Real Numbers Final Assessment | Homework Practice

Section A: Core Concepts

Question 1mcq

Which number is composite?

A.

57

B.

2

C.

13

D.

1

Question 2mcq

The prime factorisation of

150

is:

A.

2\timesimes3^2\timesimes5

B.

2^2\timesimes3\timesimes5

C.

2\timesimes3\timesimes5^2

D.

15\timesimes10

Question 3mcq

FTA applies to which set of numbers?

A.All fractions

B.Only prime numbers

C.Only even numbers

D.Integers greater than

1

Question 4mcq

What is the HCF of

32

and

48

?

A.

16

B.

8

C.

24

D.

96

Question 5mcq

What is the LCM of

8

and

14

?

A.

2

B.

28

C.

56

D.

112

Question 6mcq

If

N=2^5\timesimes3\timesimes7

, which number must divide

N

?

A.

72

B.

56

C.

63

D.

45

Section B: Skill Practice

Question 7mcq

Find the HCF of

108

and

180

.

A.

36

B.

18

C.

54

D.

72

Question 8mcq

Find the LCM of

30

,

42

, and

70

.

A.

420

B.

210

C.

140

D.

105

Question 9mcq

Two numbers have product

5400

and HCF

30

. Their LCM is:

A.

90

B.

360

C.

180

D.

162000

Question 10mcq

A florist has

45

roses and

60

lilies. What is the greatest number of identical bouquets she can make with no flowers left?

A.

5

B.

30

C.

105

D.

15

Question 11mcq

Two buses leave a stop every

18

minutes and

24

minutes. After how many minutes will they leave together again?

A.

6

minutes

B.

72

minutes

C.

42

minutes

D.

432

minutes

Question 12mcq

In contradiction proof, why must

\fracrac{p}{q}

be taken in lowest terms?

A.So that

q=0

.

B.So that

p

is always prime.

C.So that decimals can be avoided.

D.So that finding a common factor creates a contradiction.

Section C: Application and Reasoning

Question 13mcq

In proving

\sqrt2

irrational, from

p^2=2q^2

and

p=2k

, what follows?

A.

q^2=2k^2

, so

q

is even.

B.

q

is odd.

C.

p=q

.

D.

k

is irrational.

Question 14mcq

Which proof can be adapted most directly from the proof for

\sqrt2

?

A.Proof that

4

is irrational

B.Proof that

0.5

is irrational

C.Proof that

\sqrt5

is irrational

D.Proof that

9

is irrational

Question 15mcq

If

2+\sqrt7

is assumed rational, what contradiction follows?

A.

2

would be irrational.

B.

7

would be even.

C.

\sqrt7

would be zero.

D.

\sqrt7

would be rational.

Question 16mcq

Error analysis: A student concludes

\sqrt5

is irrational because

\sqrt5\approxpprox2.236

. What is wrong?

A.A decimal approximation is not a proof of irrationality.

B.The approximation is exactly equal to

\sqrt5

.

C.Every decimal is irrational.

D.The number

5

is not prime.

Question 17mcq

A carton contains

2^4\timesimes3^2

identical clips. Which pack size will divide the carton exactly?

A.

25

B.

27

C.

24

D.

45

Question 18mcq

Which of the following numbers is divisible by

2^3\timesimes3^2

but not by

5

?

A.

360

B.

72

C.

180

D.

90

Section D: Mixed Challenge

Question 19mcq

If

\timesext{HCF}(a,b)=12

and

\timesext{LCM}(a,b)=240

, can

a=36

?

A.No, because the other number would be

80

, whose HCF with

36

is

4

.

B.Yes, the other number is

80

.

C.Yes, because

36

divides

240

.

D.No, because product relation never works.

Question 20mcq

A school wants equal rows for

144

boys and

168

girls, with each row containing only boys or only girls and the same number of students. What is the largest row size?

A.

12

B.

24

C.

48

D.

312

Question 21mcq

A water pump runs every

16

minutes, another every

20

minutes, and a third every

25

minutes. How long until all start together again?

A.

100

minutes

B.

200

minutes

C.

400

minutes

D.

800

minutes

Question 22mcq

Assertion: If

p^2

is even, then

p

is even. Reason: The square of an odd integer is odd.

A.Both true, but unrelated.

B.Assertion true, reason false.

C.Assertion false, reason true.

D.Both are true, and the reason explains the assertion.

Question 23mcq

Which expression is irrational?

A.

5-3\timesimes2

B.

5-3\sqrt2

C.

\fracrac{5-3}{2}

D.

5+3-2

Question 24mcq

Case: A student assumes

\sqrt3=\fracrac{p}{q}

but forgets to state

p

and

q

are co-prime. What should be repaired?

A.Replace

3

by

2

.

B.Use a calculator decimal.

C.Conclude immediately that

p

is prime.

D.Add that

p

and

q

are integers with no common factor and

q\nee0

.