Download 1 - NCETM

3
1.
(a)
Work out
1 1
   
2 4
2
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Answer ..................................................................
(3)
(b)
Write down the value of
3
27
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Answer ..................................................................
(1)
(Total 4 marks)
2.
p and q are odd numbers.
(a)
Is p + q an odd number, an even number or could it be either?
Tick the correct box.
odd
even
either
(1)
(b)
Is pq an odd number, an even number or could it be either?
Tick the correct box.
odd
even
either
(1)
(Total 2 marks)
The Robert Smyth School
1
3.
Zoe chooses three consecutive numbers.
Show that the sum of the first and the last of these three numbers is always an even number.
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(Total 2 marks)
4.
Use your calculator to evaluate
(3.41  2.93) 2
4.12
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Answer .......................................................
(Total 2 marks)
5.
Use your calculator to find the value of
18.31
9.41  4.47
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Answer .........................................................................
(Total 2 marks)
6.
Use your calculator to find the value of
7.432
9.24  3.38
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Answer ................................................
(Total 2 marks)
The Robert Smyth School
2
7.
(a)
Find the cube root of 125.
Answer ..............................................................
(1)
(b)
2
3.6 3
Find the value of
(i)
Write down the full calculator display.
Answer ..............................................................
(1)
(ii)
Write your answer to 3 significant figures.
Answer ..............................................................
(1)
(Total 3 marks)
8.
You are given that
AB =
8.29
2
 4.55 2

Not to scale
A
4.55 cm
C
8.29 cm
B
Use your calculator to work out AB.
(a)
Write down your full calculator display.
Answer ................................................................... cm
(1)
(b)
Write your answer to 3 significant figures.
Answer ................................................................... cm
(1)
(Total 2 marks)
9.
Calculate
9.61 + 2.912
Give your answer to 3 significant figures.
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Answer .......................................................................
(Total 2 marks)
The Robert Smyth School
3
10.
Use your calculator to work out the value of
3
(a)
729 2
Answer ..........................................................................
(1)
(b)
1024 –0.5
Answer ..........................................................................
(1)
(Total 2 marks)
11.
(a)
(i)
Evaluate
13z0
Answer ............................................
(1)
(ii)
Evaluate
(13z)0
Answer ............................................
(1)
(b)
If 3x = 1 , find the value of x.
27
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Answer x = ............................................
(2)
1
(c)
If 4y = 64 2 , find the value of y.
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Answer y = ............................................
(2)
(Total 6 marks)
The Robert Smyth School
4
1
12.
(a)
Find the value of 36 2
Answer ................................................................
(1)
(b)
Simplify
1
81 4
2–2 ×
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Answer ................................................................
(3)
(Total 4 marks)
1
13.
(a)
Find the value of 64 3
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Answer ..........................................................................
(1)
(b)
Find the value of 8x
0
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Answer ..........................................................................
(1)
(Total 2 marks)
1
14.
(a)
Write down the value of
27 3
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Answer ……………………………………………
(1)
(b)
Write down the value of
(4xy)0
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Answer ……………………………………………
(1)
(c)
If 2x = 1 find the value of x.
32
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Answer x = ……………………………………….
(2)
(Total 4 marks)
The Robert Smyth School
5
1.
(a)
1
1
()
8
16
2 1

=
16 16
M1
or 0.125 (+) 0.0625
A1 ft
=
(b)
3
or 0.1875
16
A1
3
B1
Not 3
3
[4]
2.
(a)
Even
B1
(b)
Odd
B1
[2]
3.
n, n + 1, n + 2
If n is even, both numbers are even  sum even
[odd and even needed stating for B2]
B2
If n is odd, both numbers are odd  sum even
[eg 7 + 9 = 16 even, 2 such examples
(B1 for 2 numerical attempts)]
Alternative method
Sum of n and n + 2 is 2n + 2
Which is even or 2(n + 1)
OR twice the middle number
B1
B1 dep
B2
[4]
4.
40.1956
4.12
M1
M1 for 40.1956
= 9.756...
A1
Accept 9.8, 9.76
[2]
5.
4.2790 ...
13.88
M1
= 0.308
A1
Accept 0.308…
Ignore further working
SC1 0.31
[2]
The Robert Smyth School
6
6.
55 .2049
5.86
= 9.42…. or 9.42
M1
A1
B1 for 9.4
[2]
7.
(a)
5
B1
(b)
(i)
0.0428669(…)
Allow 0.042867
(ii)
0.0429
ft from value > 3 sf seen
B1
B1 ft
[3]
8.
(a)
9.45656(...)
B1
(b)
9.46
B1 ft
ft from any (a) > 3 sf
[2]
9.
11.6
B2
11.568(1)
B1
[2]
10.
(a)
19683
B1
(b)
0.03125 or 1
32
B1
[2]
11.
(a)
(b)
(i)
13
B1
(ii)
1
B1
3x = 3–3
x = –3
M1
A1
M1 for writing 1/27 as a power of 3, correctly
allow embedded answer
(c)
4y = 41½
M1
y = 1½
A1
y
M1 for 4 = 8
allow embedded answer
[6]
The Robert Smyth School
7
12.
(a)
(±)6
B1
(b)
1
B1
4
or 0.25
3
3
B1
B1
4
[4]
13.
(a)
4
B1
(b)
8
B1
[2]
14.
(a)
3
B1
(b)
1
B1
(c)
(x =) –5
B2
5
Bl for sight of 32 = 2 oe
[4]
The Robert Smyth School
8