Question 12 Marks
Why are 1, 3, 6, 10, 15, 21, 28, 36, .... called triangular numbers?
Answer
View full question & answer→Number of dots equal to any triangular number can be arranged perfectly in triangular form.
Questions
2 Marks Questions
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14 questions · timed · auto-graded
Question 22 Marks
Study the following pattern:
$
\begin{array}{ll}
1+1+2 \times 2 & =\frac{2 \times 3 \times 5}{6} \\
1 \times 1+2 \times 2+3 \times 3 & =\frac{3 \times 4 \times 7}{6} \\
1 \times 1+2 \times 2+3 \times 3+4 \times 4 & =\frac{4 \times 5 \times 9}{6}
\end{array}
$
By observing the above pattern, write next two steps.
$
\begin{array}{ll}
1+1+2 \times 2 & =\frac{2 \times 3 \times 5}{6} \\
1 \times 1+2 \times 2+3 \times 3 & =\frac{3 \times 4 \times 7}{6} \\
1 \times 1+2 \times 2+3 \times 3+4 \times 4 & =\frac{4 \times 5 \times 9}{6}
\end{array}
$
By observing the above pattern, write next two steps.
Answer
$\begin{array}{l}1 \times 1+2 \times 2+3 \times 3+4 \times 4+5 \times 5=\frac{5 \times 6 \times 11}{6} \\ 1 \times 1+2 \times 2+3 \times 3+4 \times 4+5 \times 5+6 \times 6=\frac{6 \times 7 \times 13}{6}\end{array}$
View full question & answer→$\begin{array}{l}1 \times 1+2 \times 2+3 \times 3+4 \times 4+5 \times 5=\frac{5 \times 6 \times 11}{6} \\ 1 \times 1+2 \times 2+3 \times 3+4 \times 4+5 \times 5+6 \times 6=\frac{6 \times 7 \times 13}{6}\end{array}$
Question 32 Marks
Observe the pattern in the following and fill in the blanks:
$\begin{array}{ll}9 \times 9+7 & =88 \\ 98 \times 9+6 & =888 \\ 987 \times 9+5 & =8888 \\ 9876 \times 9+4 & =\ ......... \\ 98765 \times 9+3 & =\ ......... \\ 987654 \times 9+2 & =\ ......... \\ 9876543 \times 9+1 & =\ .........\end{array}$
$\begin{array}{ll}9 \times 9+7 & =88 \\ 98 \times 9+6 & =888 \\ 987 \times 9+5 & =8888 \\ 9876 \times 9+4 & =\ ......... \\ 98765 \times 9+3 & =\ ......... \\ 987654 \times 9+2 & =\ ......... \\ 9876543 \times 9+1 & =\ .........\end{array}$
Answer
View full question & answer→88888, 888888, 8888888, 88888888
Question 42 Marks
What is 6th hexagonal number?
Answer
View full question & answer→91
Question 52 Marks
Write a number other than 1 which is both a triangular number and a square number.
Answer
View full question & answer→36
Question 62 Marks
Why are 1, 8, 27, 64, 125, 216, .... called cube numbers?
Answer
View full question & answer→A cube of side length $n$ units can be cut into $n \times n \times n=n^3$ unit cubes.
Question 72 Marks
Why are 1, 4, 9, 16, 25, 36, ... called square numbers?
Answer
View full question & answer→Number of dots representing any square number can be arranged perfectly in square form.
Question 82 Marks
Without drawing a diagram, find
6th triangular number.
6th triangular number.
Answer
View full question & answer→21
Question 92 Marks
Without drawing a diagram, find
10th square number.
10th square number.
Answer
View full question & answer→100
Question 102 Marks
Complete the following pattern:
Answer
View full question & answer→$21999978 \times 4=87999912 ; 219999978 \times 4=879999912$
Question 112 Marks
Complete the following pattern:
Answer
View full question & answer→$11111 \times 11111=123454321 ; 111111 \times 111111=12345654321$
Question 122 Marks
Complete the following pattern:
$\begin{aligned} 11 \times 11 & =121 \\ 11 \times 121 & =1331 \\ 11 \times 131 & =1441 \\ 11 \times\ ..... & =1551 \\ 11 \times 151 & =\ .......\end{aligned}$
$\begin{aligned} 11 \times 11 & =121 \\ 11 \times 121 & =1331 \\ 11 \times 131 & =1441 \\ 11 \times\ ..... & =1551 \\ 11 \times 151 & =\ .......\end{aligned}$
Answer
View full question & answer→$141 ; 1661$
Question 132 Marks
Identify the pattern in the following number pattern and write the missing numbers:
$1 =1=1 \times 1 $
$1+3 =4=2 \times 2 $
$1+3+5 =\ldots=\ldots \times 3 $
$1+3+5+\ldots =\ldots=4 \times 4$
$1 =1=1 \times 1 $
$1+3 =4=2 \times 2 $
$1+3+5 =\ldots=\ldots \times 3 $
$1+3+5+\ldots =\ldots=4 \times 4$
Answer
View full question & answer→9, 3 x 3; 7, 16
Question 142 Marks
Observe the pattern shown below and write the next two steps:
$
\begin{aligned}
0 \times 9+1 & =1 \\
1 \times 9+2 & =11 \\
12 \times 9+3 & =111 \\
123 \times 9+4 & =1111
\end{aligned}
$
$
\begin{aligned}
0 \times 9+1 & =1 \\
1 \times 9+2 & =11 \\
12 \times 9+3 & =111 \\
123 \times 9+4 & =1111
\end{aligned}
$
Answer
View full question & answer→1234 x 9 + 5 = 11111, 12345 x 9 + 6 = 11111