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1.

Example context: Shabnam is 3 years older than Aftab. When Aftab’s age is 18 years, what will Shabnam’s age be?

a)

20 years

b)

21 years

c)

22 years

d)

24 years

2.

Given Aftab’s age, how will you find out Shabnam’s age?

a)

Add 3 to Aftab’s age

b)

Subtract 3 from Aftab’s age

c)

Multiply Aftab’s age by 3

d)

Divide Aftab’s age by 3

3.

Can we write the relation as an expression? Shabnam’s age is 3 years more than Aftab’s. Choose the correct expression for this relation.

a)

$s = a + 3$

b)

$s = a - 3$

c)

$s = 3a$

d)

$s = \dfrac{a}{3}$

4.

If $a$ is 23 (Aftab’s age in years), then what is Shabnam’s age?

a)

23 years

b)

25 years

c)

26 years

d)

30 years

5.

Let a denote Aftab’s age and s denote Shabnam’s age. Aftab is 3 years younger than Shabnam. Which expression gives Aftab’s age?

a)

$a = s - 3$

b)

$a = s + 3$

c)

$a = 3s$

d)

$a = \dfrac{s}{3}$

6.

Use the expression for Aftab’s age when he is 3 years younger than Shabnam to find Aftab’s age if Shabnam’s age is 20.

a)

17

b)

20

c)

23

d)

3

7.

How many matchsticks are needed to make 5 Ls? The figure shows L-shapes made from two matchsticks each, placed next to each other.

a)

5

b)

10

c)

15

d)

25

8.

How many matchsticks are needed to make 7 Ls? The figure shows L-shapes made from two matchsticks each, placed next to each other.

a)

7

b)

14

c)

21

d)

28

9.

How many matchsticks are needed to make 45 Ls? The figure shows L-shapes made from two matchsticks each, placed next to each other.

a)

45

b)

60

c)

90

d)

100

10.

What is the relation between the number of Ls and the number of matchsticks when each L uses two matchsticks?

a)

Number of matchsticks = 2 × number of Ls

b)

Number of matchsticks = number of Ls ÷ 2

c)

Number of matchsticks = number of Ls + 2

d)

Number of matchsticks = 3 × number of Ls

11.

Coconuts cost ₹35 each and jaggery costs ₹60 per kg. How much should she pay if she buys 10 coconuts and 5 kg jaggery?

a)

₹650

b)

₹600

c)

₹700

d)

₹350

12.

Coconuts cost ₹35 each and jaggery costs ₹60 per kg. How much should she pay if she buys 8 coconuts and 9 kg jaggery?

a)

₹820

b)

₹780

c)

₹800

d)

₹860

13.

Let c represent the number of coconuts and j represent the number of kilograms of jaggery. Coconuts cost ₹35 each and jaggery costs ₹60 per kg. Which expression gives the total amount to be paid?

a)

$c \times 35 + j \times 60$

b)

$(35 + 60) \times (c + j)$

c)

$35c + j + 60$

d)

$c + 35 + j + 60$

14.

Use the expression $c \times 35 + j \times 60$ to find the total amount to be paid for 7 coconuts and 4 kg jaggery.

a)

₹485

b)

₹465

c)

₹505

d)

₹540

15.

The perimeter of a square is 4 times the length of its side. What is the perimeter of a square with sidelength 7 cm?

a)

28 cm

b)

14 cm

c)

21 cm

d)

24 cm

16.

Write formulas for the perimeter of each regular shape. Triangle with all sides equal.

a)

$2s$

b)

$3s$

c)

$4s$

d)

$s^2$

17.

Write formulas for the perimeter of each regular shape. A regular pentagon (all side lengths and angle measures are equal).

a)

$4s$

b)

$5s$

c)

$6s$

d)

$s+5$

18.

Write formulas for the perimeter of each regular shape. A regular hexagon.

a)

$5s$

b)

$6s$

c)

$7s$

d)

$s+6$

19.

Munirathna has a 20 m long pipe and joins another pipe of some length to it for his garden. Use the letter-number ‘k’ to denote the length in meters of the other pipe. Which expression gives the combined length of the pipe?

a)

$20+k$

b)

$20-k$

c)

$k-20$

d)

$20k$

20.

Krithika’s notes: What is the total amount if she has 3 notes of 100 rupees, 5 notes of 20 rupees, and 6 notes of 5 rupees? Complete based on the table.

a)

430 rupees

b)

695 rupees

c)

620 rupees

d)

515 rupees

21.

