Mathematics: Test
1
Grade 6
Operations, BODMAS, factors, multiples & Prime numbers
Question 1:
1.
Circle the correct answer from the options given:
The 9th multiple of 17 is;
a) 9
2.
b) 153
b) 46 700 ÷ 10 x 10³
b) 6
b) 1, 2, 3, 7
d) 4 670 ÷ 10² x 10⁵
c) 9
d) 18
c) 2, 3, 7
d) 2, 3, 6
If 3, 4 and 8 are the factors of two numbers, what are the possible numbers?
a) 48, 72
6.
c) 4670÷ 1 x 10⁴
Which of the following are prime factors of 42?
a) 1, 2, 3, 6
5.
d) 63
The highest common factor of 36 and 18 is;
a) 648
4.
c) 133
Which of the following is not the same as 4 670 x 1 000;
a) 4670÷ 10 x 10⁴
3.
(10)
b) 48, 64
c) 32, 48
d) 32, 108
How much more is 6 345 023 than 4 278 179?
a) 2 066 848
b) 2 623 202
c) 2 066 844
d) 2 068 644
7. What is the quotient of (9 306 x 1 00) and the square root of 81?
a) 103 400
b) 10 340
8. Find the value of
c) 20 680
d) 106 700
x in the following equation 18 000÷ (3 x 10²) + 96 ÷ 12 x 4 = x
a) 632
b) 8
c) 92
d) 38
9. Fill in the missing numbers in the following row; 51, 53, 59, _____; ______; 71
a) 61, 67
10.
b) 61, 69
c) 61, 63
d) 63, 67
____________ is 100 times more than 234.
a) 234 000
Question 2:
b) 2 340
c) 23 400
Make the following statement TRUE by inserting >, < or =:
1. 48 ÷ 4 x 12 - (2³ x 2)
(48 ÷ 16 x 12) - 8 x 2
2. 304 - (4 + 5 x 11) + 5³
(304 - 4 + 5) x 11 + 5³
3. 81 ÷ 3² x 12 ÷ 3
9² ÷ 3 x 12 ÷ 9
4. 20 x (3 000 ÷ 100 + 25 )
20 x 30 + 25
5. 5 + (10³ x 500) ÷ 5
1 005 ÷ 5 x 10² x 1 000
d) 20 340
(5)
Mathematics: Test
2
Grade 6
Operations, BODMAS, factors, multiples & Prime numbers
Question 3:
Use the number line to indicate the numbers as requested below:
50
(5)
72
1. Indicate with an M the 7th multiple of 7.
2. Indicate with a Q the quotient of 18 600 and 300.
3. Indicate with a P all the prime numbers.
4. Indicate with an L the LCM of 8 and 7.
5. Indicate with a C the common multiples of 2 and 7 on this number line.
Question 4:
a)
12
24
(16
10) + 35 = 83
b)
(75
6)
9
(5)
9=0
____________________________
___________________________________
____________________________
___________________________________
____________________________
___________________________________
____________________________
___________________________________
Question 5:
a)
Fill in the missing operators to make the following equations TRUE.
Find the value of
3 050 + (x+ 6³ x 21) -
x in the following equations:
144 = 11 379 b)
408 x (90² ÷ 300 x 2⁴) - 32 989 =
(4)
x
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
___________________________________
Question 6:
Using the following sets of factors, list two numbers each (less than 144), for
which these can be factors.
½ each (3)
Factors
9, 2, 54
18, 1, 9, 4
27, 3, 9
Numbers
Mathematics: Test
3
Grade 6
Factors, Multiples, Prime Numbers,
Factors, Multiples, Prime Numbers, BODMAS
Question 7:
Calculate the answers to the following problems;
1. Six hundred and eighty-five thousand, nine hundred and seventy-six is _____________ more
than the sum of one hundred and thirty-two thousand and eighteen, and fifty-nine thousand,
three hundred and twenty-three.
(3)
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
2. Add the sum of 245 093 and 107 345 to the product of 2 041 and 376.
(3)
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
3. What is the difference between the quotient of 10 269 and 21, and the quotient of 71 190 and
35?
(3)
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Question 8:
Arrange the following digits to make the equations below TRUE (each digit may
only be used once in each row of the equation):
(4)
5
4
8
7
3
+
3
8
7
5
4
2
>
3
4
8
2
7
5
2
>
+
1
1
3
4
1
8
4
Use some scrap paper for your calculations.
