1Say whether each of these mathematical statements is true or false: (a) The sum of 4 and 3 is 7. (b) The difference of 8 and 5 is 3. (c) 3 is an even number. (d) 2 is a digit smaller than three. (e) 5 and 6 are not equal.
2Say whether each statement is true, false or open: (a) 5 is a prime number. (b) The cube of 2 is 9. (c) The number y is smaller than 7. (d) There are three square numbers from 10 to 30. (e) x divides 15 exactly.
3What value of the letter makes each open statement true? (a) Multiplying 8 by \( x \) gives 24. (b) \( y \div 3 = 5 \) (c) \( z \) is an odd number. (d) \( x \) belongs to the set of even numbers. (e) The sum of \( x \) and 15 is 15.
4Solve using the equal axioms: (a) \( x + 4 = 5 \) (b) \( u + 2 = 8 \) (c) \( x - 9 = 1 \) (d) \( q - 5 = 9 \) (e) \( 10 - x = 3 \)
5Solve using the equal axioms: (a) \( 3x = 12 \) (b) \( 9x + 2 = 20 \) (c) \( \frac{r}{2} = 5 \) (d) \( \frac{x}{5} + 1 = 8 \) (e) \( \frac{48}{x} = 12 \)
6Form an equation and solve it: (a) Adding \( x \) to 2 gives 7. (b) Multiplying \( x \) by 3 gives 18. (c) Dividing \( x \) by 6 gives 6. (d) Dividing \( y \) by 9 and adding 5 gives 12.
7On Santosh's birthday two of his friends each give him one packet of chocolates. His father adds five more chocolates, and Santosh then has 35 chocolates. How many chocolates were there in one packet?
8In one month the Khadka family spends Rs 16,500 and saves Rs 12,500. What is their income for the month?
9Premila has 25 pencils. Keshav gives her one third of the pencils he has, and she then has 50 pencils. How many pencils did Keshav have?
10The parts of a line segment add up to its whole length. Form an equation and find \( x \): (a) \( x \) cm and 4 cm making 13 cm (b) \( x \) cm and \( 2x \) cm making 18 cm (c) \( x \) cm, \( 2x \) cm and \( 3x \) cm making 36 cm
11Say whether each of these comparisons is right or wrong: (a) \( 5 < 3 \) (b) \( 7 < 9 \) (c) \( -4 > 3 \) (d) \( -18 = -18 \) (e) \( 7 + 2 > 9 \) (f) \( 11 = 11 + 0 \) (g) \( -6 > -2 \)
12Write each of these using the sign \( < \), \( > \) or \( = \): (a) x is smaller than 5. (b) \( x - 3 \) is greater than 4. (c) \( -12 \) is smaller than 7. (d) \( -1 \) and \( -1 \) are equal.
13Solve using the equal axioms: (a) \( 3x - 8 = 1 \) (b) \( \frac{75}{z} - 8 = 7 \)
14Why is it not allowed to add or subtract a number on one side of an equation only? Explain it with the balance.
15A number is multiplied by 4 and then 5 is taken away, leaving 27. What is the number?
16What is the difference between an equation and an inequality? Give one example of each.