1.1 Prime & Composite Numbers-ilovepdf-compressed.pdf

Prime & Composite Numbers Question 1 An online personality test consists of 50 multiple-choice questions. A question is selected at random. Find the probability that the question number is (a) divisible by 4. (b) a prime number with 2 digits. (c) a factor of 50. Question 2 Given that a is a prime number such that 30 < a < 40, find the possible values of a. Question 3 (a) State all the prime numbers between 0 and 9. (b) Using your answers in (a), identify two prime numbers, such that when you add them together, the result is a prime number. Question 4 Given that x < 12, state the largest possible value of x if (a) x is a multiple of 3, (b) x is a prime number. Question 5 (a) Solve the inequality 10 − 2w <

1 w≤5. 2

(b) Given that w is a prime number that satisfies the inequality 10 − 2w <

1 w≤5, 2

write down the possible values of w. Question 6 Given that x is a prime number and 3 ≤ x < 17 , list the possible value(s) of x. Question 7 (a) Write down the prime number(s) from the list below. 17, 6, 10, 31, 4, 37, 9 (b) (i) Find the sum of first three prime numbers that ends with ‘3’. (ii) Does your answer in (b) (i) give a composite number? Show your working clearly.

1

Question 8 Given that y is a prime number between 11 and 20, indicate clearly, with a dot or cross, the possible values of y on the following number line.

11

12

13

14

15

16

17

18

19

20

Question 9 Given that x < 19, state the greatest possible value of x if x is a prime number. Question 10 A two-digit numbers ab and its reversal ba are both prime. For example, 13 and 31 are both prime. What is the largest possible sum of these two numbers ab and ba? Question 11 From the list of numbers given, 13, 15, 30, 36, 37, 42, 49, 56, find (a) the product of two prime numbers. (b) the sum of two perfect squares. Question 12 Given that x is a prime number and 1 ≤ x < 7 , write down all the possible values of x. Question 13 Given that x is a prime number and 8 < x ≤ 14 , write down the possible values of x.

Question 14 There are three prime numbers 13, 17 and 43. (a) Is the sum of the three numbers a prime number? (b) Is the product of the smallest and the biggest number a prime number? Show your workings and give reasons for your answer.

Question 15 From the set provided below, place each number into its correct group. A number may belong to more than one group.

1 − 3, 0, 2, , π , 0.15, 1 6 (a) Prime Numbers (b) Integers (c) Rational Numbers 2

Question 16 Given that x is a prime number, write down the largest value of x such that x < (3 9874 000 − 12.32 ) . Question 17

x + 2 2x −1 2 1 < ÷ ≤ 3 , find the possible value(s) of x, for which x is a 4 2 3 2 prime number. By solving

Question 18 x is a prime number such that x ≥ 1 and x < 11. Draw a number line to show clearly all possible values of x. Question 19 The ten numbers below are Henry’s scores in a bowling game. 9, 18, 27, 36, 41, 54, 64, 85, 103, 121. Write down the number(s) that are prime numbers. Question 20 (a) Find the sum of first three prime numbers that ends with “1”. (b) Is your answer in (a) a composite number? Show your working clearly. Question 21 (a) List all the prime numbers between 0 and 10. (b) From (a), list two prime numbers, such that when you add them together, the result is a prime number. Question 22 “A prime number is a whole number greater than 1 with two factors, 1 and itself.” Given that p and q are prime numbers, circle ‘True’ or ‘False’ for each statement. (a) 3p is a prime number, (b) q + q + q + q is a composite number, (c) pq 2 has only 3 factors. (d) 5r is a prime number. Question 23 (a) State the highest common factor of two or more prime numbers. (b) (i) List all the prime numbers between 20 and 40. (ii) Hence, what is the product of the largest and the smallest prime number in the range?

3

Question 24 (a) Write down all the prime numbers less than 15. (b) Hence, write down 2 possible primes in (a) such that their sum is also a prime. Question 25 x is a prime number such that x ≥ 4 and x ≤ 14 . Draw a number line to show clearly all possible values of x. Question 26 If the product of two positive integers is 37, what must be the value of the smaller integer? Question 27 (a) List all the prime numbers from 1 to 18. (b) Hence, find the sum of the smallest and biggest prime number in (a). Question 28 On the number line below, use dots to show a set of prime numbers between − 2 to 10.

