Guided practice worksheet - mrvahora · 2 5.2 Using standard form 95B 3 Write these numbers in...
11
● 2 5.1 Using zero and negative powers 93A 1 Work out the value of these expressions . a 3 2 ........................................................................................ b 8 2 ........................................................................................ c 4 3 ........................................................................................ d 2 5 ........................................................................................ e ( 2 5 ) 2 ........................................................................................ f 6 2 ........................................................................................ g (-3) 3 ........................................................................................ h 10 5 ........................................................................................ i 2 6 ........................................................................................ j ( 3 8 ) 2 ........................................................................................ k 5 3 ........................................................................................ l (-9) 2 ........................................................................................ 2 Work out the value of these expressions. a 6 0 ........................................................................................ b 7 –1 ........................................................................................ c 19 0 ........................................................................................ d 3 –1 ........................................................................................ e 2 –1 ........................................................................................ f 5 –1 ........................................................................................ g 6 –1 ........................................................................................ h (-2) –1 ........................................................................................ i 4 –1 ........................................................................................ j 10 –1 ........................................................................................ k 7 0 ........................................................................................ l (-4) –1 ........................................................................................ 3 Work out the value of these expressions. a 5 –2 ........................................................................................ b 7 –2 ........................................................................................ c 2 –3 ........................................................................................ d 9 –2 ........................................................................................ e 6 –2 ........................................................................................ f 3 –3 ........................................................................................ g 8 –2 ........................................................................................ h 10 –4 ........................................................................................ i 5 –3 ........................................................................................ j 2 –4 ........................................................................................ k 4 –2 ........................................................................................ l 2 –7 ........................................................................................ Guided practice worksheet Remember that 2 4 = 2 × 2 × 2 × 2 = 16 1 Remember that a 0 = 1, a –n = –– a n Hint Take care with signs. B Questions are targeted at the grades indicated
Transcript of Guided practice worksheet - mrvahora · 2 5.2 Using standard form 95B 3 Write these numbers in...
�2 5.1 Using zero and negative powers
93A
1 Work out the value of these expressions.
a 32 ........................................................................................ b 82 ........................................................................................
c 43 ........................................................................................ d 25 ........................................................................................
e (25)2
........................................................................................
f 62 ........................................................................................
g (−3)3 ........................................................................................ h 105 ........................................................................................
i 26 ........................................................................................ j (38)2
........................................................................................
k 53 ........................................................................................ l (−9)2 ........................................................................................
2 Work out the value of these expressions.
a 60 ........................................................................................ b 7–1 ........................................................................................
c 190 ........................................................................................ d 3–1 ........................................................................................
e 2–1 ........................................................................................ f 5–1 ........................................................................................
g 6–1 ........................................................................................ h (−2)–1 ........................................................................................
i 4–1 ........................................................................................ j 10–1 ........................................................................................
k 70 ........................................................................................ l (−4)–1 ........................................................................................
3 Work out the value of these expressions.
a 5–2 ........................................................................................ b 7–2 ........................................................................................
c 2–3 ........................................................................................ d 9–2 ........................................................................................
e 6–2 ........................................................................................ f 3–3 ........................................................................................
g 8–2 ........................................................................................ h 10–4 ........................................................................................
i 5–3 ........................................................................................ j 2–4 ........................................................................................
k 4–2 ........................................................................................ l 2–7 ........................................................................................
Guided practice worksheet
Remember that 24 = 2 × 2 × 2 × 2 = 16
1 Remember that a0 = 1, a–n = –– an
Hint Take care with signs.
B
Questions are targeted at the grades indicated
�2 5.1 Using zero and negative powers
93B
4 Work out the value of these expressions.
a (15 )–1
........................................................................................
b (45)–1
........................................................................................
c (19)–1
........................................................................................
d (27)–1
........................................................................................
e (0.5)–1 ........................................................................................ f (2 12 )–1
........................................................................................
5 Work out the value of these expressions.
a (12)–2
........................................................................................
b (15 )–2
........................................................................................
c (14)–3
........................................................................................
d (16)–2
........................................................................................
e (13)–3
........................................................................................
f ( 110)–4
........................................................................................
g (23)–2
........................................................................................
h (35)–2
........................................................................................
i (47)–2
........................................................................................
j ( 310)–3
........................................................................................
k (2 12 )–3
........................................................................................
l (113)–2
........................................................................................
Guided practice worksheet
B
�2 5.2 Using standard form
95A
1 Write these numbers in standard form.
a 6000 ................................................................................. b 200 ....................................................................................
............................................................................................ ............................................................................................
c 5 000 000 ........................................................................ d 76 000 ..............................................................................
............................................................................................ ............................................................................................
e 23 ..................................................................................... f 92 100 000 ......................................................................
........................................................................................... ...........................................................................................
g 2850 ................................................................................ h 812 000 ............................................................................
............................................................................................ ............................................................................................
i 567 ....................................,,............................................. j 981.02 ..............................................................................
