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PLC Papers
Created For:
Calculating with fractions 2
Grade 5
Objective: Calculate exactly with fractions, including solving problems
Question 1
Work out
1
1
6
x
2
3
. Give your answer as a fraction in its simplest form.
……………….
(2)
Question 2
Work out
2
2
3
2
+ 3 . Give your answer as a mixed number.
5
……………….
(3)
Question 3
Work out
4
1
3
3
- 1 . Give your answer as a mixed number.
4
……………….
(3)
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Question 4
Here are some fractions
2
8
3
10
4
16
5
10
8
24
1
Two of the fractions are not equivalent to . Circle these two fractions.
4
……………….
(2)
Total /10
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Error intervals 2
Objective:
Grade 5
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)
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(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
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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)
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b) How many hours does she need to work to make £310
………….……………………..
(3)
Total /10
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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)
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iv)
55 x 56
(52)4
…………………….
(3)
Question 3
Simplify
3x2y x 5 x y8
…………………….
(2)
Total /10
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Limits of accuracy 2
Objective:
Grade 5
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)
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Total /10
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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)
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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)
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iii)
840
……………………
(3)
Total /10
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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 – 55
5
………………………..
ii)
6 (8 - 2π) – 8 (4 π – 9)
……………………….
(3)
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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
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PLC Papers
Created For:
Calculating with fractions 2
Grade 5
Solutions
Objective: Calculate exactly with fractions, including solving problems
Question 1
1
Work out
1
6
x
2
. Give your answer as a fraction in its simplest form.
3
=
7
x =
=
7
(A1)
6
9
2
3
14
18
(M1)
……………….
(2)
Question 2
2
2
+ 3 . Give your answer as a mixed number
+
17
(M1)
Work out
3
=
8
=
40
+
91
=6
=
3
15
15
2
5
5
51
15
(M1)
1
15
(A1)
……………….
(3)
Question 3
4
Work out
1
3
3
- 1 . Give your answer as a mixed number
4
=
13
- (M1)
=
52
-
=
31
=2
3
12
12
7
4
21
12
(M1)
7
12
(A1)
……………….
(3)
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Question 4
Here are some fractions
2
8
3
10
4
16
5
10
8
24
1
Two of the fractions are not equivalent to . Circle these two fractions.
A1 For each correct answer
4
……………….
(2)
Total /10
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Error intervals 2
Objective:
SOLUTIONS
Grade 5
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)
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(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)
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Total /10
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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)
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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
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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)
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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
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Limits of accuracy 2
Objective:
SOLUTIONS
Grade 5
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=
137500��
(M1)
(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
350cm
(A1)
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(M1)
Greatest Length……350cm……………….. (2)
25 x 10= 250cm
250cm
(A1)
(M1)
Least Length ………250cm …………….. (2)
(Total 4 marks)
Total /10
PiXL PLC 2017 Certification
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)
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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
PiXL PLC 2017 Certification
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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
M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1
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)
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iii)
840
M2 for full systematic method of divisions by prime numbers oe factor trees; condone 1
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
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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 – 55
5
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)
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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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