In the table, one row shows the expression $6 \times 100 + 4 \times 20 + 3 \times 5$ . What is the total amount for that row?

a)

615 rupees

b)

695 rupees

c)

645 rupees

d)

705 rupees

22.

Using the table, choose the correct algebraic expression for the total amount if Krithika has 8 notes of 100 rupees, 4 notes of 20 rupees, and z notes of 5 rupees.

a)

$8 \times 100 + 4 \times 20 + z \times 5$

b)

$8 + 4 + z$

c)

$100 \times z + 20 \times 4 + 5 \times 8$

d)

$(8+4+z) \times 5$

23.

Using the table, choose the correct algebraic expression for the total amount if Krithika has x notes of 100 rupees, y notes of 20 rupees, and z notes of 5 rupees.

a)

$100x + 20y + 5z$

b)

$x + y + z$

c)

$(x+y+z) \times 5$

d)

$20x + 100y + 5z$

24.

Venkatalakshmi owns a flour mill. It takes 10 seconds for the roller mill to start running. Once it is running, each kg of grain takes 8 seconds to grind into powder. Which expression describes the time taken to grind y kg of grain, assuming the machine is off initially?

a)

$10 + 8 + y$

b)

$(10 + 8) \times y$

c)

$10 \times 8 \times y$

d)

$10 + 8 \times y$

e)

$10 \times y + 8$

25.

Write an algebraic expression using letters of your choice: 5 more than a number.

a)

$n+5$

b)

$5-n$

c)

$n-5$

d)

$5n$

26.

Write an algebraic expression using letters of your choice: 4 less than a number.

a)

$n+4$

b)

$4-n$

c)

$n-4$

d)

$4n$

27.

Write an algebraic expression for 2 less than 13 times a number n.

a)

$13n - 2$

b)

$2n - 13$

c)

$13(n - 2)$

d)

$(13 - 2)n$

28.

Write an algebraic expression for 13 less than 2 times a number n.

a)

$2n - 13$

b)

$13n - 2$

c)

$2(n - 13)$

d)

$(2 - 13)n$

29.

Which situation is correctly represented by $8 \times x + 3 \times y$ ?

a)

Total cost of 8 items priced x each plus 3 items priced y each

b)

Total cost of 8 items priced y each minus 3 items priced x each

c)

Difference between 8 times x and 3 times y

d)

Product of 8 and x and y added together

30.

Which situation is correctly represented by $15 \times j - 2 \times k$ ?

a)

You gain 15 units of j and then subtract 2 units of k

b)

You subtract 15 units of j from 2 units of k

c)

You add 15 units of j and 2 units of k

d)

You gain 2 units of k and subtract 15 units of j

31.

In a calendar month, consider a 2 × 3 grid of consecutive dates. The bottom middle cell shows date w, and the bottom left shows w − 1, as in the picture. What expression gives the date in the top left cell?

a)

$w - 8$

b)

$w - 7$

c)

$w + 6$

d)

$w + 8$

32.

In the same 2 × 3 grid of dates where the bottom middle cell is w and the bottom left is w − 1, what expression gives the date in the top middle cell?

a)

$w - 7$

b)

$w - 6$

c)

$w + 7$

d)

$w + 1$

33.

In the same 2 × 3 grid of dates where the bottom middle cell is w and the bottom left is w − 1, what expression gives the date in the top right cell?

a)

$w - 6$

b)

$w - 7$

c)

$w + 6$

d)

$w + 2$

34.

In the same 2 × 3 grid of dates where the bottom middle cell is w and the bottom left is w − 1, what expression gives the date in the bottom right cell?

a)

$w + 1$

b)

$w - 1$

c)

$w + 7$

d)

$w - 7$

35.

Find the value of $23 - 10 \times 2$ .

a)

$3$

b)

$13$

c)

$-3$

d)

$43$

36.

Find the value of $83 + 28 - 13 + 32$ .

a)

$130$

b)

$150$

c)

$98$

d)

$136$

37.

Find the value of $34 \div 14 + 20$ . Give the exact value.

a)

$\tfrac{157}{7}$

b)

$\tfrac{147}{7}$

c)

$\tfrac{167}{7}$

d)

$\tfrac{140}{7}$

38.

Find the value of $42 + 15 - (8 - 7)$ .

a)

$56$

b)

$50$

c)

$64$

d)

$58$

39.

