DEPARTMENT OF
EDUCATION
MOPANI WEST DISTRIC
GET BAND
MATHEMATICS
GRADE 9
07 MARCH 2019
MARKS: 100
DURATION: 2 HOURS
INTRUCTIONS:
1. This paper consist of 6 pages including the cover page.
2. Read the questions carefully before answering.
3. Answer all questions.
4. Show all your calculations.
5. Write neatly and legibly.
1|Page
QUESTION 1
[10 MARKS]
NUMBER, OPERATIONS AND RELATIONSHIPS
1.1
Which ONE of the following numbers is an irrational number?
A.
1.2
1.6
8
B.
12
(1)
2
3
7
C.
9
D.
12
6
B. 9
12
(1)
C.
−9
D.
−6
(1)
14
B.
8
C.
10
D.
100
(1)
1,45 × 10−6
B.
C.
14,5 × 10−7
D.
0,145 × 10−5
145 × 10−8
(1)
The lowest common multiple (LCM) of 12 and 18 is ….
6
B.
216
C.
36
C.
15, 67
D.
72
(1)
D. 18, 13
(1)
Calculate: 9,3 − (7,6 − 1,23)
0, 47
B.
2, 93
The HCF of 27;36; and 90
A.
1.9
12
2
√27
D.
and on a number line?
A.
A.
1.8
6
1
0 ÷ 27
C.
0.00000145 written in scientific notation is:
A.
1.7
√−27
Simplify: √64 + 36 =
A.
1.5
3
B.
Complete: (−3)2 =
A.
1.4
√27
Which fraction lies between
A.
1.3
3
132
96
A.
2|Page
18
B.
9
C.
3
D.
72
(1)
in its simplest form is:
22
16
B.
33
23
C.
11
8
D
132
96
(1)
1.10
54
100
as decimal fraction :
A.
0.054
B.
54
C. 0.54
QUESTION 2
D.
54%
(1)
[14 MARKS]
NUMBER, OPERATIONS AND RELATIONSHIPS
2.1.
Classify the following numbers as rational or irrational.
2.1.1.
0, 3̇7̇
(1)
2.1.2.
√121
(1)
1
2.1.3.
2.1.4.
2.1.5.
2.2.
(1)
2
√2
(1)
−2
(1)
3
Copy and complete the following table: (common fractions must be in their
simplest form)
Common fraction
1
20
Decimal fraction
5%
0,375
3
10
Percentage
37,5%
0,3
(3)
2.3.
Write 24 and 32 each as the product of their prime factors and then write their
LCM.
(3)
2.4.
Calculate by rounding off and compensating:
2 342 − 1 876
3|Page
(3)
QUESTION 3
[13 MARKS]
NUMBER, OPERATIONS AND RELATIONSHIP
3.1. Consider the following table:
Time in hours
Average speed in
km/h
12
60
9
80
8
90
6
A
B
144
3.1.1. Is this an example of direct or indirect proportion? Give reason for your
answer.
(2)
3.1.2. What are the values of A and B?
(2)
3.1.3. A car travelling at a constant speed travels 60 𝑘𝑚 𝑖𝑛 18 𝑚𝑖𝑛𝑢𝑡𝑒𝑠. How far will
the car travel in 1 ℎ𝑜𝑢𝑟 12 𝑚𝑖𝑛𝑢𝑡𝑒𝑠.
(6)
3.3. Write 18 days to 4 weeks as a ratio.
(3)
QUESTION 4 [11 MARKS]
PATTERNS, FUNCTIONS AND ALGEBRA
4.1. Write the missing number in each sequence:
4.1.1.
1; 4; 9; …
(1)
4.1.2.
1; 3; 6; 10; …
(1)
4.2. Consider the table below:
Position in sequence
Term value
1
1
2
3
3
5
4
7
5
9
100
……
4.2.1. Describe, in words, the relationship between the position in the sequence and
the term value
4.2.2. Describe, in words, the pattern formed by the term values.
4|Page
(1)
(1)
4.2.3. What set of numbers do the term values represent?
(1)
4.2.4. Write the 100th term of the sequence.
(1)
4.3. Pattern below is made from squares:
1
2
3
4
4.3.1.
How many squares will there be in pattern 5?
(1)
4.3.2.
Describe, in your own words, how to get the number of squares in each
pattern.
(1)
4.3.3.
Write down the general term of the given pattern of the squares in the form
𝑇𝑛 =
(1)
4.3.4. Which pattern number will have 79 squares?
(2)
QUESTION 5 [24 MARKS]
NUMBERS, OPERATIONS AND RELATIONSHIP
5.1.
Calculate each of the following:
5.1.1.
24 × (−53) + (−27) × (−34) − (−55) × 76
(2)
5.1.2.
(0.12)2
(1)
5.1.3.
4,2 − 0,4 × 1,2 + 7,37
(2)
5.2.
Write in scientific notation: 0.000000065
5.3.
Calculate and leave your answer in simplest form:
5.3.1.
5.3.2.
5.3.3.
5.3.4.
5|Page
6
5
÷
9
(3)
10
1
3
1
5
5
4
(1 ) + (3 ) × 1
3
1000
√
3
4
64
−
3 2
(3)
2
+( ) ×
4
3
5−3
6
(1)
7
+ =
8
(4)
(3)
5.3.5.
5.4.
Simplify:
3
√4 × √8 =
(3)
2𝑥(𝑥 + 1) − 3(𝑥 + 1)
(2)
QUESTION 6 [10 MARKS]
NUMBERS, OPERATIONS AND RELATIONSHIP
6.1. Copy and complete the following flow diagram:
1
0
2𝑥 − 3
-2
−13
(4)
6.2. What is 20% of 𝑅140?
(2)
6.3. Calculate the percentage increase in the price of sephahlo (kota) if it increases from
R10, 00 to R13, 50.
(4)
Question 7 [8 MARKS]
FINANCE
Use the following formulas:
𝒓
𝑺𝑰 = 𝟏𝟎𝟎 . 𝒑. 𝒏
𝒓
𝑨 = 𝑷(𝟏 + 𝟏𝟎𝟎 )𝒏
7.1. Calculate the compound interest on a loan of 𝑅3 450 𝑎𝑡 6,5% per annum for five
years.
(4)
7.2. How long will it take for 𝑅3 000 invested at 6% per annum simple interest to grow to
𝑅4 260?
(4)
QUESTION 8 [10 MARKS]
PATTERNS, FUNCTION AND ALGEBRA
Consider the algebraic expressions:
8𝑥 2 − 2𝑥 + 1 and
7𝑥 2 + 4𝑥 − 2
8.1. Find the sum of the two expressions.
(3)
8.2.
Find the difference between the first and second expressions.
(3)
8.3. If𝑥 = −2 , what is the number value of the sum of the expressions?
(2)
8.4. If𝑥 = −3, what is the number value of the difference between expressions?
(2)
6|Page