Sec 1 G1 Maths Four operations worksheet with answers

A free Sec 1 G1 Maths worksheet on four operations: 8 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: Four operations

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

By writing each number correct to 1 significant figure, estimate the value of

\dfrac{812 \times 2.07}{38.6}

Answer[2]

Calculate

3\dfrac{3}{4} \times 2\dfrac{3}{5}

, giving your answer in its simplest form.

Answer[2]

(a)Calculate

8 \times (-9)

Answer (a)[1]

(b)Calculate

(-72) \div 8 \times 4

Answer (b)[1]

Calculate

36 \div 6 \times 3

Answer[2]

(a)Express

0.0625

as a fraction in its simplest form.

Answer (a)[2]

(b)Express

0.375

as a fraction in its simplest form.

Answer (b)[2]

(a)The mass of a parcel is

350

g, correct to the nearest 10 g. Write down the least possible mass of the parcel.

Answer (a)g[1]

(b)The number of books in a library is

5730

, correct to 3 significant figures. Find the smallest and the largest possible number of books.

Answer (b)[3]

Section B

(a)(i)Calculate

-15 - (-9) - 7

Answer (a)(i)[2]

(a)(ii)Calculate

(-84) \div 12

Answer (a)(ii)[1]

(b)(i)Write

38

correct to the nearest 10.

Answer (b)(i)[1]

(b)(ii)Use a calculator to evaluate

\dfrac{\sqrt[3]{61.2} + 1.85^{2}}{12.6 - 1.9}

, giving your answer correct to 3 significant figures.

Answer (b)(ii)[2]

(a)A tank is full of water.

\dfrac{3}{5}

of the water is used to water a garden and

\dfrac{1}{5}

of the whole tank is used to wash a car. There are

30

litres of water left in the tank. Find the volume of water in the tank at first.

Answer (a)litres[2]

(b)Use a calculator to evaluate

\dfrac{\sqrt[3]{61.2} + 0.72^{2}}{12.6 - 4.05}

, giving your answer correct to 3 significant figures.

Answer (b)[2]

(c)(i)Write

0.000706

correct to 2 significant figures.

Answer (c)(i)[1]

(c)(ii)State the number of significant figures in

8.000

Answer (c)(ii)[1]

(d)By writing each number correct to 1 significant figure, estimate the value of

\dfrac{315 \times 0.0618}{0.488}

Answer (d)[2]

END OF PAPER

Answers and worked solutions

Question 1

Answer:

= 40

[2]

\dfrac{812 \times 2.07}{38.6} \approx \dfrac{800 \times 2}{40}

= \dfrac{1600}{40}

= 40

Question 2

Answer:

= 9\dfrac{3}{4}

[2]

3\dfrac{3}{4} \times 2\dfrac{3}{5}

= \dfrac{15}{4} \times \dfrac{13}{5}

= \dfrac{195}{20}

= \dfrac{39}{4}

= 9\dfrac{3}{4}

Question 3

(a)Answer:

8 \times (-9) = -72

[1]

So the answer is negative.

8 \times (-9) = -72

(b)Answer:

(-72) \div 8 \times 4 = -36

[1]

Number of negative numbers:

1

So the answer is negative.

(-72) \div 8 \times 4 = -36

Question 4

Answer:

= 18

[2]

36 \div 6 \times 3

= 6 \times 3

= 18

Question 5

(a)Answer:

= \dfrac{1}{16}

[2]

0.0625 = \dfrac{625}{10000}

= \dfrac{625 \div 625}{10000 \div 625}

= \dfrac{1}{16}

(b)Answer:

= \dfrac{3}{8}

[2]

0.375 = \dfrac{375}{1000}

= \dfrac{375 \div 125}{1000 \div 125}

= \dfrac{3}{8}

Question 6

(a)Answer:

350 - 5 = 345

g[1]

Half of

10

= 5

350 - 5 = 345

(b)Answer:

\phantom{\text{Largest}} = 5734

(

5735

itself rounds up to

5740

).[3]

5730

to 3 significant figures is rounded to the nearest

10

.Half of

10

5

\text{Smallest} = 5730 - 5

\phantom{\text{Smallest}} = 5725

\text{Largest} = 5730 + 5 - 1

\phantom{\text{Largest}} = 5734

(

5735

itself rounds up to

5740

Question 7

(a)(i)Answer:

= -13

[2]

-15 - (-9) - 7

= -15 + 9 - 7

= -13

(a)(ii)Answer:

(-84) \div 12 = -7

[1]

So the answer is negative.

(-84) \div 12 = -7

(b)(i)Answer:

38 = 40

(nearest 10)[1]

The deciding digit is

8

.It is 5 or more, so round up.

38 = 40

(nearest 10)

(b)(ii)Answer:

= 0.688

(3 s.f.)[2]

\sqrt[3]{61.2} + 1.85^{2} = 7.3632\ldots

12.6 - 1.9 = 10.7

\dfrac{7.3632\ldots}{10.7} = 0.6881\ldots

= 0.688

(3 s.f.)

Question 8

(a)Answer: There were

150

litres of water at first.[2]

1 - \dfrac{3}{5} - \dfrac{1}{5} = \dfrac{1}{5}

\text{Whole} = 30 \div \dfrac{1}{5}

\phantom{\text{Whole}} = 30 \times \dfrac{5}{1}

\phantom{\text{Whole}} = 150

There were

150

litres of water at first.

