plc papers - king's lynn...

PLC Papers

Created For:

PiXL PLC 2017 Certification

Calculating with fractions 2 Grade 5

Objective: Calculate exactly with fractions, including solving problems

Question 1

Work out 116 x

23 . Give your answer as a fraction in its simplest form.

………………. (2)

Question 2

Work out 223 + 3

25. Give your answer as a mixed number.

………………. (3)

Question 3

Work out 413 - 1 34. Give your answer as a mixed number.

………………. (3)


Question 4

Here are some fractions

2

8

3

10

4

16

5

10

8

24

Two of the fractions are not equivalent to 14. Circle these two fractions.

………………. (2)

Total /10


Error intervals 2 Grade 5

Objective: Use inequality notation to specify simple error intervals due to truncation or rounding.

Question 1.

(a) Find the range of numbers that would round to 500 (to one significant figure)

…………………….. (2)

(b) Find the range of numbers that would round to 5000 (to 1 significant figure)

…………………….. (2)

(Total 4 marks)

Question 2

Use inequality signs to show the range of possible values for

(a) � =0.5 (1.d.p)

…………………….. (2)


(b) � =50 (1 s.f0

…………………….. (2)

(Total 4 marks)

3. Question 3.

Complete the inequality to show the range of values that would round to 0.4 (to 1 decimal place)

… .≤ 0.4 < ⋯

(2)

(Total 2 marks)

Total /10


Finance 2 Grade 6

Objective: To work with decimals in a financial context, e.g. profit, loss, balance, debit, credit.

Question 1

Anna’s bank account was £564.70 in debit before she withdrew £600 to pay her rent. What is her account balance after this transaction?

£……………………..

(2)

Question 2

What is Anna’s total shopping bill if she buys

2 magazines for £1.65 each

5 bread rolls for 60p each

4 pints of milk for £1.05 per pint.

………….……………………..

(3)

Question 3

Charlie is paid £6.20 per hour for her part time job.

a) How much will she earn if she works 15 hours

………….……………………..

(2)


b) How many hours does she need to work to make £310

………….……………………..

(3)

Total /10


Index Laws 2 Grade 5

Objective: Calculate with roots and with integer indices

Question 1

Simplify

i) x7 x x8

…………………….

(1)

ii) y8 ÷ y3

…………………….

(1)

Question 2

Write as a power of 5

i) 54 x 52

…………………….

(1)

ii) 512 ÷ 56

…………………….

(1)

iii) 58 ÷ 510

…………………….

(1)


iv) 55 x 56 (52)4

…………………….

(3)

Question 3

Simplify

3x2y x 5 x y8

…………………….

(2)

Total /10


Limits of accuracy 2 Grade 5

Objective: Apply and Interpret Limits of Accuracy.

Question 1.

(a) A field measures 500m by 200m when rounded to the nearest 100m. What is the greatest possible area of the field?

…………………….. (2)

(b) David runs around the edge of the field twice. What is the least possible distance that he would run?

…………………….. (4)

(Total 6 marks)

Question 2

A pen measures 30 cm to the nearest 10cm. 10 pencils are joined together. What is the total greatest and

least possible total length of the pencils? Give your answer in centimetres.

Greatest Length…………………….. (2)

Least Length …………………….. (2)

(Total 4 marks)


Total /10


Powers and Roots 2 Grade 6

Objective: Calculate and estimate powers and roots

You will need to use a calculator

Question 1

Find the value of

i) 2.63

…………………

ii) 1.25

…………………

iii) 5-2 x 73

…………………

(3)

Question 2

Evaluate

i) √6889

…………………

ii) 3√0.6

…………………

iii) 4√625

…………………

(3)

Question 3

Work out (6.05)3 - 3√8.4 and give your answer to 3 significant figures.

…………………

(2)


Question 4

Work out 3√5.6 + 4.22 and give your answer to 2 decimal places.

…………………

(2)

Total /10

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Product of prime factors 2 Grade 6

Objective: Understand the unique factorisation theorem and perform prime factor decompositions

Question 1

Look at the numbers below

11, 13, 15, 17, 19

a) Which number in the list is not prime

………………………..

b) Explain why it is not prime.

