Question 1 of 40

The following figure are made up of unit cubes stacked at a corner of a room and painted. The first three figures are shown below. \begin{array}{|c|c|c |} \hline \mbox{Figure No.} & \mbox{No. of cubes} & \mbox{No. of faces of the cubes that are painted} \\ \hline 1 & 1 & 3 \\ \hline 2 & 4 & 9 \\ \hline 3 & 10 & 18\\ \hline 4 & (i) & (ii) \\ \hline \end{array} (a) Find the number of Cubes and Number of painted faces of cubes for figure 4.
(b) In which figure number would 165 faces of the cubes be painted?

Michael Uses identical shaded and unshaded triangles to form figures that follow a pattern as shown below. \begin{array}{|c|c|c | c |} \hline \mbox{Figure No.} & \mbox{No. of shaded triangles} & \mbox{No. of unshaded triangles} & \mbox{Total No. of shaded and unshaded triangles} \\ \hline 1 & 4 & 3 & 7 \\ \hline 2 & 9 & 5 & 14 \\ \hline 3 & 16 & 7 & 23 \\ \hline \end{array} (a) A figure in the pattern has a total of 529 shaded triangles. What is the Figure Number?
(b) Another figure in the pattern has a total of 63 unshaded triangles. What is the total number of shaded and unshaded triangles in this figure?

The pattern below shown a series of hexagons which are made using beads and strings. Study the patterns and answer the questions that follow. (a) How many beads are there in Pattern 5?
(b) Which patterns will have 253 beads?
(c) Ahmad wants to make a pattern consisting of 43 hexagons. He has 151 beads. How many more beads does he need?

Hailey used 4 identical sticks to form a square as shown below. She then formed a pattern using more of the sticks.
(a) How many sticks are used to form 13 squares?
(b) How many squares are formed using 100 sticks?

Haoming made patterns using triangles. Circles and sticks and recorded the pattern in the table shown below. \begin{array}{|c|c|c |} \hline \mbox{Figure Number} & \mbox{Number of Cicles} & \mbox{Number of Sticks} \\ \hline 1 & 3 & 3 \\ \hline 2 & 4 & 5 \\ \hline 3 & 5 & 7\\ \hline 4 & 6 & 7 \\ \hline \cdots & \cdots & \cdots \\ \hline 20 & (a) & (b) \\ \hline \cdots & \cdots & \cdots \\ \hline (c) & \cdots & 115 \\ \hline \end{array}
(a) How many cicles are needed for Figure 20?
(b) How many sticks are needed for Figure 20?
(c) Which Figure needed a total of 115 sticks?

Numbers are written in order beginning from 1 as shown in the below image.
(a) Find the number represented by the letter N.
(b) Find the greatest number inn Row 8.
(c) Find the number in the middle of Row 12.

Study the pattern below and answer the questions, showing your working clearly whenever possible. \begin{array}{|c|c|c | c |} \hline \mbox{Figure No.} & \mbox{No. of rows of sqr grids} & \mbox{No. of colm of sqr grids} & \mbox{Area of shaded triangles} \\ \hline 1 & 2 & 3 & 2 \\ \hline 2 & 4 & 5 & 8 \\ \hline 3 & 6 & 7 & 18 \\ \hline 4 & 8 & 9 & ? \\ \hline \end{array} (a) What is the aarea of shaded triangle in Figure 4?
(b) What is the number of columns of square grids in Figure 20?
(c) In which would the area of shaded triangle be 2312 square units?

A table with 4 columns is filled with numbers in a certain pattern. The first 4 rows of the table are shown in below image. In which row and columns will the number 295 appear?

Oliver used identical cubes to build some structures. The first four structures are shown below. For each structure. He first stacked the cube together and then painted some of the faces of each structure. The shaded faces shown are the faces he painted. The table below shown the number of cubes and the number of faces painted in each structure. \begin{array}{|c|c|c |} \hline \mbox{Structure Number} & \mbox{Number of cubes} & \mbox{Number of faces painted} \\ \hline 1 & 1 & 1 \\ \hline 2 & 10 & 4 \\ \hline 3 & 35 & 9\\ \hline 4 & 84 & 16 \\ \hline 5 & (i) & (ii) \\ \hline \end{array}
(a) Find the number of cubes and Number of faces painted for figure 5
(b) How many cubes do not have any of its faces painted in structure 10?

Isaac drew some dots and triangles $( of different sizes )$ in a certain pattern. The first four figures are shown below.
(a) Study the below figure and complete the table for figure 5. \begin{array}{|c|c|c |} \hline \mbox{Figure No.} & \mbox{No. of dots} & \mbox{No. of non-overlapping triangles} \\ \hline 1 & 6 & 5 \\ \hline 2 & 11 & 10 \\ \hline 3 & 16 & 20\\ \hline 4 & 21 & 25 \\ \hline 5 & (i) & (ii) \\ \hline \end{array}
(b) In which figure number will there be 230 non-overlapping triangles?

Study the below pattern and find the number of cans in figure 9.

How many circles are there in Pattern 25?

A table can seat 6 people as shown in figure A. Following the pattern shown below, how many such tables are needed to seat 42 people?

