1. |
Consider the sequence: 2 ; 5; 8; a; b; . . . |
1.1 |
Explain how the next number in the sequence is formed, e.g.
how is 5 formed if we start with 2? |
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Is your rule also valid for 8? |
1.2 |
Find the values of a and b. |
1.3 |
Write down the 8th number in the sequence. |
1.4 |
Which number in the sequence will be equal to 17? |
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2. |
Consider the number pattern: –4 ; –1; 2; 5; f; g; . . . |
2.1 |
Explain how the next number in the pattern is formed. |
2.2 |
Find the values of f en g. |
2.3 |
Write down the 7th number in the pattern. |
2.4 |
Which number in the pattern will be equal to 26? |
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3. |
Consider the sequence: 4; 2; 0; a; b; . . . |
3.1 |
Explain how the next number in the sequence is formed. |
3.2 |
Find the values of a en b. |
3.3 |
Write down the 11th number in the sequence. |
3.4 |
Which number in the sequence will be equal to -12? |
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4. |
Consider the sequence: –8 ; –13; –18; p; q; . . . |
4.1 |
Explain how the next number in the sequence is formed. |
4.2 |
Find the values of p en q. |
4.3 |
Write down the 8th number in the sequence. |
4.4 |
Which number in the sequence will be equal to -63? |
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5. |
Consider the number pattern: 118 ; 124; 130; r; s; . . . |
5.1 |
Explain how the next number in the pattern is formed |
5.2 |
Find the values of r en s. |
5.3 |
Write down the 9th number in the pattern. |
5.4 |
Which number in the pattern will be equal to 178? |
5.5 |
Which number in the pattern will be the first number that is greater than 200 and what is |
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is this number? |
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6. |
Consider the sequence: 2; 4; 8; 16; a; b; . . . |
6.1 |
Explain how the next number in the sequence is formed. |
6.2 |
Determine the value of a and of b. |
6.3 |
Write down the 8th number in the sequence. |
6.4 |
What is the number of the number in the pattern that is equal to 2048? |
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7. |
Consider the pattern: 3; 9; 27; c; d; . . . |
7.1 |
Explain how the next number in the pattern is formed. |
7.2 |
Find the value of c and of d. |
7.3 |
Write down the 7th number in the pattern. |
7.4 |
Which number in the pattern is equal to 19 683? |
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8. |
Consider the sequence: 768; 384; 192; f; g; . . . |
8.1 |
Explain how the next number in the sequence is formed. |
8.2 |
Determine the value of f and of g. |
8.3 |
Write down the value of the 7th number in the sequence. |
8.4 |
Which number in the sequence will be the first number smaller than 1? |
8.5 |
Write doen the number of the number in the sequence that is equal to 0,1875. |
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9. |
Consider the sequence: 1; -2; 4; -8; p; q; . . . |
9.1 |
Explain how the next number in the sequence is formed. |
9.2 |
Find the values of p en q. |
9.3 |
Write down the 10th number in the sequence. |
9.4 |
Which number in the sequence will be equal to -2048? |
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10. |
Consider the sequence: –4; –1; 2; 5; s; t; . . . |
10.1 |
Explain how the next number in the sequence is formed. |
10.2 |
Find the values of s en t. |
10.3 |
Write down the 10th number in the sequence. |
10.4 |
Which number in the sequence will be equal to 20? |
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11. |
Consider the sequence: 576; 288; 144; v; w; . . . |
11.1 |
Explain how the next number in the sequence is formed. |
11.2 |
Find the values of v en w. |
11.3 |
Write down the 10th number in the sequence. |
11.4 |
Which number in the sequence will be equal to 4,5? |
11.5 |
Which number in the sequence will be the first number that is smaller than 1? |
11.6 |
Which number in the sequence will be the first number that is smaller than 0? Explain your answer. |
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12. |
Consider the sequence: 0,15; 0,6; 2,4; f; g; . . . |
12.1 |
Explain how the next number in the sequence is formed. |
12.2 |
Find the values of f en g. |
12.3 |
Write down the 6th number in the sequence. |
12.4 |
Which number in the sequence will be the first number that is greater than 300? What is |
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this number? |
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13.1 |
Complete the following table : |
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Position number |
1 |
2 |
3 |
4 |
5 |
c |
d |
Number |
4 |
7 |
10 |
a |
b |
25 |
37 |
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13.2 |
Explain how you will find the values of a and of b. Write down these values. |
13.3 |
Explain how you will find the values of c and of d. Write down these values. |
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14.1 |