…………………………………………………………………………………………………

…………………………………………………………………………………………………

(2)

Question 2

Write each of the following number as a product of its prime factors

i) 44

……………………

(2)

ii) 325

……………………

(3)

[Type here]


iii) 840

……………………

(3)

Total /10


Using Pi 2 Grade 7

Objective: Understand the value of pi and calculate exactly with it

Question 1

If the area of a circle is 49 π cm2, state, with appropriate units, its

i) Radius

………………………….. ii) Diameter

……………………….….

iii) Circumference

…………………………. (3)

Question 2

Simplify the following expressions

i) 100 π – 555

……………………….. ii) 6 (8 - 2π) – 8 (4 π – 9)

……………………….

(3)


Question 3

Calculate the circumference of the circle, leaving your answer in terms of π.

11cm

……………….cm

(2) Question 4

Calculate the area of the circle, leaving your answer in terms of π.

16cm

……………….cm2

(2)

Total /10

PLC Papers

Created For:


Calculating with fractions 2 Grade 5 Solutions

Objective: Calculate exactly with fractions, including solving problems

Question 1

Work out 116 x

23 . Give your answer as a fraction in its simplest form.

= 76 x

23 = 1418 (M1)

= 79 (A1)

……………….

(2) Question 2

Work out 223 + 3

25. Give your answer as a mixed number

= 83 +

175 (M1)

= 4015 +

5115 (M1)

= 9115 = 6

115 (A1)

……………….

(3) Question 3

Work out 413 - 1 34. Give your answer as a mixed number

= 133 -

74 (M1)

= 5212 - 2112 (M1)

= 3112 = 2

712 (A1)

………………. (3)


Question 4

Here are some fractions

2

8

3

10

4

16

5

10

8

24

Two of the fractions are not equivalent to 14. Circle these two fractions.

A1 For each correct answer

………………. (2)

Total /10


Error intervals 2 SOLUTIONS Grade 5

Objective: Use inequality notation to specify simple error intervals due to truncation or rounding.

Question 1.

(a) Find the range of numbers that would round to 500 (to one significant figure)

450… .≤ 500 < 550… (A2)

…………………….. (2)

(b) Find the range of numbers that would round to 5000 (to 1 significant figure)

(c) 4500… .≤ 5000 < 5500… (A2)

…………………….. (2)

(Total 4 marks)

Question 2

Use inequality signs to show the range of possible values for

(a) � =0.5 (1.d.p)

(d) 0.45… .≤ 0.5 < 0.55… (A2)

…………………….. (2)


(b) � =50 (1 s.f0

(e) 45… .≤ 50 < 55… (A2)

…………………….. (2)

(Total 4 marks)

3. Question 3.

Complete the inequality to show the range of values that would round to 0.4 (to 1 decimal place)

… .≤ 0.4 < ⋯

(a) 0.35… .≤ 0.4 < 0.45… (A2)

(2)

(Total 2 marks)


Total /10


Finance 2 Grade 6 Solutions

Objective: To work with decimals in a financial context, e.g. profit, loss, balance, debit, credit.

Question 1

Anna’s bank account was £564.70 in debit before she withdrew £600 to pay her rent. What is her account balance after this transaction?

564.70 – 600 (M1)

-£35.30 (A1)

£……………………..

(2)

Question 2

What is Anna’s total shopping bill if she buys

2 magazines for £1.65 each

5 bread rolls for 60p each

4 pints of milk for £1.05 per pint.

M1 one of (2 x 1.65) = 3.30 or (5 x 0.6) = 3 or (4 x 1.05) = 4.20

M1 for total of their three products

A1 for £10.50

………….……………………..

(3)

Question 3

Charlie is paid £6.20 per hour for her part time job.

a) How much will she earn if she works 15 hours

£6.20 x 15 = (M1)

£90 (A1)

………….……………………..

(2)


b) How many hours does she need to work to make £310

310 ÷ 6.2 or 3100 ÷ 62 or attempt at division with only one error (M2)

50 hours (A1)

………….……………………..

(3)

Total /10


Index Laws 2 Grade 5 Solutions

Objective: Calculate with roots and with integer indices

Question 1

Simplify

i) x7 x x8

x15 (A1)

…………………….

(1)

ii) y8 ÷ y3

y5 (A1)

…………………….

(1)

Question 2

Write as a power of 5

i) 54 x 52

56 (A1)

…………………….

(1)

ii) 512 ÷ 56

56 (A1)

…………………….

