Number System: Final Assessment

Section A: Core Review

Question 1mcq

Evaluate

(-2)^{3}-(-2)^{2}

.

A.

-4

B.

-12

C.

4

D.

12

Question 2mcq

Which classification is correct?

A.

-3

is an integer and a rational number.

B.

0

is not a whole number.

C.Every rational number is a natural number.

D.

\sqrt{5}

is a rational number.

Question 3mcq

Which rational number is equivalent to

\frac{3}{4}

?

A.

\frac{4}{3}

B.

\frac{9}{8}

C.

\frac{3}{8}

D.

\frac{6}{8}

Question 4mcq

Which number is rational because it can be written in the form

p/q

, where

p

and

q

are integers and

q \neq 0

?

A.

\pi

B.

\sqrt{2}

C.

-7/5

D.A number with no possible fraction form

Question 5mcq

Which decimal expansion is non-terminating and recurring?

A.

0.25

B.

0.\overline{3}

C.

0.5

D.

2.0

Question 6mcq

Where should

-\frac{2}{3}

be placed on a number line?

A.Between

-1

and

0

.

B.Between

1

and

2

C.At

2

D.Between

0

and

1

Question 7mcq

Which rational number lies between

2

and

3

?

A.

\frac{7}{2}

B.

1.5

C.

3.2

D.

\frac{5}{2}

Question 8mcq

On a number line,

0.68

should be placed:

A.Exactly at

0.6

B.Between

0.7

and

0.8

C.Between

0.6

and

0.7

, closer to

0.7

.

D.Between

0.5

and

0.6

Section B: Application and Reasoning

Question 9mcq

What does the density of rational numbers mean?

A.Two rational numbers must always be consecutive.

B.Between any two rational numbers, another rational number can be found.

C.There are no rational numbers between two integers.

D.Rational numbers are only whole numbers.

Question 10mcq

Which number lies between

\frac{1}{3}

and

\frac{2}{3}

?

A.

\frac{1}{2}

B.

\frac{1}{6}

C.

\frac{4}{3}

D.

\frac{5}{6}

Question 11mcq

Which list contains only rational numbers between

0

and

1

?

A.

-\frac{1}{4}, \frac{1}{2}, \frac{3}{4}

B.

\sqrt{2}, \sqrt{3}, \sqrt{5}

C.

1,2,3

D.

\frac{1}{4}, \frac{1}{2}, \frac{3}{4}

Question 12mcq

Convert

\frac{7}{8}

to decimal form.

A.

0.78

B.

8.75

C.

0.875

D.

0.0875

Question 13mcq

What is the decimal form of

\frac{1}{3}

?

A.

0.3

exactly

B.

0.\overline{3}

C.

3.0

D.

0.13

Question 14mcq

Which fraction has a terminating decimal expansion?

A.

\frac{7}{20}

B.

\frac{1}{7}

C.

\frac{5}{6}

D.

\frac{2}{3}

Question 15mcq

Which fraction equals

0.\overline{6}

?

A.

\frac{6}{10}

B.

\frac{1}{6}

C.

\frac{3}{2}

D.

\frac{2}{3}

Question 16mcq

Which number is irrational?

A.

-4

B.

0.25

C.

\sqrt{7}

D.

\frac{7}{10}

Section C: Challenge and Mixed Practice

Question 17mcq

Which comparison is correct?

A.

\frac{2}{3} = \frac{3}{5}

B.

\frac{2}{3} > \frac{3}{5}

C.

\frac{2}{3} < \frac{3}{5}

D.

\frac{2}{3}

cannot be compared with

\frac{3}{5}

Question 18mcq

Between which two integers does

\sqrt{20}

lie?

A.Between

4

and

5

.

B.Between

5

and

6

C.Exactly at

10

D.Between

2

and

3

Question 19mcq

In a proof by contradiction that

\sqrt{2}

is irrational, what assumption is made first?

A.Assume

\sqrt{2}=2

exactly.

B.Assume

\sqrt{2}

is negative.

C.Assume

2

is odd.

D.Assume

\sqrt{2}=\frac{p}{q}

in lowest terms.

Question 20mcq

If

\sqrt{3}=\frac{p}{q}

in lowest terms, which equation follows after squaring?

A.

3p^{2}=q

B.

p^{2}=q^{2}+3

C.

p^{2}=3q^{2}

D.

p=3q^{2}

Question 21mcq

In constructing the square root spiral, what length is obtained after forming a right triangle with legs

1

and

1

?

A.

\sqrt{3}

B.

\sqrt{2}

C.

2

D.

1/2

Question 22mcq

A student must solve a computational thinking with numbers problem accurately. Which approach shows good step-by-step mathematical thinking?

A.Apply the relevant formula step by step, showing all working.

B.Memorise the answer from a previous similar question without re-deriving.

C.Skip straight to the answer without checking intermediate steps.

D.Round all values to the nearest ten before starting the calculation.

Question 23mcq

Which approach correctly demonstrates the idea: Use logical steps to classify real numbers?

A.Use only a guess because diagrams are always exact.

B.Change the question so the answer becomes easier.

C.Ignore the given conditions and choose any formula.

D.Use the correct definition or theorem and justify each step with mathematical reasoning.

Question 24mcq

Which number is rational because it can be written in the form

p/q

, where

p

and

q

are integers and

q \neq 0

?

A.A number with no possible fraction form

B.

\pi

C.

-7/5

D.

\sqrt{2}