Complete the following table : |
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Position number |
1 |
2 |
3 |
4 |
5 |
c |
d |
9 |
e |
Number |
58 |
51 |
44 |
f |
g |
23 |
16 |
h |
− 5 |
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14.2 |
Explain how you will find the values of c, d and of e. Write down these values. |
14.3 |
Explain how you will find the values of f, g and of h. Write down these values. |
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15.1 |
Complete the following table : |
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Position number |
1 |
2 |
3 |
4 |
j |
6 |
k |
Number |
4 |
12 |
36 |
m |
324 |
n |
2916 |
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15.2 |
Explain how you will find the values of c, d and of e. Write down these values. |
15.3 |
Explain how you will find the values of c, d and of e. Write down these values. |
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16.1 |
Complete the following table : |
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Position number |
1 |
2 |
3 |
4 |
p |
7 |
q |
Number |
2 |
8 |
32 |
s |
512 |
t |
131072 |
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16.2 |
Explain how you will find the values of c, d and of e. Write down these values. |
16.3 |
Explain how you will find the values of c, d and of e. Write down these values. |
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17.1 |
Complete the following table : |
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Position number |
1 |
2 |
3 |
4 |
v |
8 |
w |
Number |
128 |
64 |
32 |
x |
4 |
y |
0,125 |
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17.2 |
Explain how you will find the values of c, d and of e. Write down these values. |
17.3 |
Explain how you will find the values of c, d and of e. Write down these values. |
17.4 |
What is the number of the first number in the pattern that will be smaller than 0,05? |
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18. |
The numbers in a pattern are formed by adding 3 to the previous number. |
18.1 |
The first number is 6. Complete the table . |
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Number of number in pattern, n |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
Number |
6 |
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Number of 3's added to 6 |
0 |
1 |
2 |
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18.3 |
How do the numbers in the third row compare to that in the first row? |
18.4 |
We call the first number in the pattern a. In this case a = ? |
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We call the number of the number in the pattern n. For a n = 1. |
18.5 |
We can write the second number as 6 + 1 x 3 or as 6 + (2 - 1) x 3 |
18.6 |
We can write the third number as 6 + 2 x 3 or as 6 + (3 - 1) x 3 |
18.7 |
We can write the sixth number as ? or as ? |
18.8 |
We can write the nth number as 6 + (n - 1) x 3 and that gives us a method/ formula with which |
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we can calculate any number in the pattern. |
18.9 |
Now use this formula to calculate the value of the 7th number in the pattern. Does your answer correspond to |
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the value in the table? |
18.10 |
Use this formula to show that the 12th number in the pattern is equal to 39. |
18.11 |
Show that the 16th number is greater than 48 |
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19. |
The numbers in a pattern are formed by adding 7 to the previous number. |
19.1 |
The first number in the pattern is 8. Now complete the table. |
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n |
1 |
2 |
3 |
4 |
5 |
6 |
Number |
8 |
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Number of 7's added to 8 |
0 |
1 |
2 |
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19.3 |
The first number in te pattern is a. In this case a = ? |
19.4 |
The number that we add to form the next number is called the common difference and is represented by a d. |
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In this case d = ? |
19.5 |
The third number can be written as 8 + 2 x 7 or as 8 + (3 - 1) x 7 |
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or also as a + (n − 1)d where a = 8, n = 3 (the third number) and d = 7 (we add 7 to get the next number). |
19.6 |
The formula is thus : the nth number = 8 + (n - 1) x 7 |
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Now calculate the value of the 9th number in the pattern. |
19.7 |
Show that number 22 is greater than 148 |
19.8 |
The nth number in the pattern is equal to 78. Calculate the value of n. |
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20. |
The first number in a sequence is 65. A number in the sequence is formed by subtracting 6 from its predecessor. |
20.1 |
Complete the table. |
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20.2 |
Write down the value of a and of d. |
20.3 |
