NUMBER BASES
1. What is the value of the digit 6, in base ten, in the number 6008?
A 600
B 384
C 60
D 48
2. 1000012 – 11012 =
A 101002
B 100102
C 11002
D 10102
3. Express 26+ 25+ 22+ 1 as a number in base eight.
A 1018
B 1118
C 1458
D 1608
4. Given X5 = 1278, find the value of X.
A 87
B 134
C 322
D 432
5. 11001002 – 1110112 =
A 1010012
B 1100012
C 1101002
D 1101012
6. Given 6 381 2 1 2 2 11 × + × + = p , find the value of p.
A 0
B 1
C 2
D 3
7. Express 3028 as a number in base five.
A 10115
B 12345
C 13245
D 22025
GRAPH OF FUNCTION II
1. (a) Complete the following table for y = 15x.
X
|
-4
|
-3
|
-2
|
-1
|
-0.5
|
1
|
1.5
|
2
|
3
|
4
| |
Y
|
-3.75
|
-5
|
-15
|
-30
|
15
|
7.5
|
5
|
3.75
| |||
(b) For this part of the question, use graph paper. You may use a flexible curve rule.
By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis,
draw the graph of y = 15x for –4 ≤ x ≤ 4.
(c) From your graph, find
(i) the value of y when x = –2.8,
(ii) the value of x when y = 11.
(d) By drawing a suitable straight line on your graph, find a value of x which satisfies the equation
2x² – 18x = 15 for –4 ≤ x ≤ 4.
2. (a) Complete the table below for the equation y = x(3x – 2) – 7.
X
|
-4
|
-3.5
|
-3
|
-2
|
-1
|
0
|
1
|
2
|
3
|
4
|
Y
|
49
|
26
|
9
|
-2
|
-7
|
-6
|
14
|
33
|
(b) By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis,
draw the graph of y = x(3x – 2) – 7 for –4 ≤ x ≤ 4.
(c) From your graph, find the values of x which satisfy 3x2 – 2x – 7 = 0.
(d) By drawing a suitable straight line on your graph, find the values of x which
satisfy the equation 3x – 4 = 17x.
3. (a) Complete the following table for the equation y = 2x³+16
X
|
-3
|
-2.5
|
-2
|
-1
|
0
|
1
|
2
|
3
|
Y
|
-15.25
|
0
|
14
|
16
|
18
|
70
|
(b) By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 10 units on the y-axis,
draw the graph of y = 2x3 + 16 for –3 ≤ x ≤ 3.
(c) From your graph find
(i) the value of y when x = –1.8,
(ii) the value of x when y = 40.
(d) Draw a suitable straight line on your graph to find the value of x which satisfies
the equation x3 + x – 4 = 0. State this value of x.
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