CBSE Class 8 Mathematics Practice Worksheet Set 05

Question 1. How many triangles are contained in the given figure?
Answer: Let us systematically count the triangles in the given square figure divided by diagonals and cross-bars:
1. Small individual triangles formed inside the four quadrants = 8 small triangles.
2. Medium triangles formed by combining adjacent small triangles = 4 medium triangles.
3. Large triangles formed by the major corner-to-corner diagonals = 4 large triangles.
Total number of triangles = \(8 + 4 + 4 = 16\).
In simple words: By counting the small, medium, and large triangles separately and adding them up, we get 16 triangles in total.

Exam Tip: Always categorize geometric shapes by size (small, medium, large) to avoid counting any triangle twice or missing one.

Question 2. Shivani saw the restaurant sign shown below: Manager's Special: Choose 1 main dish, 1 side dish and 1 bread for Rs. 880. (Main dish: Meat loaf, Chicken-fried steak; Side dish: Corn, Beans, Mashed Potatoes, Macaroni and; Bread: Dinner roll, Biscuit). How many different combinations are possible if Shivani buys the mangoes special?
Answer: Using the Fundamental Counting Principle, the total number of combinations is the product of the number of choices available for each category:
Number of choices for Main dish = 2 (Meat loaf, Chicken-fried steak)
Number of choices for Side dish = 4 (Corn, Beans, Mashed Potatoes, Macaroni)
Number of choices for Bread = 2 (Dinner roll, Biscuit)
Total combinations = \(2 \times 4 \times 2 = 16\)
In simple words: Multiply the number of options in each category together to find the total possible meal combinations.

Exam Tip: Remember the fundamental counting principle: if there are \(a\) ways to do one thing, \(b\) ways for another, and \(c\) ways for a third, total ways = \(a \times b \times c\).

Question 3. The given chart shows how much the party house charges for pizza parties for different number of people. If n stands for the number of people and c stands for the cost in Rs. which equation represents the information in the chart.

1. C = 5n + 100
2. C = n + 45
3. C = 5n + 40
4. C = 2n + 35
Answer: (3) C = 5n + 40
Let us test the given options with \(n = 5\):
Option 1: \(C = 5(5) + 100 = 25 + 100 = 125\) (Matches for first row, but test \(n = 8\): \(5(8) + 100 = 140\) - incorrect, gives 140 instead of 140? Wait, let's test Option 3)
Option 3: For \(n = 5\), \(C = 5(5) + 40 = 25 + 40 = 65\) - wait, let's recalculate slope \(m = \frac{140 - 125}{8 - 5} = \frac{15}{3} = 5\).
Using equation \(C = 5n + b\), substitute \(n = 5, C = 125\):
\(125 = 5(5) + b \implies 125 = 25 + b \implies b = 100\).
Let us check with option 1: \(C = 5n + 100\).
Let us verify for \(n = 8\): \(C = 5(8) + 100 = 40 + 100 = 140\) (Matches table!).
Let us verify for \(n = 12\): \(C = 5(12) + 100 = 60 + 100 = 160\) (Matches table!).
Let us verify for \(n = 20\): \(C = 5(20) + 100 = 100 + 100 = 200\) (Matches table!).
Therefore, the correct equation is \(C = 5n + 100\), which corresponds to option 1.
In simple words: Find the rate of change per person (slope) and the fixed base charge (y-intercept) to determine the correct linear equation.

Exam Tip: Always test at least two coordinate pairs from the table to verify a linear equation \(C = mn + b\).

Question 4. In a primary school, the parents were asked about the number of hours they spend per day in helping their children to do homework. There were 90 parents who helped for \(\frac{1}{2}\) hour to \(1\frac{1}{2}\) hours. The distribution of parents according to the time for which they said they helped is given in the adjoining figure:
1. 20% helped for more than \(1\frac{1}{2}\) hours per day.
2. 30% helped for \(\frac{1}{2}\) hour to \(1\frac{1}{2}\) hours.
3. 50% did not help at all.
Answer: Given that 90 parents represent 30% of the total parents (who helped for \(\frac{1}{2}\) hour to \(1\frac{1}{2}\) hours):
Total number of parents = \(\frac{90}{0.30} = 300\)
Number of parents who helped for more than \(1\frac{1}{2}\) hours = \(20\% \text{ of } 300 = 0.20 \times 300 = 60\)
Number of parents who did not help at all = \(50\% \text{ of } 300 = 0.50 \times 300 = 150\)
In simple words: Use the given percentage and count for one category to find the total number of parents, then calculate the counts for the other categories.

Exam Tip: When a specific percentage corresponds to a given number, divide the number by that percentage (as a decimal) to find the total 100% quantity.

Question 5. Nalini and three of her friends worked together to make a quilt. The given table lists the fractional part of the quilt that each of the girls made. Arrange list of names which shows the girls in order from the one who sewed the most to the one who sewed the least?

Answer: To compare the fractions, convert them to a common denominator or convert them to decimals or percentages:
LCM of denominators \(8, 5, 5, 40\) is 40.
Nalini: \(\frac{3}{8} = \frac{3 \times 5}{8 \times 5} = \frac{15}{40} = 0.375\)
Kamini: \(\frac{1}{5} = \frac{1 \times 8}{5 \times 8} = \frac{8}{40} = 0.200\)
Shalini: \(\frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} = 0.400\)
Reena: \(\frac{1}{40} = 0.025\)
Ordering from the most to the least: Shalini (\(\frac{16}{40}\)), Nalini (\(\frac{15}{40}\)), Kamini (\(\frac{8}{40}\)), Reena (\(\frac{1}{40}\)).
Order of names: Shalini, Nalini, Kamini, Reena.
In simple words: Convert all fractions to have the same denominator (40) and compare their numerators from largest to smallest.

Exam Tip: Finding the Least Common Multiple (LCM) of denominators is the quickest and most accurate way to compare and order fractions.