-
2
3
8
7
5
4
2
8
5
6
3
3
Mathematics: Test
4
Grade 6
Operations, BODMAS, factors, multiples & Prime numbers
Question 9:
Refer to the grid and answer the questions below:
1. Colour all the multiples of 8 in green.
(2)
A
B
C
D
E
F
G
H
1
31
32
33
34
35
36
37
38
_________________________________________
2
39
40
41
42
43
44
45
46
_________________________________________
3
47
48
49
50
51
52
53
54
4
55
56
57
58
59
60
61
62
5
63
64
65
66
67
68
69
70
6
71
72
73
74
75
76
77
78
7
79
80
81
82
83
84
85
86
(1)
8
87
88
89
90
91
92
93
94
6. What is the difference between a Prime number
and a Composite number?
(2)
9
95
96
97
98
99 100 101 102
2. In which column will the next multiple of 8 be?
Give a reason for your answer.
(2)
_________________________________________
3. Colour the prime numbers in red.
(6)
4. Four columns will never have Prime numbers.
Name the columns and explain your answer. (2)
_________________________________________
_________________________________________
_________________________________________
5. Colour the 17th multiple of 4 in yellow.
______________________________________________________________________________
______________________________________________________________________________
7. If another column is added to the right, list the Prime numbers that will then be in row
number 5.
(2)
______________________________________________________________________________
8. What is the HCF of the numbers found in positions B4 and F7?
(2)
______________________________________________________________________________
9. State the numbers found in positions F7 and B9 as a product of their Prime factors.
(4)
F7 = ________________________________ B9 = ____________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
Question 10:
1.
Answer the following questions:
½ each
(3½)
The number 1 is called a _____________________ and is not a ____________________
number or a ___________________________ number.
2.
The symbol used to indicate a square root is called a _____________________________.
3.
When a number is divided by ____________________ is called undefined.
4.
A factor is a number that ___________________________________________________.
5.
Multiples are ________________________________________________________ .
Mathematics: Test
5
Grade 6
Operations, BODMAS, factors, multiples & Prime numbers
Question 11:
Solve the following problems:
(4)
1. 785 x 700 = __________________
2.
20 280 ÷ 30 = ___________________
3.
4.
121 x 8 x 10⁴ = ___________________
46 x 9 000 = _________________
Question 12:
Problem solving. Write one number sentence for each problem and then solve
the problem.
1. A third of the 3,3 million residents of Johannesburg has to commute to work daily. Of these,
one half travel by taxi, 425 689 people travel by bus and the rest travel with their own
transport. Calculate how many people travel with their own transport to work everyday. (3)
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
2. Sarah’s dad agreed that he will pay her R2 a day, doubled everyday, if she helps with chores in
the house for one week. She says that is not enough money, she wants to be paid R10 a day
or she will not do the work. Using your knowledge of exponents, think of a clever number
sentence and proof to Sarah that she is making the wrong decision.
(3)
______________________________________________________________________________
______________________________________________________________________________
________________________________________________________________________
_______________________________________________________________
Mathematics: Test
6
Grade 6
Operations, BODMAS, factors, multiples & Prime numbers
3.1
One Direction tickets were sold at R750.00 per ticket. A third of the ticket sales went to Big
Concerts, the organisers of the event. In the first 15 minutes of ticket sales, 6 786 tickets were
sold. How much money did Big Concerts make in the first 15 minutes of ticket sales?
(3)
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
3.2
Some people decided to resell their tickets. If 1 689 people, who each bought 4 tickets,
decided to resell their tickets, at a price of R999.00 per ticket, what would the total profit, made
by all together, be?
(3)
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
Question 13:
Help me to figure out what number Charlie is thinking of. He has given me the
following clues:
½ each
(3½)
The number is a 7-digit odd number.
The number is divisible by 5.
The digit in the Hundred Thousands place is a multiple of the number in
the Units place.
The digit in the Hundreds place is the product of a number and zero.
The digit in the Millions place is the digit in the Tens place, to the power of 3.
The digit in the Tens place is a universal factor.
The digit in the Ten Thousands place is the highest single digit Prime number.
The digit in the Thousands place is the HCF of 21 and 49.
