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PLC Papers
Created For:
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 (Negative and Fractional) 2
Grade 7
Objective: Calculate with negative and fractional indices
Question 1
Write each expression in negative index form
i)
 1 
 4
2 
…………………….
(1)
ii)
 1
 
 12 
3
…………………….
iii)
 5 
 7
x 
(1)
…………………….
(1)
Question 2
Evaluate
i)
2
 
3
−4
…………………….
(2)
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ii)
 64 


 125 
−
1
3
…………………….
(2)
iii)
64
−5
6
…………………….
(3)
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 Rule 2
Grade 7
Objective: Use the product rule for counting
Question 1
James’ teacher gave him the three cards below
5
1
9
She asks him to use the cards to make as many three digit numbers as he can. How many
different numbers can James make?
……………………..
(2)
Question 2
Mr Green owns black, brown and blue shoes and red, green and purple socks. How many
combinations of shoes and socks can he wear?
……………………
(2)
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Question 3
Stephanie has to set a new code for her combination lock. The lock is made up of four parts
and each part contains the digits from 0 to 9.
a) How many possible codes are there for the lock?
……………………
(2)
b) Stephanie decides to use even numbers only in her code. How many possible codes are
there for the lock now?
……………………
(2)
c) As well as only using even numbers, Stephanie decides that no digits should be
repeated. How many possible codes are there for the lock now?
……………………
(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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Recurring Decimals 2
Grade 7
Objective: Change recurring decimals into fractions and vice versa.
Question1
a) Change
15
24
into a decimal.
(2)
b) Is the answer from part a recurring decimal or a terminating decimal? Explain your choice below.
(2)
Question 2
.
Change 0.307 into a fraction.
(2)
Question 3
..
Change 0.047 into a fraction.
(2)
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Question 4
..
Convert the recurring decimal 0.78 in to a fraction.
(2)
Total /10
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Upper and Lower Bounds 2
Objective:
Grade 7
Calculate upper and lower bounds.
Question 1.
(a) A man weighs 80kg to the nearest kg. Find the greatest possible amount that he could weigh.
…………………….. (2)
(Total 2 mark)
Question 2
Find the upper and lower bounds of xy where � = �� ��� � = �� when both have been rounded to the
nearest whole number
Upper Bound …………………………...
Lower Bound ……………………………
(2)
(Total 2 marks)
Question 3.
The following numbers have been rounded to two significant figures. Find the upper and lower bounds for
each value.
(a) 13
Upper Bound …………………………...
Lower Bound ……………………………
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(2)
(b) 0.16
Upper Bound …………………………...
Lower Bound ……………………………
(2)
(Total 4 marks)
Question 4.
Complete the table
Value
Level of Accuracy
30
Lower Bound
Upper Bound
21.5
22.5
1.S.F.
Nearest whole number
(Total 2 marks)
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:
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 (Negative and Fractional) 2
Grade 7
Solutions
Objective: Calculate with negative and fractional indices
Question 1
Write each expression in negative index form
i)
 1 
 4
2 
2-4
(A1)
…………………….
(1)
i)
 1
 
 12 
3
12-3
(A1)
…………………….
ii)
 5 
 7
x 
(1)
5x-7
(A1)
…………………….
(1)
Question 2
Evaluate
i)
2
 
3
−4
2-4 =
1
16
or 3-4 =
81
16
1
81
(M1)
(A1)
…………………….
(2)
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ii)
 64 


 125 
−
1
3
( 64 )
−
1
3
=
1
4
5
4
or (125 ) 3 = (M1)
−
1
(A1)
1
5
…………………….
(2)
−5
iii)
64 6
( 64 )
−
1
6
=
1
2
(M1)
25 = 32 (M1)
1
32
(A1)
…………………….
(3)
Total /10
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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
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Product Rule 2
Grade 7
Solutions
Objective: Use the product rule for counting
Question 1
James’ teacher gave him the three cards below
5
1
9
She asks him to use the cards to make as many three digit numbers as he can. How many
different numbers can James make?
3 x 2 x 1 or starting to list combinations (M1)
6 (A1)
……………………..
(2)
Question 2
Mr Green owns black, brown and blue shoes and red, green and purple socks. How many
combinations of shoes and socks can he wear?
3 x 3 or starting to list combinations (M1)
9 (A1)
……………………
(2)
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Question 3
Stephanie has to set a new code for her combination lock. The lock is made up of four parts
and each part contains the digits from 0 to 9.
a) How many possible codes are there for the lock?
10 x 10 x 10 x 10 or starting to list combinations (M1)
10000 (A1)
……………………
(2)
b) Stephanie decides to use even numbers only in her code. How many possible codes are
there for the lock now?
5 x 5 x 5 x 5 or starting to list combinations (M1)
625 (A1)
……………………
(2)
b)As well as only using even numbers, Stephanie decides that no digits should be
repeated. How many possible codes are there for the lock now?
5 x 4 x 3 x 2 or starting to list combinations (M1)
120 (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
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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Recurring Decimals 2
Grade 7
Solutions
Objective: Change recurring decimals into fractions and vice versa.
Question1
a) Change
15
24
into a decimal.
(M1)
0.625 (A1)
(2)
b) Is the answer from part a recurring decimal or a terminating decimal? Explain your choice below.
Terminating, as the decimal doesn’t go on for infinity place values. (A2)
(2)
Question 2
.
Change 0.307 into a fraction.
1000X= 307.7777
100X = 30.777
(2)-(1)
-(1)
-(2)
900X = 277 (M1)
X = 277/900 (A1)
(2)
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Question 3
..
Change 0.047 into a fraction.
X= 0.0474747
-(1)
100X = 4.7474747 -(2)
(2) – (1)
99X = 4.7
(M1)
X=47/990
(A1)
(2)
Question 4
..
Convert the recurring decimal 0.78 in to a fraction.
X= 0.78 78 78
-(1)
100X = 78.78 78 78 -(2)
(2) – (1)
99 X = 78
X = 26/33
(M1)
(A1)
(2)
Total /10
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Upper and Lower Bounds 2
Objective:
SOLUTIONS
Grade 7
Calculate upper and lower bounds.
Question 1.
(a) A man weighs 80kg to the nearest kg. Find the greatest possible amount that he could weigh.
80.5kg(A2)
…………………….. (2)
(Total 2 mark)
Question 2
Find the upper and lower bounds of xy where � = �� ��� � = �� when both have been rounded to the
nearest whole number
Upper Bound ………(B1)………12.5X10.5=131.25…………...
Lower Bound …9.5X11.5=109.25……(B1)……………………
(2)
(Total 2 marks)
Question 3.
The following numbers have been rounded to two significant figures. Find the upper and lower bounds for
each value.
(a) 13
Upper Bound ………13.5…………B1………...
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Lower Bound ………12.5…… B1………………
(2)
(b) 0.16
Upper Bound……0.165……B1………………...
Lower Bound ………0.155 B1……………………
(2)
(Total 4 marks)
Question 4.
Complete the table
Value
Level of Accuracy
30
22
1.S.F.
Nearest whole number
Lower Bound
25
Upper Bound
35 B1
21.5
22.5 B1
(Total 2 marks)
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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