Find the value of $68 - (18 + 13)$ .

a)

$37$

b)

$41$

c)

$49$

d)

$31$

40.

Find the value of $7 \times 4 + 9 \times 6$ .

a)

$82$

b)

$78$

c)

$84$

d)

$90$

41.

Find the value of $20 \div 8 \times (16 - 6)$ .

a)

$25$

b)

$20$

c)

$30$

d)

$15$

42.

Evaluate $83 + 28 - 13 + 32$ .

a)

120

b)

126

c)

130

d)

136

43.

Evaluate $68 + -(18 + 13)$ .

a)

31

b)

37

c)

50

d)

−37

44.

Look at this number sequence: 4, 8, 12, 16, 20, 24, 28, ... How can we describe this sequence or pattern?

a)

Multiples of 3 in increasing order

b)

Multiples of 4 in increasing order

c)

Powers of 4

d)

Prime numbers in increasing order

45.

Look at this number sequence: 4, 8, 12, 16, 20, 24, 28, ... What is the third term of this sequence?

a)

8

b)

12

c)

16

d)

24

46.

Look at this number sequence: 4, 8, 12, 16, 20, 24, 28, ... What is the 29th term of this sequence?

a)

112

b)

116

c)

120

d)

124

47.

Look at this number sequence: 4, 8, 12, 16, 20, 24, 28, ... Find an algebraic expression to get the nth term of this sequence.

a)

$4n$

b)

$n + 4$

c)

$4n + 4$

d)

$4(n - 1)$

48.

Find the value of the expression $7k$ when $k = 4$ .

a)

$11$

b)

$24$

c)

$28$

d)

$47$

49.

Find the value that the expression $5m + 3$ takes when $m = 2$ .

a)

$7$

b)

$10$

c)

$13$

d)

$15$

50.

Mind the Mistake, Mend the Mistake: Given $a = -4$ , find the correct value of $10 - a$ .

a)

$6$

b)

$-6$

c)

$14$

d)

$-14$

51.

Mind the Mistake, Mend the Mistake: Given $d = 6$ , find the correct value of $3d$ .

a)

$12$

b)

$18$

c)

$24$

d)

$36$

52.

Mind the Mistake, Mend the Mistake: Given $s = 7$ , find the correct value of $3s - 2$ .

a)

$13$

b)

$17$

c)

$19$

d)

$21$

53.

Mind the Mistake, Mend the Mistake: Given $r = 8$ , find the correct value of $2r + 1$ .

a)

$15$

b)

$17$

c)

$19$

d)

$29$

54.

Mind the Mistake, Mend the Mistake: Given $j = 5$ , find the correct value of $2j$ .

a)

$8$

b)

$9$

c)

$10$

d)

$12$

55.

Mind the Mistake, Mend the Mistake: Given $m = -6$ , find the correct value of $3(m + 1)$ .

a)

$-21$

b)

$-18$

c)

$-15$

d)

$19$

56.

Mind the Mistake, Mend the Mistake: Given $f = 3$ and $g = 1$ , find the correct value of $2f - 2g$ .

a)

$2$

b)

$3$

c)

$4$

d)

$5$

57.

Mind the Mistake, Mend the Mistake: Given $t = 4$ and $b = 3$ , find the correct value of $2t + b$ .

a)

$9$

b)

$10$

c)

$11$

d)

$24$

58.

Mind the Mistake, Mend the Mistake: Given $h = 5$ and $n = 6$ , find the correct value of $h - (3 - n)$ .

a)

$4$

b)

$6$

c)

$7$

d)

$8$

59.

Simplification of Algebraic Expressions: Find an expression for the perimeter of a rectangle in terms of its length $l$ and breadth $b$ .

a)

$l + b$

b)

$2(l + b)$

c)

$2lb$

d)

$l^2 + b^2$

60.

Refer to the table showing items sold in a shop: Pencils (Price " $c$ ") – Day 1: 5, Day 2: 3, Day 3: 10; Erasers (Price " $d$ ") – Day 1: 4, Day 2: 6, Day 3: 1. What is the money earned by selling pencils on Day 2?

a)

$3c$

b)

$5c$

c)

$3d$

d)

$c+3$

61.

Using the same table (Pencils priced at " $c$ " with counts Day 1: 5, Day 2: 3, Day 3: 10), what is the money earned by selling pencils on Day 3?

a)

$10c$

b)

$1c$

c)

$10d$

d)

$c+10$

62.