Study the number pattern below.
$3 \times 37 = 111$
$6 \times 37 = 222$
$9 \times 37 = 333$
$\vdots \s \s \s \vdots$
$\vdots \t \vdots$
$G \times 37 = 88$
Find the value that G represents.

Study the pattern below. The pattern is made up of Identical triangle tiles.
If the Pattern Continues. Which figure will have total of 162 triangular tiles?

The figure which are made up of shaded and unshaded squares follow a pattern as shown below.
(a) Find the number of shaded and unshaded squares in Figure 5. \begin{array}{|c|c|c |} \hline \mbox{Figure Number} & \mbox{Number of shaded squares} & \mbox{Number of unshaded squares} \\ \hline 1 & 2 & 2\\ \hline 2 & 3 & 6\\ \hline 3 & 4 & 12\\ \hline 4 & 5 & 20\\ \hline 5 & (i) & (ii) \\ \hline \end{array}
(b) In which figure is there a total of 256 squares?
(c) A figure in the pattern has a total of 529 shaded and unshaded squares. What is the number of shaded squares in the figure?

Fabian Used identical square tiles to form a sequence of patterns. The first four patterns are shown in figure below. The vertical height of Pattern 1 is 3cm.
What is the vertical height of Pattern 50?

Study the number pattern below

12, 15, 18, $\cdots\cdots\cdots$, 93, 96, 99.

The pattern is made up of all the 2-digit multiples of 3 written in increasing order.
(a) Find the the sum of all the numbers in the pattern.
(b) How many numbers in the pattern do not contain the digit 3?

The following pattern is formed using letters A, B, C, D.
What is the 160$^t$$^h$ letter?

Ali uses rods to foam that follow a pattern. The first five figures are shown in below image.
(a) The table shown the number of rods used and the number of triangles found in each figure. Complete table for figure 6. \begin{array}{|c|c|c |} \hline \mbox{Figure No.} & \mbox{No. of rods used} & \mbox{No. of triangles} \\ \hline 1 & 6 & 4 \\ \hline 2 & 9 & 4 \\ \hline 3 & 16 & 12\\ \hline 4 & 17 & 8 \\ \hline 5 & 26 & 20 \\ \hline 6 & 25 & \\ \hline \end{array}
(b) How many rods would he use in figure 7?
(c) How many rods would he use in figure 30?

A repeated pattern is formed using the 4 letters A, B, C and D. The first 26 letters are shown in below figure.
How many ‘D’ are there in the first 125 letters?

Two types of square-shaped tiles, tile 1 and tile 2 are available to make a larger pattern on the floor. The pattern of each square-shaped tile is shown below.

Tile 1 is made up of 3 white squares and 1 black squares.
Tile 2 is made up of 2 white squares and 2 black squares.

Figure 1 shows a floor laid Tile 1 and Tiles 2 in a repeated patterns.
(a) 90 pieces of Tile 1 were used to cover part of the floor in the room in the pattern shown in figure 1. Find the total number of tiles needed to tile the floor in figure 1.
(b) What percentage of the floor in figure 1 was covered with black squares?

Study the following pattern.
(a) In which column will the number 80 appear?
(b) What number will appear in Row 99 Column D?

The Structure below are formed using identical solids stacked on top of each other. The height of Figure 1 is 26cm when the solids are stacked two levels high. It is 35cm when the solids are stacked three levels high.
(a) How many levels must the solids be stacked in order for the structure to reach a height of 89cm?
(b) How many solids are needed to form the structure of height 89cm?

The pattern below are made up of identical shaded and unshaded squares.
(a) Find the total number of squares in Pattern 4.
(b) Find the total number of shaded squares in Pattern 10.
(c) Find the total number of unshaded squares in Pattern 43.

The following figure are made up of small squares and dots. Look at the figure below and answer the following questions. \begin{array}{|c|c|c |} \hline \mbox{Figure No.} & \mbox{No. of small squares} & \mbox{No. of dots} \\ \hline 1 & 1 & 4 \\ \hline 2 & 4 & 9 \\ \hline 3 & 9 & 16 \\ \hline \end{array}
Calculate the number of small squares for figure 4.
(b) Calculate the number of dots for figure 10.

Helen uses some toothpicks to form the pattern below.
\begin{array}{|c|c|} \hline \mbox{Pattern} & \mbox{Number of toothpick} \\ \hline 1 & 6\\ \hline 2 & 15\\ \hline 3 & 25\\ \hline 4 & 35\\ \hline 5 & \\ \hline \end{array}
(a) How many toothpicks will she need to form Pattern 5?
(b) How many toothpick will she need to form Pattern 40?
(c) Helen uses 4955 toothpicks to form a Pattern. Which Pattern is it?

Farah uses black and white buttons to form figure that follow a pattern. The first four figure are shown below.
(a) A figure in the pattern has a total of 176 black and white buttons What is the Figure Number? \begin{array}{|c|c|c | c | c |} \hline \mbox{Figure Number} & 1 & 2 & 3 & 4\\ \hline \mbox{Number of black buttons} & 0 & 1 & 3 & 6 \\ \hline \mbox{Number of white buttons} & 1 & 4 & 9 & 16 \\ \hline \mbox{Total number of buttons}& 1 & 5 & 12 & 22 \\ \hline \end{array}
(b) A figure in the pattern has 784 white buttons. How many black buttons are there in that figure?

