PLC Papers
Created For:
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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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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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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Surds 2
Grade 8
Objective: Simplify expressions involving surds, including rationalising the denominator and calculate
exactly with surds
Question 1
Simplify
192
…………………
(1)
Question 2
Expand and simplify
i)
ii)
(3 − 7) 2
(7 + 2 2)(7 − 2 2)
…………………
…………………
(4)
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Question 3
Rationalise the denominators
i)
ii)
1
2+ 2
…………………
1− 5
2− 5
…………………
(5)
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
PiXL PLC 2017 Certification
PLC Papers
Created For:
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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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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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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Surds 2
Grade 8
Solutions
Objective: Simplify expressions involving surds, including rationalising the denominator and calculate
exactly with surds
Question 1
Simplify
192
8√3 (A1)
…………………
(1)
Question 2
Expand and simplify
i)
(3 − 7) 2
9 - 3√7 - 3√7 -√7√7 (M1 for any three correct terms)
2 - 6√7 (A1)
ii)
…………………
(7 + 2 2)(7 − 2 2)
49 - 14√2 + 14√2 -4√2√2 (M1 for any three correct terms)
41 (A1)
…………………
(4)
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Question 3
Rationalise the denominators and simplify as far as possible.
i)
1
2+ 2
2 - √2
(2 + √2)(2 - √2)
2 - √2
2
ii)
(M1)
(A1)
…………………
1− 5
2− 5
(1 - √5)(2 + √5)
(2 - √5)(2 + √5)
- 3 - √5
-1
3 + √5
(M1)
(M1)
(A1)
…………………
(5)
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
PiXL PLC 2017 Certification