(b)Answer:

= 0.522

(3 s.f.)[2]

\sqrt[3]{61.2} + 0.72^{2} = 4.4591\ldots

12.6 - 4.05 = 8.55

\dfrac{4.4591\ldots}{8.55} = 0.5215\ldots

= 0.522

(3 s.f.)

(c)(i)Answer:

0.000706 = 0.00071

(2 s.f.)[1]

The 3rd significant figure is

6

.It is 5 or more, so round up.

0.000706 = 0.00071

(2 s.f.)

(c)(ii)Answer:

8.000

has

4

significant figures.[1]

The number starts with a non-zero digit, so start counting from the first digit.A zero at the end of a decimal is significant: it shows the accuracy.

8.000

has

4

significant figures.

(d)Answer:

= 36

[2]

\dfrac{315 \times 0.0618}{0.488} \approx \dfrac{300 \times 0.06}{0.5}

= \dfrac{18}{0.5}

= 36

Sec 1 G1 Maths Four operations 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.

Section B

(a)(i)Calculate

-15 - (-9) - 7

Answer (a)(i)[2]

(a)(ii)Calculate

(-84) \div 12

Answer (a)(ii)[1]

(b)(i)Write

38

correct to the nearest 10.

Answer (b)(i)[1]

(b)(ii)Use a calculator to evaluate

\dfrac{\sqrt[3]{61.2} + 1.85^{2}}{12.6 - 1.9}

, giving your answer correct to 3 significant figures.

Answer (b)(ii)[2]

Answers and worked solutions

Question 1

Answer:

= 40

[2]

\dfrac{812 \times 2.07}{38.6} \approx \dfrac{800 \times 2}{40}

= \dfrac{1600}{40}

= 40

Question 2

Answer:

= 9\dfrac{3}{4}

[2]

3\dfrac{3}{4} \times 2\dfrac{3}{5}

= \dfrac{15}{4} \times \dfrac{13}{5}

= \dfrac{195}{20}

= \dfrac{39}{4}

= 9\dfrac{3}{4}

Question 3

(a)Answer:

8 \times (-9) = -72

[1]

So the answer is negative.

8 \times (-9) = -72

(b)Answer:

(-72) \div 8 \times 4 = -36

[1]

Number of negative numbers:

1

So the answer is negative.

(-72) \div 8 \times 4 = -36

Question 4

Answer:

= 18

[2]

36 \div 6 \times 3

= 6 \times 3

= 18

Question 5

(a)Answer:

= \dfrac{1}{16}

[2]

0.0625 = \dfrac{625}{10000}

= \dfrac{625 \div 625}{10000 \div 625}

= \dfrac{1}{16}

(b)Answer:

= \dfrac{3}{8}

[2]

0.375 = \dfrac{375}{1000}

= \dfrac{375 \div 125}{1000 \div 125}

= \dfrac{3}{8}

Question 6

(a)Answer:

350 - 5 = 345

g[1]

Half of

10

= 5

350 - 5 = 345

(b)Answer:

\phantom{\text{Largest}} = 5734

(

5735

itself rounds up to

5740

).[3]

5730

to 3 significant figures is rounded to the nearest

10

.Half of

10

5

\text{Smallest} = 5730 - 5

\phantom{\text{Smallest}} = 5725

\text{Largest} = 5730 + 5 - 1

\phantom{\text{Largest}} = 5734

(

5735

itself rounds up to

5740

Question 7

(a)(i)Answer:

= -13

[2]

-15 - (-9) - 7

= -15 + 9 - 7

= -13

(a)(ii)Answer:

(-84) \div 12 = -7

[1]

So the answer is negative.

(-84) \div 12 = -7

(b)(i)Answer:

38 = 40

(nearest 10)[1]

The deciding digit is

8

.It is 5 or more, so round up.

38 = 40

(nearest 10)

(b)(ii)Answer:

= 0.688

(3 s.f.)[2]

\sqrt[3]{61.2} + 1.85^{2} = 7.3632\ldots

12.6 - 1.9 = 10.7

\dfrac{7.3632\ldots}{10.7} = 0.6881\ldots

= 0.688

(3 s.f.)

Question 8

(a)Answer: There were

150

litres of water at first.[2]

1 - \dfrac{3}{5} - \dfrac{1}{5} = \dfrac{1}{5}

\text{Whole} = 30 \div \dfrac{1}{5}

\phantom{\text{Whole}} = 30 \times \dfrac{5}{1}

\phantom{\text{Whole}} = 150

There were

150

litres of water at first.

(b)Answer:

= 0.522

(3 s.f.)[2]

\sqrt[3]{61.2} + 0.72^{2} = 4.4591\ldots

12.6 - 4.05 = 8.55

\dfrac{4.4591\ldots}{8.55} = 0.5215\ldots

= 0.522

(3 s.f.)

(c)(i)Answer:

0.000706 = 0.00071

(2 s.f.)[1]

The 3rd significant figure is

6

.It is 5 or more, so round up.

0.000706 = 0.00071

(2 s.f.)

(c)(ii)Answer:

8.000

has

4

significant figures.[1]

The number starts with a non-zero digit, so start counting from the first digit.A zero at the end of a decimal is significant: it shows the accuracy.

8.000

has

4

significant figures.

(d)Answer:

= 36

[2]

\dfrac{315 \times 0.0618}{0.488} \approx \dfrac{300 \times 0.06}{0.5}

= \dfrac{18}{0.5}

= 36