John used black and white tiles to create the pattern shown in below figure. Use the patterns that he has created to answer the following questions.
(a) How many tiles will there be in Pattern 15?
(b) Which pattern will be made up of 176 tiles?

Azlinda formed the pattern below using white grey tiles. Study the pattern carefully.
How many white tiles would Azlinda use to build Pattern 7?

The figure is made up of identical triangles.
(a) Complete the table for layers 5 and 10.
\begin{array}{|c|c|} \hline \\ \mbox{Layer} & \mbox{Number of Triangles} \\ \hline 1 & 1\\ \hline 2 & 3 \\ \hline 3 & 5 \\ \hline 4 & 7 \\ \hline 5 & (i) \\ \hline \vdots & \vdots \\ \hline \\ 10 & (ii) \\ \hline \end{array}
(b) Each small triangle has a base of 4 cm and a perpendicular height of 3 cm. Find the area of all the triangles at the 30$^t$$^h$ layer.

Study the pattern below. The first four figures are shown below.
The table below shows the number of sticks and dots used to form each figure. \begin{array}{|c|c|c |} \hline \mbox{Figure} & \mbox{No. of sticks} & \mbox{No. of dots} \\ \hline 1 & 6 & 5 \\ \hline 2 & 11 & 10 \\ \hline 3 & 16 & 20\\ \hline 4 & 21 & 25 \\ \hline 5 & (i) & (ii) \\ \hline \end{array}
(a) How many dots are used to form figure 12?
(b) Which figure has 612 sticks?

The square of pattern is formed with squares. The first patterns are shown below. How many squares are needed in Pattern 10?

The pattern below is made up of circles and triangles. Study the pattern carefully and answer the questions below.
(a) How many circles are needed to form pattern 5?
(b) How many triangles are needed to form pattern 10?
(c) The number of circles used in pattern X is exactly the same triangles used to form pattern 32. What is X?

Look at the pattern in figure below.
(a) Complete the table below by finding the totals number of tiles for pattern 4. \begin{array}{|c|c|c | c |} \hline \mbox{Pattern No.} & \mbox{No. of unshaded}
\mbox{tiles} & \mbox{No. of shaded tiles} & \mbox{Total No. of tiles} \\ \hline 1 & 0 & 1 & 1 \\ \hline 2 & 1 & 2 & 3 \\ \hline 3 & 3 & 3 & 6 \\ \hline 4 & 6 & 4 & ? \\ \hline \end{array}
(b) How many unshaed tiles will there be in pattern number 15?

Hatta formed some figures that followed a pattern using squares and circles as shown in figure below.
The table Shows the number of squares and circles for the first four figures. \begin{array}{|c|c|c | c | c |} \hline \mbox{Figure Number} & 1 & 2 & 3 & 4 \\ \hline \mbox{Number of squares} & 1 & 4 & 9 & 16 \\ \hline \mbox{Nunmber of circles} & 2 & 3 & 4 & 5 \\ \hline \mbox{No. of squares divided by No. circles} & 0R1 & 1R1 & 2R1 & 3R1 \\ \hline \end{array} Note: “R” denotes remainder in the above columns.
(a) A Figure has 3481 squares. Find the answer when its number of squares is divided by its number of circles.
(b) In a certain Figure number, 99 R1 is obtained when its number of squares is divided by its number of circles. Find the total number of squares and circles in that Figure number.

3. Zach used some white and gray tiles to form some patterns. The first four patterns are shown below. The table below shows the number of white and gray tiles used to form the patterns. \begin{array}{|c|c|c | C |} \hline \mbox{Pattern Number} & \mbox {No. of Grey tiles} & \mbox{No. of white tiles} & \mbox{Total No. of tiles} \\ \hline 1 & 2 & 2 & 4 \\ \hline 2 & 5 & 4 & 9 \\ \hline 3 & 8 & 8 & 16 \\ \hline 4 & 13 & 12 & 25 \\ \hline 5 & & & \\ \hline \end{array}
(a) How many tiles were used form pattern 80?
(b) How many grey tiles were used form pattern 120?

Roy uses the four letters, C, A, R, E to form a pattern. The first 16 letters are shown below. Which letter is in the 59$^t$$^h$ position?

Jeremy arrange 5 letters to form a pattern. The first 4 rows are as shown below. \begin{array}{|c|c|c |} \hline \mbox{Row1} & AB & CDE\\ \hline \mbox{Row 2} & BA & ECD \\ \hline \mbox{Row3} & AB & DEC \\ \hline \mbox{Row4}& BA & CDE\\ \hline \vdots & \vdots & \vdots \\ \hline \end{array} Write the arrangement of the 5 letters in Row 83

Kenny and Dylan each used some letters to make a set of patterns on rectangular cards as shown below. They make repeated patterns with the cards created.
Which letter will first appear in the same position in both patterns?