . Find the area and the perimeter of the garden. Area = Length × width = 12 square units Perimeter = 2 length + 2 width

Practice Questions 1. 6 01 7. Rationalise the denominator in each of the following and express your answer in its simplest form. (i) To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 7. Rationalise the denominator in each of the following and express your answer in its simplest form. (ii) To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 7. Rationalise the denominator in each of the following and express your answer in its simplest form. (iii) To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 7. Rationalise the denominator in each of the following and express your answer in its simplest form. (iv) To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 8. Express in the form , where a and b are positive integers. We need to rationalise the denominator by multiplying the numerator and the denominator by.

01 9. Practice Questions 1. 6 Given the area of a circle is πr 2, find the area of a circle of radius cm, correct to two decimal places. Area = πr 2 = π(4 × 7) = π 28 = 87· 96 cm 2

01 10. (i) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (ii) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (iii) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (iv) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (v) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (vi) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (vii) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (viii) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (ix) Practice Questions 1. 6 Expand simplify the following expressions:

01 10. (x) Practice Questions 1. 6 Expand simplify the following expressions:

01 11. Practice Questions 1. 6 Expand simplify . . Give your answer in the form , where a and b are integers.

01 12. Practice Questions 1. 6 Expand simplify

01 13. Practice Questions 1. 6 Expand . Give your answer in the form , where a and b are integers.

01 14. (i) Practice Questions 1. 6 Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. (ii) Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. Rewrite the following expressions with rational denominators: (iii) To rationalise the denominator, multiply the numerator and the denominator by

01 14. (iv) Practice Questions 1. 6 Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominatorby

Practice Questions 1. 6 01 14. (v) Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. (vi) Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. (vii) Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. Rewrite the following expressions with rational denominators: (viii) To rationalise the denominator, multiply the numerator and the denominator by

01 14. (ix) Practice Questions 1. 6 Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

01 14. (x) Practice Questions 1. 6 Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. Rewrite the following expressions with rational denominators: (xi) To rationalise the denominator, multiply the numerator and the denominator by

01 14. (xii) Practice Questions 1. 6 Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

01 14. (xiii) Practice Questions 1. 6 Rewrite the following expressions with rational denominators: To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. Rewrite the following expressions with rational denominators: (xiv) To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 14. Rewrite the following expressions with rational denominators: (xv) To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 15. Write in the form , where p and q are integers. To rationalise the denominator, multiply the numerator and the denominator by

Practice Questions 1. 6 01 16. Work out . Give your answer in its simplest form. First we need to simplify the numerator To rationalise the denominator, multiply the numerator and the denominator by