Total:
/90
Mathematics: Test
7
Grade 6
Memo:
Question 1:
Circle the correct answer from the options given:
1. b)
2. c)
3. d)
8. c)
9. a)
10. c)
Question 2:
4. c)
5. a)
(10)
6. c)
7. a)
Make the following statement TRUE by inserting >, < or =:
1. 48 ÷ 4 x 12 - (2³ x 2)
=
= 128
(5)
(48 ÷ 16 x 12) - 8 x 2
= 128
2. 304 - (4 + 5 x 11) + 5³
<
= 370
(304 - 4 + 5) x 11 + 5³
= 3 370
2. 81 ÷ 3² x 12 ÷ 3
=
= 36
9² ÷ 3 x 12 ÷ 9
= 36
4. 20 x (3 000 ÷ 100 + 25 )
>
= 700
20 x 30 + 25
= 625
4. 5 + (10³ x 500) ÷ 5
<
= 100 005
Question 3:
1 005 ÷ 5 x 10² x 10
= 201 000
Use the number line to indicate the numbers as requested below:
M
48
P
50
52
LC
54
56
P
58
P Q
60
62
P
64
C
66
68
P
70
(6)
P
72
1. Indicate with an M the 7th multiple of 7.
2. Indicate with a Q the quotient of 18 600 and 300.
3. Indicate with a P all the prime numbers.
4. Indicate with an L the LCM of 8 and 7.
5. Indicate with a C the common multiples of 2 and 7 on this number line.
Question 4:
a)
12
x
Fill in the missing operators to make the following equations TRUE.
24
÷ (16 -
10) + 35 = 83
b)
(75
+
6)
÷
9
-
(5)
9=0
This is trial and error to an extend—keep in mind the answer when deciding the operators.
Question 5:
a)
Find the value of
x in the following equations:
3 050 + (x+ 6³ x 21) - 144 = 11 379
3 050 + (x + 216 x 21) - 12 = 11 379
050 +
b)
(4)
408 x (90² ÷ 300 x 2⁴) - 32 989 =
x
408 x (8 100 ÷ 300 x 16) - 32 989 =
x + 4 536 - 12 = 11 379
408 x (27 x 16) - 32 989 =
x
574 + x = 11 379
408 x 432- 32 989 =
x
176 256 - 32 989 =
x
x = 3 805
x =143 267
x
Mathematics: Test
8
Grade 6
Memo:
Question 6:
Using the following sets of factors, list two number each (less than 144), for
which these can be factors.
(3)
Question 7:
Factors
Numbers
9, 2, 54
54, 108
18, 1, 9, 4
36, 72
27, 3, 9
27, 81, 108
Calculate the answers to the following problems;
1. Six hundred and eighty-five thousand, nine hundred and seventy-six is 494 635more than the
sum of one hundred and thirty-two thousand and eighteen, and fifty-nine thousand, three hundred and twenty-three.
132 018 + 59 323 = 191 341
685 976 - 191 341 = 494 635
2. Add the sum of 245 093 and 107 345 to the product of 2 041 and 376.
245 093 + 107 345 = 352 438
2041 x 376 = 767 416
352 438 + 767 416 = 1 119 854
3. What is the difference between the quotient of 10 269 and 21, and the quotient of 71 190 and
35?
10 269 ÷ 21 = 489
71 190 ÷ 35 = 2 034
2 034 - 489 = 1 545
Question 8:
Arrange the following digits to make the equations below TRUE (each digit may
only be used once in each row of the equation):
(4)
5
+
1
8
7
5
4
3
2
3
8
7
5
4
2
2
6
2
9
7
4
>
4
8
+
1
7
3
2
3
4
8
7
5
2
7
8
5
4
3
2
1
3
4
1
8
4
>
-
5
2
4
3
8
7
2
3
8
7
5
4
2
8
5
6
3
3
1.
Any number as long as the answer is greater than sum number 2.
3.
Reverse the calculation - 285 633 + 238 754
Mathematics: Test
9
Grade 6
Memo:
Question 9:
Refer to the grid and answer the questions below:
1. Colour all the multiples of 8 in green.
(2)
2. In which column will the next multiple of 8 be?
Give a reason for your answer.
(2)
Column B—the grid has 8 columns which means the
multiples of 8 will always be in the same column.
3. Colour the prime numbers in red.
(6)
4. Four columns will never have prime numbers.
Name the columns and explain your answer. (2)
Columns B, D, F and H. These columns only have
even numbers, which means they will always be divisible by themselves, 1 and 2 and are therefore
composite numbers.
5. Colour the 17th multiple of 4 in yellow.
(1)
A
B
C
D
E
F
G
H
1
31
32
33
34
35
36
37
38
2
39
40
41
42
43
44
45
46
3
47
48
49
50
51
52
53
54
4
55
56
57
58
59
60
61
62
5
63
64
65
66
67
68
69
70
6
71
72
73
74
75
76
77
78
7
79
80
81
82
83
84
85
86
8
87
88
89
90
91
92
93
94
9
95
96
97
98
99 100 101 102
6. What is the difference between a Prime number
and a Composite number?