The total money earned by the sale of pencils is expressed as 5c + 3c + 10c. Can this expression be simplified to reduce the number of terms? Choose the simplified form.

a)

$18c$

b)

$15c$

c)

$5c$

d)

$18d$

63.

Refer to the table with prices " $c$ " per pencil and " $d$ " per eraser and counts: Pencils (Day 1: 5, Day 2: 3, Day 3: 10), Erasers (Day 1: 4, Day 2: 6, Day 3: 1). What is the total money earned by the shopkeeper during these three days?

a)

$18c + 11d$

b)

$18c + 7d$

c)

$8c + 11d$

d)

$5c + 3c + 10c$

64.

If c is ₹50, the total amount earned by the sale of pencils is given by the expression $18c$ . What is the amount?

a)

₹900

b)

₹850

c)

₹1,000

d)

₹750

65.

During these three days, the total money earned by selling erasers is represented and simplified by which expression?

a)

$11d$

b)

$18d$

c)

$11c$

d)

$18c$

66.

The combined earnings from selling pencils and erasers during these three days are given by $18c + 11d$ . Can this expression be simplified further?

a)

No, it is already in its simplest form.

b)

Yes, to $29c$ .

c)

Yes, to $29cd$ .

d)

Yes, to $18c$ .

e)

Yes, to $11d$ .

67.

Which pair of expressions always take the same value for any number substituted for $c$ ?

a)

$5c + 3c + 10c$ and $18c$

b)

$5c + 3c + 10c$ and $19c$

c)

$5c + 10c$ and $18c$

d)

$5c + 3c$ and $18c$

68.

A big rectangle is split into two smaller rectangles as shown: the height is $v$ , and the widths are 4 and 3 units placed side by side. Which expression describes the area of the bigger rectangle?

a)

$7v$

b)

$4v + 3$

c)

$v + 7$

d)

$4 + 3v$

69.

A shop rents out chairs and tables for a day. The amount to pay per piece at the beginning is ₹40 for a chair and ₹75 for a table. When the furniture is returned, the shopkeeper pays back ₹6 per chair and ₹10 per table. Write the expression for the total rupees finally paid if x chairs and y tables are rented.

a)

$40x + 75y - (6x + 10y)$

b)

$40x + 75y + (6x + 10y)$

c)

$34x + 65y$

d)

$46x + 85y$

70.

A shop rents out chairs and tables for a day. The customer pays ₹40 per chair and ₹75 per table at the beginning, and on returning, gets back ₹6 per chair and ₹10 per table. Which procedure correctly finds the total rupees finally paid for x chairs and y tables?

a)

Find the amount paid at the beginning and the amount returned, then subtract the returned amount from the amount paid at the beginning.

b)

Add the amount paid at the beginning to the returned amount.

c)

Subtract the amount paid at the beginning from the returned amount.

d)

Add both amounts and divide by two.

71.

Given the expression for the total amount finally paid is 40x + 75y − (6x + 10y) for renting x chairs and y tables (₹40 per chair, ₹75 per table, with ₹6 and ₹10 returned per chair and table respectively), can this expression be simplified, and if yes, how?

a)

Yes, it simplifies to $34x + 65y$ by combining like terms.

b)

No, it cannot be simplified because the terms are unlike.

c)

Yes, it simplifies to $46x + 85y$ by adding coefficients.

d)

Yes, it simplifies to $34x + 75y$ by subtracting only the chair return.

72.

Could we have written the initial expression as $(40x + 75y) + (-6x - 10y)$ instead of $(40x + 75y) - (6x + 10y)$ ?

a)

Yes

b)

No

73.

In the quiz context where $p$ is the score for a correct answer and $q$ is the penalty for a wrong answer, what does an expression like $7p - 3q$ , $8p - 4q$ , or $6p - 2q$ represent?

a)

The total score for a round computed as (number of correct answers) times $p$ minus (number of wrong answers) times $q$

b)

The number of questions Charu attempted in all rounds

c)

The average score per question across the quiz

d)

The score difference between Charu and her friend

74.

If $p = 4$ and $q = 1$ , what is Charu’s score in the first round given by $7p - 3q$ ?

a)

25

b)

24

c)

28

d)

21

75.

With $p = 4$ and $q = 1$ , what are Charu’s scores in the second and third rounds given by $8p - 4q$ and $6p - 2q$ ?

a)

28 and 22

b)

32 and 24

c)

25 and 21

d)

30 and 20

76.