Make a formula to ca;cu;ate a number in this sequence. |
20.4 |
Test your formula by calculating the 5th and 6th numbers in the sequence. |
20.5 |
What is the value of the 9th number? |
20.6 |
The nth number in the sequence is equal to − 1. Calculate the value of n. |
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21. |
The first number in a sequence of numbers is 5. A number in the sequence is formed by multiplying |
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its predecessor by 2. |
21.1 |
Complete the table. |
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21.2 |
Write down the value of a. |
21.3 |
The number by which the predecessor is multiplied is called the common ratio and is represented by an r. |
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22. |
The first number in a sequence of numbers is 1 024. A number in the sequence is formed by dividing its |
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predecesor by 4. |
22.1 |
Complete the table. |
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22.2 |
Write down the value of a and of r. |
22.3 |
Which number is the first number that is smaller than 1? What is the number of its position? |
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23. |
Given the formula: b = 3a - 5. |
23.1 |
Write down the relationship between a and b in words. |
23.2 |
Say which is the independent variable and which is the dependent variable. |
23.3 |
Calculate at least 4 values of a and b and write them down in a table (tabulate the results). |
23.4 |
Calculate the value of b if a = –16. |
23.5 |
Calcuate the value of a if b = 4. |
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24. |
Given the formula: c = 2 - 3d |
24.1 |
Write down the relationship between a and b in words. |
24.2 |
Say which is the independent variable and which is the dependent variable. |
24.3 |
Calculate at least 4 values of a and b and write them down in a table (tabulate the results). |
24.4 |
Calculate the value of c if d = –6. |
24.5 |
Calculate the value of d if c = 5. |
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25. |
Given the formula: p = 6 - 7q |
25.1 |
Write down the relationship between p and q in words. |
25.2 |
Say which is the independent variable and which is the dependent variable. |
25.3 |
Calculate at least 4 values of p and q and tabulate the results. |
25.4 |
Is this an example of an ascending / a rising relationship? Explain. |
25.5 |
Calculate the value of p if q = –2. |
25.6 |
Calculate the value of q if p = -22. |
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26. |
Given the formula: y = 2x - 7 |
26.1 |
Write down the relationship between x and y in words. |
26.2 |
Say which is the independent variable and which is the dependent variable. |
26.3 |
Calculate at least 4 values of x and y and tabulate the results. |
26.4 |
Is this an example of a descending relationship? Explain. |
26.5 |
Calculate the value of y if x = –3. |
26.6 |
Calculate the value of x if y = 3. |
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27. |
Given the formula: xy = 36 |
27.1 |
Write down the relationship between p and q in words. |
27.2 |
Say which is the independent variable and which is the dependent variable. |
27.3 |
Calculate at least 4 values of x and y and tabulate the results. |
27.4 |
Are x and y directly proportional to one another? Explain. |
27.5 |
How does the value of y change if the value of x increases / becomes greater in the same proportion? Explain. |
27.6 |
Can x or y ever be equal to zero? Explain. |
27.7 |
Calculate the value of y if x = 3. |
27.8 |
Calculate the value of x if y = 10. |
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28. |
Given the formula: pq = 24 |
28.1 |
Write down the relationship between p and q in words. |
28.2 |
Say which is the independent variable and which is the dependent variable. |
28.3 |
Calculate at least 4 values of p and q and tabulate the results. |
28.4 |
Are p and q directly proportional to one another? Explain. |
28.5 |
How does the value of q change if the value of p increases / becomes greater in the same proportion? Explain. |
28.6 |
Can x or y ever be equal to zero? Explain. |
28.7 |
Calculate the value of q if p = 12. |
28.8 |
Calculate the value of p if q = 6. |
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29. |
Given the formula: ab = 18 |
29.1 |
Write down the relationship between p and q in words. |
29.2 |
Say which is the independent variable and which is the dependent variable. |
29.3 |
Calculate at least 4 values of a and b and tabulate the results. |
29.4 |
Are a and b inversely proportional to one another? Explain. |
29.5 |
How does the value of b change if the value of a decreases / becomes smaller in the same proportion? Explain. |
29.6 |
Can x or y ever be equal to zero? Explain. |
29.7 |
Calculate the value of b if a = 12. |
29.8 |
Calculate the value of a if b = 4. |
29.9 |
For which value(s)) is a = b? |
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