(2)
A prime number is a number that is divisible only by 1 and by itself. The number 1 is not a prime
number. A composite number is divisible by more numbers than just 1 and itself and therefore has
more than just 2 factors.
7. If another column is added to the right, list the Prime numbers that will then be in row
number 5.
(3)
67, 71 and 73
8. What is the HCF of the numbers found in positions B4 and F7?
B4 = 56 and F7 = 84
HCF (Highest Common Factor) = 28
9. State the numbers found in positions F7 and B9 as a product of their Prime factors.
F7 = 84
(2)
(4)
B9 = 96
= 14 x 6
= 16 x 6
=7x2x2x3
=4x4x2x3
= 7 x 2² x 3
=2x2x2x2x2x3
= 2⁵ x 3
Question 10:
Answer the following questions:
(3½)
1.The number 1 is called a universal factor and is not a Prime number or a Composite number.
2.The symbol used to indicate a square root is called a radical
3.When a number is divided by zero is called undefined.
4.A factor is a number that divides exactly into a larger number, without a remainder.
5.Multiples are endless and are the product of a number multiplied by another. .
Mathematics: Test
10
Grade 6
Memo:
Question 11:
Solve the following problems:
1. 785 x 700 = 549 500
2.
(4)
20 280 ÷ 30 = 676
Use the knowledge of multiply and divide by 10, 100 and 1000 e.g.
785 x 7 x 100
20 280 ÷ 10 ÷ 3
= 5 495 x 100
= 2 038 ÷ 3
= 549 500
= 676
3.
46 x 9 000 = 414 000
4.
121 x 8 x 10⁴ = 11 x 8 x 10 000
= 880 000
Question 12:
Problem solving. Write one number sentence for each problem and then solve
the problem.
1. A third of the 3,3 million residents of Johannesburg has to commute to work daily. Of these,
one half travel by taxi, 425 689 people travel by bus and the rest travel with their own
transport. Calculate how many people travel with their own transport to work everyday. (3)
(3 300 000 ÷ 3) ÷ 2 - 425 689 = x
x = 124 311
124 311 people travel with their own transport to work everyday.
2. Sarah’s dad agreed that he will pay her R2 a day, doubled everyday, if she helps with chores in
the house for one week. She says that is not enough money, she wants to be paid R10 a day
or she will not do the work. Using your knowledge of exponents, think of a clever number
sentence and proof to Sarah that she is making the wrong decision.
(3)
Try to work out exponents.
Day 1 = R2
= 2¹
Day 2 = R2 x 2
= 2²
Day 3 = R4 x 2 (or R2 x R2 x 2) = 2³
Therefore we can see that a pattern
Day 7
= 2⁷ - Now try to make your number sentence.
R2⁷ - (R10 x 7) = x
R128 - R70 = R58
Sarah will earn R58 more in one week.
Mathematics: Test
11
Grade 6
Memo:
3.1
One Direction tickets were sold at R750.00 per ticket. A third of the ticket sales went to Big
Concerts, the organisers of the event. In the first 15 minutes of ticket sales, 6 786 tickets were
sold. How much money did Big Concerts make in the first 15 minutes of ticket sales?
(3)
R750 ÷ 3 x 6 786 = x
R250 x 6 786 = R1 696 500
Big Concerts made R1 696 500 in the first 15 minutes of ticket sales.
3.2
Some people decided to resell their tickets. If 1 689 people, who each bought 4 tickets,
decided to resell their tickets, at a price of R999.00 per ticket, what would the total profit, made
by all together, be?
(3)
(R999.00 - R750) x (1 689 x 4) = x
R249 x 6 756 = R1 682 244
All the people together would make a profit of R1 682 244.00
Question 13:
Help me to figure out what number Charlie is thinking of. He has given me the
following clues:
½ each
(3½)
The number is a 7-digit odd number.
The number is divisible by 5.
The digit in the Hundred Thousands place is a multiple of the number in the Units place.
The digit in the Hundreds place is the product of a number and zero.
The digit in the Millions place is the digit in the Tens place, to the power of 3.
The digit in the Tens place is a universal factor.
The digit in the Ten Thousands place is the highest single digit Prime number.
The digit in the Thousands place is the HCF of 21 and 49.
1 577 015
Total:
/90