(1)

iii) 58 ÷ 510

5-2 (A1)

…………………….

(1)


iv) 55 x 56 (52)4 55+6 = 511 or 52x4 = 58 seen (M1)

511 ÷ 58 or 511-8 seen (M1)

53 (A1)

…………………….

(3)

Question 3

Simplify

3x2y x 5 x y8

15x3y9 (M1 for any two correct terms, A1 for fully correct answer)

…………………….

(2)

Total /10


Limits of accuracy 2 SOLUTIONS Grade 5

Objective: Apply and Interpret Limits of Accuracy.

Question 1.

(a) A field measures 500m by 200m when rounded to the nearest 100m. What is the greatest possible area of the field? 550 X 250= (M1) 137500�� (A1)

………137500��…………….. (2)

(b) David runs around the edge of the field twice. What is the least possible distance that he would run?

2(450 + 150)= 1200m (M1)

1200� (A1)

…………1200� ………….. (4)

(Total 6 marks)

Question 2

A pen measures 30 cm to the nearest 10cm. 10 pencils are joined together. What is the total greatest and

least possible total length of the pencils? Give your answer in centimetres.

35 x 10= 350cm (M1) 350cm (A1)


Greatest Length……350cm……………….. (2)

25 x 10= 250cm (M1) 250cm (A1)

Least Length ………250cm …………….. (2)

(Total 4 marks)

Total /10


Powers and Roots 2 Grade 6 Solutions

Objective: Calculate and estimate powers and roots

You will need to use a calculator

Question 1

Find the value of

i) 2.63 17.576 (A1)

…………………

ii) 1.25 2.48832 (A1)

…………………

iii) 5-2 x 73 13.72 (A1)

…………………

(3)

Question 2

Evaluate

i) √6889 83 (A1)

…………………

ii) 3√0.125 0.5 (A1)

…………………

iii) 4√625 5 (A1)

…………………

(3)

Question 3

Work out (6.05)3 - 3√8.4 and give your answer to 3 significant figures.

219.4123323 (M1)

219 (A1)

…………………

(2)


Question 4

Work out 3√5.6 + 4.22 and give your answer to 2 decimal places.

19.415808 (M1)

19.42 (A1)

…………………

(2)

Total /10

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Product of prime factors 2 Grade 6 Solutions

Objective: Understand the unique factorisation theorem and perform prime factor decompositions

Question 1

Look at the numbers below

11, 13, 15, 17, 19

a) Which number in the list is not prime

……………15…………..

b) Explain why it is not prime.

15 has factors other than 1 and itself, such as 5 and 3 (C1)

(2)

Question 2

Write each of the following number as a product of its prime factors

i) 44

M1 for full systematic method of divisions by prime numbers oe factor trees; condone 1

calculation error

A1 for 2 x 2 x 11

……………………

(2)

ii) 325


calculation error

(M1 for 325 written as a correct product with only one non-prime or equivalent division

or a full process with 2 calculation errors.)

A1 for 5 x 5 x 13

……………………

(3)

[Type here]


iii) 840


calculation error

(M1 for 840 written as a correct product with only one non-prime or equivalent division

or a full process with 2 calculation errors.)

A1 for 2 x 2 x 2 x 3 x 5 x 7

……………………

(3)

Total /10


Using Pi 2 Grade 7 Solutions

Objective: Understand the value of pi and calculate exactly with it

Question 1

If the area of a circle is 49 π cm2, state, with appropriate units, its

i) Radius 7cm

………………………….. ii) Diameter 14cm

……………………….….

iii) Circumference 14 π cm

…………………………. (3)

A1 for each correct answer, including units.

Question 2

Simplify the following expressions

i) 100 π – 555 20 π – 11 (A1)

……………………….. ii) 6 (8 - 2π) – 8 (4 π – 9)

48 - 12 π -32 π + 72 (M1 for any three correct terms) 120 - 44 π (A1)

……………………….

(3)


Question 3

Calculate the circumference of the circle, leaving your answer in terms of π.

11cm

2 x π x 11 or π x 22 (M1) 22 π (A1)

……………….cm

(2) Question 4

Calculate the area of the circle, leaving your answer in terms of π.

16cm

π x 82 or π x 64 (M1) 64 π (A1)

……………….cm2

(2)

Total /10

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