........................................................................................... ...........................................................................................
k 30 ..................................................................................... l 2318 .................................................................................
........................................................................................... ...........................................................................................
2 Write these as ordinary numbers.
a 8 × 102 ............................................................................ b 6 × 104 .............................................................................
............................................................................................ ............................................................................................
c 7 × 101 ............................................................................ d 2 × 105 ............................................................................
............................................................................................ ............................................................................................
e 5 × 100 ............................................................................ f 8.3 × 104 .........................................................................
............................................................................................ ............................................................................................
g 9.3 × 102 .......................................................................... h 6.07 × 105 .......................................................................
............................................................................................ ............................................................................................
i 5.672 × 102 ..................................................................... j 3.2 × 107 ..........................................................................
............................................................................................ ............................................................................................
Guided practice worksheet Questions are targeted at the grades indicated
B
�2 5.2 Using standard form
95B
3 Write these numbers in standard form.
a 0.0008 ............................................................................. b 0.06 ..................................................................................
........................................................................................... ...........................................................................................
c 0.000 002 ....................................................................... d 0.9 ....................................................................................
........................................................................................... ...........................................................................................
e 0.036 ............................................................................... f 0.000 872 .......................................................................
........................................................................................... ...........................................................................................
g 0.000 005 62 ................................................................. h 0.080 54 .........................................................................
........................................................................................... ...........................................................................................
i 0.34 ................................................................................. j 0.000 002 .......................................................................
........................................................................................... ...........................................................................................
k 0.003 ............................................................................... l 0.004 523 .......................................................................
........................................................................................... ...........................................................................................
4 Write these as ordinary numbers.
a 5 × 10–3 ........................................................................... b 8 × 10–2 ...........................................................................
........................................................................................... ...........................................................................................
c 7 × 10–4 ........................................................................... d 1 × 10–1 ...........................................................................
........................................................................................... ...........................................................................................
e 3 × 10–6 ........................................................................... f 9.2 × 10–3 .......................................................................
........................................................................................... ...........................................................................................
g 3.5 × 10–2 ...................................................................... h 8.04 × 10–6 .....................................................................
........................................................................................... ...........................................................................................
i 8.15 × 10–1 ..................................................................... j 4.9 × 10–5 .......................................................................
........................................................................................... ...........................................................................................
Guided practice worksheet
B
�2 5.2 Using standard form
95C
5 These numbers are not in standard form.
Rewrite each number so that it is in standard form.
a 67 × 102 ......................................................................... b 85 × 105 ..........................................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
c 0.027 × 104 .................................................................... d 156 × 108 .......................................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
e 0.0093 × 106 ................................................................. f 721 × 10–3 ......................................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
g 38 × 10–2 ......................................................................... h 0.034 × 10–3 ..................................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
i 815 × 10–6 ...................................................................... j 0.006 × 10–5 ..................................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
6 Work out and give your answer in standard form.
a (3 × 105) × (2 × 102) ................................................... b (4 × 103) × (2 × 107) ...................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
c (1.3 × 106) × (5 × 10–2) ............................................. d (5 × 104) × (7 × 103) ...................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
e (8 × 10–4) × (5 × 108) ................................................. f (4.3 × 101) × (6 × 107) ................................................
........................................................................................... ...........................................................................................
........................................................................................... ...........................................................................................
Guided practice worksheet
B
A
�2 5.3 Working with fractional indices
97A
1 Write down the value of the following.
a 52 ............................................................................. b 23 .............................................................................
c 82 ............................................................................. d 103 .............................................................................
e 42 .............................................................................
2 Write down the value of
a 9 .............................................................................
b 83 .............................................................................
c 100 .............................................................................
d 1253 .............................................................................
e 4 .............................................................................
3 Work out the value of
a 6412
............................................................................. b 25
12
.............................................................................
c 3612
............................................................................. d ( 1
25
12) .............................................................................
e (4912) .............................................................................
4 Work out the value of
a 813
............................................................................. b 125
13
.............................................................................
c 2713
............................................................................. d (27
64
13
) .............................................................................
e ( 11000
13
) .............................................................................
5 Work out the value of
a 5–2 ............................................................................. b 6–2 .............................................................................
c 3–3 ............................................................................. d 2–5 .............................................................................
e 10–4 .............................................................................
6 Work out the value of
a 2512–
............................................................................. b 8
13–
.............................................................................
....................................................................................... .......................................................................................
c 2713– .............................................................................
d 10012–
.............................................................................
....................................................................................... .......................................................................................
e (49
12–)
.............................................................................
.......................................................................................
Guided practice worksheet
Remember 92 = 81 so √–81 = 9, 43 = 64 so 3√–64 = 4.
Remember 811–2 = √–81, 64
1–3 = 3√–64 .
1 Remember that a–n = –– an
B
Questions are targeted at the grades indicated
�2 5.3 Working with fractional indices
97B
Guided practice worksheet
7 Work out the value of
a 432 ............................................................................. b 9
32 .............................................................................