If there is no penalty in the quiz, what is the value of $q$ ?

a)

$0$

b)

$1$

c)

$p$

d)

$-1$

77.

What is Charu’s final score after the three rounds when the round scores are $7p - 3q$ , $8p - 4q$ , and $6p - 2q$ ?

a)

$21p - 9q$

b)

$21p + 9q$

c)

$21p - 7q$

d)

$23p - 7q$

78.

Choose a set of three round scores for Krishita that add up to the total 23p − 7q. Select the option in which the three given expressions sum to 23p − 7q.

a)

8p − 2q, 7p − 3q, 8p − 2q

b)

9p − q, 7p − 2q, 7p − 3q

c)

12p − 4q, 6p − q, 4p − 2q

d)

15p − 5q, 3p − q, 4p − q

79.

How much more has Krishita scored than Charu? Simplify the expression 23p − 7q − (21p − 9q).

a)

$2p$ + $2q$

b)

$2p$ − $16q$

c)

− $2p$ + $16q$

d)

$44p$ − $16q$

80.

Example 9: Simplify the expression 4 (x + y) − y using the distributive property.

a)

$4x$ + $3y$

b)

$4x$ − $y$

c)

$4x$ + $5y$

d)

$3x$ + $4y$

81.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 2, what value does 5u take?

a)

$10$

b)

$7$

c)

$5$

d)

$12$

82.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 2, what value does 5 + u take?

a)

$7$

b)

$10$

c)

$5$

d)

$12$

83.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 11, what value does 5u take?

a)

$55$

b)

$16$

c)

$15$

d)

$22$

84.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 11, what value does 5 + u take?

a)

$16$

b)

$55$

c)

$15$

d)

$22$

85.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 5, what value does 5u take?

a)

$25$

b)

$10$

c)

$30$

d)

$5$

86.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 5, what value does 5 + u take?

a)

$10$

b)

$25$

c)

$30$

d)

$5$

87.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 8, what value does 5u take?

a)

$40$

b)

$13$

c)

$8$

d)

$45$

88.

Fill the blanks by replacing the letter-numbers by numbers; then compare the values that 5u and 5 + u take. For u = 8, what value does 5 + u take?

a)

$13$

b)

$40$

c)

$8$

d)

$45$

89.

Are the expressions $10y - 3$ and $10(y - 3)$ equal?

a)

Yes, they are equal for all values of y

b)

No, they are not equal

90.

After filling in the two diagrams comparing $10y - 3$ and $10(y - 3)$ for y values shown, do you think the two expressions are equal?

a)

Yes, they are equal for the given y values

b)

No, they are not equal for the given y values

91.

What is the sum of the numbers in the picture (unknown values are denoted by letters)?

a)

$2r + 2s + 24$

b)

$r + s + 12$

c)

$4r + 4s + 24$

d)

$2r + s + 24$

92.

Simplify the expression $p + p + p + p$ .

a)

$4p$

b)

$p^4$

c)

$2p$

d)

$0$

93.

Simplify the expression $p + p + p + q$ .

a)

$3p + q$

b)

$p + 3q$

c)

$4p + q$

d)

$3p - q$

94.

Simplify the expression $p - q + p - q$ .

a)

$2p - 2q$

b)

$p - 2q$

c)

$2p - q$

d)

$0$

95.

Simplify the expression $p + q - (p + q)$ .

a)

$0$

b)

$p + q$

c)

$2p$

d)

$2q$

96.

Simplify the expression $2d - d - d - d$ .

a)

$-d$

b)

$d$

c)

$0$

d)

$2d$

97.

Simplify the expression $2d - d - (d - c)$ .

a)

$c$

b)

$d + c$

c)

$2d - c$

d)

$d - c$

98.

Simplify the expression $2d - d - c - c$ .

a)

$d - 2c$

b)

$2d - c$

c)

$d + c$

d)

$-d - 2c$

99.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $3a + 2b$ .

a)

$3a + 2b$

b)

$5$

c)

$3a + b$

d)

$5a + 2b$

100.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $3b - 2b$ .

a)

$b$

b)

$0$

c)

$5b$

d)

$-b$

101.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $6(p + 2)$ .

a)

$6p + 12$

b)

$6p + 8$

c)

$6p + 2$

d)

$6 + 2p$

102.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $(4x + 3y) - (3x + 4y)$ .

a)

$x - y$

b)

$x + y$

c)

$7x + 7y$

d)

$y - x$

103.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $5 - (2 - 6z)$ .

a)

$3 + 6z$

b)

$3 - 6z$

c)

$7 - 6z$

d)

$5 - 2 - 6z$

104.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $2 + (x + 3)$ .

a)

$x + 5$

b)

$2x - 6$

c)

$x + 1$

d)

$5x + 2$

105.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $2y + (3y - 6)$ .

a)

$5y - 6$

b)

$-y + 6$

c)

$2y - 3y - 6$

d)

$5y + 6$

106.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $7p - p + 5q - 2q$ .

a)

$6p + 3q$

b)

$7p + 3q$

c)

$8p + 7q$

d)

$6p - 3q$

107.

