Sec 1 G1 Maths Numbers worksheet with answers

A free Sec 1 G1 Maths worksheet on numbers: 7 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 G1 Maths worksheet: Numbers

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

One morning, the temperature in Harbin was

15^\circ\text{C}

and the temperature in Helsinki was

-10^\circ\text{C}

. Find the difference between the two temperatures.

Answer°C[2]

Find the highest common factor (HCF) of

42

and

56

Answer[3]

(a)State whether

53

is a prime number.

Answer (a)[2]

(b)Express

405

as a product of its prime factors, giving your answer in index notation.

Answer (b)[1]

(a)Arrange the following numbers in ascending order:

-17,\ -3,\ 4,\ -10,\ 15

Answer (a)[1]

(b)One morning, the temperature in Helsinki was

-5^\circ\text{C}

and the temperature in Seoul was

-23^\circ\text{C}

. Find the difference between the two temperatures.

Answer (b)°C[2]

Find the lowest common multiple (LCM) of

48

and

72

Answer[3]

Section B

(a)The number line is divided into equal parts. Write down the number that the point T represents.

Answer (a)[2]

(b)(i)Find the lowest common multiple (LCM) of

36

and

90

Answer (b)(i)[3]

(b)(ii)Find the lowest common multiple (LCM) of

42

and

63

Answer (b)(ii)[3]

(a)One morning, the temperature in Oslo was

-1^\circ\text{C}

and the temperature in Harbin was

-9^\circ\text{C}

. Find the difference between the two temperatures.

Answer (a)°C[2]

(b)(i)State whether

143

is a prime number.

Answer (b)(i)[2]

(b)(ii)Express

48

as a product of its prime factors, giving your answer in index notation.

Answer (b)(ii)[1]

(c)Find the lowest common multiple (LCM) of

90

and

108

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 25

°C[2]

Difference

= 15 - (-10)

= 15 + 10

= 25

°C

Question 2

Answer:

= 14

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;42\;} \\ 3 & \underline{\;21\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

42 = 2 \times 3 \times 7

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;56\;} \\ 2 & \underline{\;28\;} \\ 2 & \underline{\;14\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

56 = 2^{3} \times 7

Take only the primes common to every number, each with its lowest power.HCF

= 2 \times 7

= 14

Question 3

(a)Answer: YES[2]

\sqrt{53} = 7.28\ldots

Primes to test:

2, 3, 5, 7

None of

2, 3, 5, 7

divides

53

exactly.So

53

is a prime number.

(b)Answer:

405 = 3^{4} \times 5

[1]

\def\arraystretch{1.8}\begin{array}{r|l} 3 & \underline{\;405\;} \\ 3 & \underline{\;135\;} \\ 3 & \underline{\;45\;} \\ 3 & \underline{\;15\;} \\ 5 & \underline{\;5\;} \\ & \;1 \end{array}

405 = 3^{4} \times 5

Question 4

(a)Answer:

-17 < -10 < -3 < 4 < 15

[1]

-17 < -10 < -3 < 4 < 15

(b)Answer:

= 18

°C[2]

Difference

= -5 - (-23)

= -5 + 23

= 18

°C

Question 5

Answer:

= 144

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;48\;} \\ 2 & \underline{\;24\;} \\ 2 & \underline{\;12\;} \\ 2 & \underline{\;6\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

48 = 2^{4} \times 3

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;72\;} \\ 2 & \underline{\;36\;} \\ 2 & \underline{\;18\;} \\ 3 & \underline{\;9\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

72 = 2^{3} \times 3^{2}

Take every prime that appears, each with its highest power.LCM

= 2^{4} \times 3^{2}

= 144

Question 6

(a)Answer:

= -6

[2]

From

-12

-7

there are

5

divisions.One division

= \dfrac{-7 - (-12)}{5}

= 1

T = -7 + 1 \times 1

= -6

(b)(i)Answer:

= 180

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;36\;} \\ 2 & \underline{\;18\;} \\ 3 & \underline{\;9\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

36 = 2^{2} \times 3^{2}

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;90\;} \\ 3 & \underline{\;45\;} \\ 3 & \underline{\;15\;} \\ 5 & \underline{\;5\;} \\ & \;1 \end{array}

90 = 2 \times 3^{2} \times 5

Take every prime that appears, each with its highest power.LCM

= 2^{2} \times 3^{2} \times 5

= 180

(b)(ii)Answer:

= 126

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;42\;} \\ 3 & \underline{\;21\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

42 = 2 \times 3 \times 7

\def\arraystretch{1.8}\begin{array}{r|l} 3 & \underline{\;63\;} \\ 3 & \underline{\;21\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

63 = 3^{2} \times 7

Take every prime that appears, each with its highest power.LCM

= 2 \times 3^{2} \times 7

= 126

Question 7

(a)Answer:

= 8

°C[2]

Difference

= -1 - (-9)

= -1 + 9

= 8

°C

(b)(i)Answer: NO[2]

\sqrt{143} = 11.95\ldots

Primes to test:

2, 3, 5, 7, 11

143 \div 11 = 13

143 = 11 \times 13

, so

143

is not a prime number.