Question 29 Given that m and n are prime numbers such that m × n = 91 , find the two possible values of 2m + n. Question 30 Given that x is a prime number and − 1 < x ≤ 3 , write down the possible values of x. Question 31 (a) Write down all the prime numbers between 15 to 30. (b) Find the difference between the smallest and the largest prime number that are between 15 and 30. Question 32 (a) Express 5400 as a product of its prime factors, giving your answer in index notation. (b) Hence, find the smallest positive integer m such that 5400m is a perfect square.

4

Question 33 (a) Write down all the prime numbers between 35 and 50. (b) Find the difference between the smallest and the largest prime number between 35 and 50. Question 34 Given that x is a prime number and 3x < 55, find the largest possible value of x. Question 35 Given that x is an integer, such that 2x > 9 and x − 1 ≤ 10 . Write down all the possible prime values of x. Question 36 (a) List all the prime numbers between 0 and 10. (b) Hence, find the sum of the smallest prime number and largest prime number in (a). Question 37 Given that x is a prime number and 1 ≤ x < 11 , write down the possible values of x. Question 38 (a) List all the prime numbers between 10 and 20. (b) Hence, find the product of the smallest and the largest prime number in (a). Question 39 Given that a is a prime number and that a < 20. Write down all the possible values of a. Question 40 A 2-digit prime number is less than 50 and the product of its digits is 12. What is the number?

Question 41 Given that 1 ≤ x < 13 , find the largest possible value of x if x is a prime number.

5

[Answer Key] Question 1 6 (a) 25

(b)

11 50

(c)

3 25

Question 2 31, 37 Question 3 (a) 2, 3, 5, 7

(b) 2 and 3 or 2 and 5

Question 7 (a) 17, 31, 37

(b) (i) 39

(ii) Yes

Question 9 17 Question 10 176 Question 11 False Question 12 True Question 13 False Question 16 61 Question 17 2 Question 19 41, 103

6

Question 20 (a) 83 (b) No, it is a prime number. Question 21 (a) 2, 3, 5, 7

(b) 2 and 3 or 2 and 5

Question 22 More than 2 factors. Therefore, it is composite. So, statement is false. More than 2 factors. Therefore, statement is true. It has 6 factors. Therefore, statement is false. Question 27 (a) 2, 3, 5, 7, 11, 13, 17

(b) 19

Question 29 27 or 33 Question 30 2 and 3 Question 31 (a) 17, 19, 23, 29 Question 32 (a) 23 × 33 × 52 Question 33 (a) 37, 41, 43, 47

(b) 12

(b) 6

(b) 10

Question 34 17 Question 35 5, 7, 11

7

Question 36 (a) 2, 3, 5, 7

(b) 9

Question 37 2, 3, 5, 7 Question 38 (a) 11, 13, 17, 19

(b) 209

Question 39 2, 3,5, 7, 11, 13, 17, 19 Question 40 43 Question 41 (a) 481 (b) 85 Question 42 2, 3, 5 Question 43 11 and 13 Question 47 11

8

[Solution] Question 1 (a) P(divisible by 4) 12 = 50 6 = 25 (c)

6 50 3 = 25

P(factor of 50) =

Question 3 (b) 2 + 3 = 5 or 2+5=7 Question 4 3 p = 1× 3 p

= 3× p More than 2 factors. Therefore, it is composite. So, statement is false. Question 5 q + q + q + q = 4q

= 1 × 4q = 2 × 2q = 4× q More than 2 factors. Therefore, statement is true. Question 6 pq 2 = 1 × pq 2

= p × q2 = pq × q It has 6 factors. Therefore, statement is false.

9

Question 8 39 (b) (ii) = 13 or 39 = 1 × 39, 3 × 13 3 Question 10 The largest possible sum = 79 + 97

= 176 Question 16 x < (3 9874 000 − 12.3 2 )

x < 63.24 Largest x value and prime number = 61 Question 18

Question 20 (a) 11 + 31 + 41 = 83 Question 27 (b) Sum = 2 + 17

= 19 Question 28

Question 29 2m + n = 2(7) + 13

= 27 Or

2m + n = 2(13) + 7 = 33 10

Question 32 (a) 2 5400 2 2700 2 1350 3 675 3 225 3 75 5 25 5 5 1

5400 = 2 3 × 33 × 5 2 (b)

5400m = 2 3 × 33 × 5 2 × m = 2 3 × 33 × 5 2 × 2 × 3 m=6 Question 34 3x < 55

x<

55 3

x < 18

1 3

Question 36 (b) 2 + 7 = 9 Question 38 (b) 11 × 19 = 209 Question 41 (a) Product of two prime no. = 13 × 37

= 481 (b)

Sum of two perfect squares = 36 + 49 = 85

11