Mind the Mistake, Mend the Mistake: The expression on the right-hand side should be in its simplest form. Choose the correct simplest form of $5(2w + 3x + 4w)$ .

a)

$30w + 15x$

b)

$10w + 15x + 20w$

c)

$10w + 15x$

d)

$5(6w + 3x)$

108.

Take a look at all the corrected simplest forms (i.e. brackets are removed, like terms are added, and terms with only numbers are also added). Is there any relation between the number of terms and the number of letter-numbers these expressions have?

a)

The number of terms equals the number of letter-numbers

b)

The number of terms is one more than the number of letter-numbers

c)

The number of terms is two more than the number of letter-numbers

d)

There is no consistent relation

109.

Find out the formula of this number machine. The machine takes two input numbers at the top of the Y-shaped diagram and produces one result at the bottom, performing the same operation each time.

a)

Two times the first number minus the second number

b)

The sum of the two input numbers

c)

Two times the second number plus the first number

d)

The first number minus twice the second number

110.

For the first case shown with inputs 5 and 2 in the number machine, which numeric expression matches the machine’s rule?

a)

$2 \times 5 - 2$

b)

$5 - 2$

c)

$5 + 2$

d)

$2 \times 5 + 2$

111.

Find the formulas of the number machines below and write the expression for each set of inputs.

a)

Identify the rule for each machine and write the expression using the given inputs.

b)

Draw the machines neatly and colour the outputs.

c)

Copy the inputs into the boxes without changing them.

d)

Replace all variables with the number 10.

112.

Now, make a formula on your own. Write a few number machines as examples using that formula. Challenge your classmates to figure it out!

a)

Create a rule, build example machines, and invite others to determine your formula.

b)

Erase the machines and rewrite the page title.

c)

Memorize the examples provided without creating anything new.

d)

Only list random numbers without explaining a rule.

113.

Somjit noticed a repeating pattern along the border of a saree.

a)

A repeating decorative motif appears along the saree’s border.

b)

A single large design is printed once at the centre.

c)

No designs appear anywhere on the saree.

d)

Only stripes are present without any motifs.

114.

Somjit wonders if there is a way to describe all the positions where the designs occur along the border: (i) Design A, (ii) Design B, and (iii) Design C.

a)

He seeks expressions that describe the positions of Designs A, B, and C along the border.

b)

He wants to count how many colours were used in each design.

c)

He plans to measure the length of the saree without considering the motifs.

d)

He intends to rename the designs without tracking their positions.

115.

Design C appears for the first time at position 3 and the second time at position 6. Where would Design C appear for the nth time?

a)

$2n$

b)

$3n$

c)

$n+3$

d)

$3n - 1$

116.

The positions where Design B occurs are 2, 5, 8, 11, 14, and so on. Which expression gives the position of the nth occurrence of Design B?

a)

$3n$

b)

$3n - 1$

c)

$3n - 2$

d)

$n + 2$

117.

Which expression describes the position at which Design A appears for the nth time?

a)

$3n$

b)

$3n - 1$

c)

$3n - 2$

d)

$n + 3$

118.

Given a position number, determine the design that appears there using these rules: if the position is a multiple of 3, it has Design C; if the position is one less than a multiple of 3, it has Design B; if it is 2 less than a multiple of 3, it has Design A. Which design appears at position 122?

a)

Design A

b)

Design B

c)

Design C

119.

Use the remainder obtained by dividing the position number by 3 to decide the design. Refer to the table. Which design appears at position 99?

a)

Design A

b)

Design B

c)

Design C

120.

Use the remainder obtained by dividing the position number by 3 to decide the design. Refer to the table. Which design appears at position 122?

a)

Design A

b)

Design B

c)

Design C

121.

Use the remainder obtained by dividing the position number by 3 to decide the design. Refer to the table. Which design appears at position 148?

a)

Design A

b)

Design B

c)

Design C

122.