....................................................................................... .......................................................................................
c 452 ............................................................................. d 100
32 .............................................................................
....................................................................................... .......................................................................................
e ( 925
32
) .............................................................................
.......................................................................................
8 Work out the value of
a 823 ............................................................................. b 27
23 .............................................................................
....................................................................................... .......................................................................................
c 873 ............................................................................. d 1000
43 .............................................................................
....................................................................................... .......................................................................................
e 12523 .............................................................................
.......................................................................................
9 Work out the value of
a 432– ............................................................................. b 27
23– .............................................................................
....................................................................................... .......................................................................................
....................................................................................... .......................................................................................
....................................................................................... .......................................................................................
c 6423– ............................................................................. d 16
32– .............................................................................
....................................................................................... .......................................................................................
....................................................................................... .......................................................................................
....................................................................................... .......................................................................................
e 853– ............................................................................. f (1
8
23–
) .............................................................................
....................................................................................... .......................................................................................
....................................................................................... .......................................................................................
....................................................................................... .......................................................................................
Remember an–m = a
1–m x n
= (a1–m )n
A
�2 5.3 Working with fractional indices
97C
Guided practice worksheet
g (259
32–
) .............................................................................
h ( 1125
23–
) .............................................................................
....................................................................................... .........................................................................................
....................................................................................... .........................................................................................
....................................................................................... .........................................................................................
i ( 11000
23–
) ......................................................................... j 32
25– ...............................................................................
....................................................................................... .........................................................................................
....................................................................................... .........................................................................................
....................................................................................... .........................................................................................
A
�2 5.4 Using surds
99A
1 Find the value of the integer k.
a 18 2= k ...........................................................................
.....................................................................................................
b 32 2= k ...........................................................................
.....................................................................................................
c 200 2= k ...........................................................................
.....................................................................................................
d 50 2= k ...........................................................................
.....................................................................................................
2 Find the value of the integer k.
a 12 3= k ............................................................................. b 75 3= k .............................................................................
..................................................................................................... ......................................................................................................
c 27 3= k ............................................................................. d 108 3= k .............................................................................
..................................................................................................... ......................................................................................................
3 Find the value of the integer k.
a 20 5= k ............................................................................. b 98 2= k .............................................................................
..................................................................................................... ......................................................................................................
c 28 7= k ............................................................................. d 44 11= k .............................................................................
..................................................................................................... ......................................................................................................
4 Simplify
a 72 ......................................................................................... b 80 ...........................................................................................
..................................................................................................... ......................................................................................................
c 128 ......................................................................................... d 300 ...........................................................................................
..................................................................................................... ......................................................................................................
e 63 ..........................................................................................
.....................................................................................................
Guided practice worksheet
The square numbers will be useful in simplifying surds.12 = 1 22 = 432 = 9 42 = 1652 = 25 62 = 3672 = 49 82 = 6492 = 81 102 = 100
Questions are targeted at the grades indicated
A
�2 5.4 Using surds
99B
Guided practice worksheet
5 Expand and simplify these expressions. Write your answers in the form a b c+ where a, b and c are integers.
a 2 3 2( )+ ...................................................................................
..........................................................................................................
b 5 5 1( – ) ..................................................................................... c 7 4 7( – ) ...................................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
d ( )( )1 2 3 2+ + ........................................................................... e ( )( )3 5 2 3+ + ..........................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
f ( )( )3 2 5 2– + ........................................................................... g ( )( – )7 5 5 2+ ..........................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
h ( )3 2 2+ ....................................................................................... i ( – )5 3 2 .......................................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
.......................................................................................................... ..........................................................................................................
6 Rationalise the denominators.
a 13
..........................................................................
b 111
..........................................................................
.................................................................................. ...................................................................................
c 35
..........................................................................
d 43
..........................................................................
.................................................................................. ...................................................................................
e 27
..........................................................................
..................................................................................
Remember that √–a × √–a = a.
A*
A
Remember that to rationalise the adenominator of ––– you multiply top and √–bbo� om of the fraction by √–b.
�2 5.4 Using surds
99C
Guided practice worksheet
7 Rationalise the denominators and simplify your answers.
a 42
..........................................................................
b 21
3
.................................................................................
.................................................................................. .........................................................................................
c 21
7
.......................................................................... d
205
.................................................................................
.................................................................................. .........................................................................................
e 24
2
..........................................................................
..................................................................................
8 Rationalise the denominators and give your answers in the form a b c+ where a, b and c are integers.
a 6 2
2+
.............................................................................
b 8 2
2–
..........................................................................
.......................................................................................... .........................................................................................
.......................................................................................... .........................................................................................
c 15 5
5–
..........................................................................
d 3 15
3+
..........................................................................
.......................................................................................... .........................................................................................
.......................................................................................... .........................................................................................
e 7 35
7–
..........................................................................
..........................................................................................
..........................................................................................
A*
A