(b)(ii)Answer:

48 = 2^{4} \times 3

[1]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;48\;} \\ 2 & \underline{\;24\;} \\ 2 & \underline{\;12\;} \\ 2 & \underline{\;6\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

48 = 2^{4} \times 3

(c)Answer:

= 540

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;90\;} \\ 3 & \underline{\;45\;} \\ 3 & \underline{\;15\;} \\ 5 & \underline{\;5\;} \\ & \;1 \end{array}

90 = 2 \times 3^{2} \times 5

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;108\;} \\ 2 & \underline{\;54\;} \\ 3 & \underline{\;27\;} \\ 3 & \underline{\;9\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

108 = 2^{2} \times 3^{3}

Take every prime that appears, each with its highest power.LCM

= 2^{2} \times 3^{3} \times 5

= 540

Sec 1 G1 Maths Numbers worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Answers and worked solutions

Question 1

Answer:

= 25

°C[2]

Difference

= 15 - (-10)

= 15 + 10

= 25

°C

Question 2

Answer:

= 14

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;42\;} \\ 3 & \underline{\;21\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

42 = 2 \times 3 \times 7

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;56\;} \\ 2 & \underline{\;28\;} \\ 2 & \underline{\;14\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

56 = 2^{3} \times 7

Take only the primes common to every number, each with its lowest power.HCF

= 2 \times 7

= 14

Question 3

(a)Answer: YES[2]

\sqrt{53} = 7.28\ldots

Primes to test:

2, 3, 5, 7

None of

2, 3, 5, 7

divides

53

exactly.So

53

is a prime number.

(b)Answer:

405 = 3^{4} \times 5

[1]

\def\arraystretch{1.8}\begin{array}{r|l} 3 & \underline{\;405\;} \\ 3 & \underline{\;135\;} \\ 3 & \underline{\;45\;} \\ 3 & \underline{\;15\;} \\ 5 & \underline{\;5\;} \\ & \;1 \end{array}

405 = 3^{4} \times 5

Question 4

(a)Answer:

-17 < -10 < -3 < 4 < 15

[1]

-17 < -10 < -3 < 4 < 15

(b)Answer:

= 18

°C[2]

Difference

= -5 - (-23)

= -5 + 23

= 18

°C

Question 5

Answer:

= 144

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;48\;} \\ 2 & \underline{\;24\;} \\ 2 & \underline{\;12\;} \\ 2 & \underline{\;6\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

48 = 2^{4} \times 3

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;72\;} \\ 2 & \underline{\;36\;} \\ 2 & \underline{\;18\;} \\ 3 & \underline{\;9\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

72 = 2^{3} \times 3^{2}

Take every prime that appears, each with its highest power.LCM

= 2^{4} \times 3^{2}

= 144

Question 6

(a)Answer:

= -6

[2]

From

-12

-7

there are

5

divisions.One division

= \dfrac{-7 - (-12)}{5}

= 1

T = -7 + 1 \times 1

= -6

(b)(i)Answer:

= 180

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;36\;} \\ 2 & \underline{\;18\;} \\ 3 & \underline{\;9\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

36 = 2^{2} \times 3^{2}

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;90\;} \\ 3 & \underline{\;45\;} \\ 3 & \underline{\;15\;} \\ 5 & \underline{\;5\;} \\ & \;1 \end{array}

90 = 2 \times 3^{2} \times 5

Take every prime that appears, each with its highest power.LCM

= 2^{2} \times 3^{2} \times 5

= 180

(b)(ii)Answer:

= 126

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;42\;} \\ 3 & \underline{\;21\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

42 = 2 \times 3 \times 7

\def\arraystretch{1.8}\begin{array}{r|l} 3 & \underline{\;63\;} \\ 3 & \underline{\;21\;} \\ 7 & \underline{\;7\;} \\ & \;1 \end{array}

63 = 3^{2} \times 7

Take every prime that appears, each with its highest power.LCM

= 2 \times 3^{2} \times 7

= 126

Question 7

(a)Answer:

= 8

°C[2]

Difference

= -1 - (-9)

= -1 + 9

= 8

°C

(b)(i)Answer: NO[2]

\sqrt{143} = 11.95\ldots

Primes to test:

2, 3, 5, 7, 11

143 \div 11 = 13

143 = 11 \times 13

, so

143

is not a prime number.

(b)(ii)Answer:

48 = 2^{4} \times 3

[1]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;48\;} \\ 2 & \underline{\;24\;} \\ 2 & \underline{\;12\;} \\ 2 & \underline{\;6\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

48 = 2^{4} \times 3

(c)Answer:

= 540

[3]

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;90\;} \\ 3 & \underline{\;45\;} \\ 3 & \underline{\;15\;} \\ 5 & \underline{\;5\;} \\ & \;1 \end{array}

90 = 2 \times 3^{2} \times 5

\def\arraystretch{1.8}\begin{array}{r|l} 2 & \underline{\;108\;} \\ 2 & \underline{\;54\;} \\ 3 & \underline{\;27\;} \\ 3 & \underline{\;9\;} \\ 3 & \underline{\;3\;} \\ & \;1 \end{array}

108 = 2^{2} \times 3^{3}

Take every prime that appears, each with its highest power.LCM

= 2^{2} \times 3^{3} \times 5

= 540