In the endless calendar grid shown (rows continue beyond 30), consider any marked $2 \times 2$ square like the one with 12, 13, 19, and 20. Are the sums of the two diagonals equal in every $2 \times 2$ square of this grid?

a)

Yes, the diagonal sums are always equal in every $2 \times 2$ square.

b)

No, they are never equal.

c)

Only squares that include weekend dates have equal diagonal sums.

d)

They are equal only within November 2024 but not in the extended rows.

123.

Let the top-left number of a $2 \times 2$ square in this calendar grid be $a$ . The grid increases by 1 to the right and by 7 downward. Which set correctly gives the other three entries of the square (top-right, bottom-left, bottom-right)?

a)

$a+1,\ a+7,\ a+8$

b)

$a+7,\ a+1,\ a+8$

c)

$a+1,\ a+6,\ a+7$

d)

$a+2,\ a+7,\ a+9$

124.

Which reasoning guarantees that the diagonal sums are equal for any $2 \times 2$ square in this calendar grid?

a)

Let the entries be $a,\ a+1,\ a+7,\ a+8$ ; the diagonal sums are $(a+a+8)$ and $(a+1+a+7)$ , both equal to $2a+8$ .

b)

Check many examples by hand until convinced; some will match and that is sufficient.

c)

Use a calculator on the first five weeks only; extended rows may differ.

d)

Assume all diagonals are equal because calendars are symmetrical by design.

125.

In a 2 × 2 square, the top left number is a. The number to its right is 1 more, the number below is 7 more, and the diagonal bottom-right is 8 more. What is the sum along either diagonal of this square?

a)

$2a + 8$

b)

$2a + 7$

c)

$2a + 1$

d)

$a + 8$

126.

Consider the calendar shape shown: a plus-shaped set of five cells arranged with the centre number 15, the numbers directly above and below it, and the numbers directly to its left and right. The visible example shows 8 above, 22 below, 14 to the left, 16 to the right, and 15 in the centre. What is the sum of these five numbers?

a)

$75$

b)

$70$

c)

$73$

d)

$80$

127.

For any such plus-shaped selection on a calendar, what relationship holds between the total sum of the five numbers and the centre number?

a)

The sum is $5$ times the centre number.

b)

The sum is $4$ times the centre number.

c)

The sum equals the centre number plus $30$ .

d)

The sum is twice the centre number.

128.

Take the centre number of the plus-shaped calendar selection to be a. Which expressions correctly represent the five numbers in the shape? Select all that apply.

a)

$a - 7$

b)

$a - 1$

c)

$a$

d)

$a + 1$

e)

$a + 7$

129.

Using the general form where the plus-shaped selection on a calendar has numbers $a - 7$ , $a - 1$ , $a$ , $a + 1$ , and $a + 7$ , what is the total sum of the five numbers?

a)

$5a$

b)

$a$

c)

$3a$

d)

$a + 14$

130.

Look at the picture of matchstick triangles for Steps 1 to 4, where each new figure adds one triangle to the row. What is the pattern shown?

a)

The number of triangles increases by one at each step

b)

The number of squares increases by one at each step

c)

The number of triangles decreases by one at each step

d)

Circles are formed and increase by one at each step

131.

Using the matchstick triangle pattern shown for Steps 1 to 4, how many matchsticks will there be in Step 5?

a)

9

b)

11

c)

12

d)

13

132.

Refer to the table where Step Number 1 to 6 correspond to 3, 5, 7, 9, 11, 13 matchsticks (an increase of 2 each step). How many matchsticks are needed in Step 33?

a)

65

b)

67

c)

69

d)

71

133.

Using the same table pattern (3, 5, 7, 9, 11, 13 for Steps 1–6; increase of 2 each step), how many matchsticks are needed in Step 84?

a)

167

b)

169

c)

171

d)

173

134.

Using the same table pattern (increase of 2 matchsticks per step starting at 3 in Step 1), how many matchsticks are needed in Step 108?

a)

215

b)

217

c)

219

d)

221

135.

According to the table of matchstick counts (3, 5, 7, 9, 11, 13 for Steps 1–6), what is the general rule for how the number of matchsticks changes from one step to the next?

a)

It increases by 2 each step

b)

It increases by 3 each step

c)

It doubles each step

d)

It stays the same each step

136.

Using the matchstick pattern described: in Step 10, the number of matchsticks is given by 3 + 2 × 9, and in Step 11 by 3 + 2 × 10. For Step y, which expression gives the number of matchsticks?

a)

$3 + 2 \times (y - 1)$

b)

$3 + 2y$

c)

$2y - 1$

d)

$y^2 + 3$

137.

Which statement correctly describes the relationship between the expressions $3 + 2 \times (y - 1)$ and $2y + 1$ for the number of matchsticks at Step y?

a)

They are equivalent for all values of y.

b)

They are different and give different totals.

c)

$3 + 2 \times (y - 1)$ works only for even values of y.

d)

$2y + 1$ works only for y greater than 10.

138.

Refer to the pictured growing pattern of triangles made of matchsticks. Matchsticks are placed in two orientations: horizontal ones at the top and bottom, and diagonal ones in the middle. In Step 2 there are 2 horizontal and 3 diagonal matchsticks. In Step 3, how many matchsticks are horizontal and how many are diagonal?

a)

3 horizontal and 4 diagonal

b)

3 horizontal and 3 diagonal

c)

4 horizontal and 3 diagonal

d)

2 horizontal and 4 diagonal

139.

Using the same matchstick pattern, in Step 4 how many matchsticks are horizontal and how many are diagonal?

a)

4 horizontal and 5 diagonal

b)

5 horizontal and 4 diagonal

c)

4 horizontal and 4 diagonal

d)

3 horizontal and 5 diagonal

140.

For Step y in the matchstick pattern, which expression gives the number of horizontal matchsticks (top and bottom bars) at that step?

a)

$y$

b)

$y + 1$

c)

$2y$

d)

$y - 1$

141.

For Step y in the matchstick pattern, which expression gives the number of diagonal matchsticks (slanted middle bars) at that step?

a)

$y + 1$

b)

$y$

c)

$2y - 1$

d)

$y - 2$

142.

When you add the expressions for the horizontal and diagonal matchsticks at Step y, which expression correctly gives the total number of matchsticks?

a)

$2y + 1$

b)

$y + y$

c)

$2y - 1$

d)

$y^2 + 1$

143.

One plate of Jowar roti costs $₹30$ and one plate of Pulao costs $₹20$ . If x plates of jowar roti and y plates of pulao were ordered in a day, which expression(s) describe the total amount in rupees earned that day?

a)

30x + 20y

b)

(30 + 20) × (x + y)

144.

Pushpita sells two types of flowers on Independence day: champak and marigold. ‘p’ customers only bought champak, ‘q’ customers only bought marigold, and ‘r’ customers bought both. On the same day, she gave away a tiny national flag to every customer. How many flags did she give away that day?

a)

p + q + r

b)

p + q + 2r

145.

A snail climbs up $u$ cm during the day and slips down $d$ cm during the night. This happens for 10 days and 10 nights. Which expression describes how far the snail is from its starting position after this period?

a)

10(u − d)

b)

u − d

146.

A snail climbs up $u$ cm during the day and slips down $d$ cm during the night. This happens for 10 days and 10 nights. What can we say about the snail’s movement if $d > u$ ?

a)

It moves down overall.

b)

It stays at the same level.

147.

Radha cycles 5 km every day in the first week. Every week she increases the daily distance by $z$ km. How many kilometers will she have cycled after 3 weeks?

a)

105 + 21z

b)

35 + 7z

148.

A local train from Yahapur to Vahapur stops at three stations at equal distances along the way. The time in minutes to travel from one station to the next is the same and is denoted by $t$ . The train stops for 2 minutes at each of the three stations. If $t = 4$ , what is the total time taken to travel from Yahapur to Vahapur?

a)

14 minutes

b)

20 minutes

c)

22 minutes

d)

24 minutes

149.

A local train from Yahapur to Vahapur stops at three stations at equal distances along the way. The time in minutes to travel from one station to the next is the same and is denoted by $t$ . The train stops for 2 minutes at each of the three stations. What is the algebraic expression for the total time taken to travel from Yahapur to Vahapur?

a)

$3t + 6$

b)

$4t + 6$

c)

$4t + 3$

d)

$3t + 3$

150.

Simplify the expression $3a + 9b - 6 + 8a - 4b - 7a + 16$ . Choose the result.

a)

$4a + 5b + 10$

b)

$4a + 13b + 10$

c)

$12a + 5b + 22$

d)

$4a + 5b - 10$

Page 1

Total questions: 150

Worksheet time: 1hrs 15mins

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