Questions and Answers
Which letter has only rotational symmetry?
In Hetal's linear equation solution, which step contains the mistake?
What is the excluded number if the mean of eight numbers is 10 and the mean of the remaining numbers is 9?
If the base of a parallelogram is 7 cm and the height is 5 cm more than the base, what is the area of the parallelogram?
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If two angles of a triangle are each 40 degrees, what is the measure of the third angle?
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What is the area of each triangle formed by dividing a rectangle with a length of 16 cm, which is twice its breadth?
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Which data value can be added to the dataset 12, 10, 6, 19, 15, 14, 9, 16, 6, 21 without changing its median?
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How many faces does the given solid shape have as drawn on isometric dot paper?
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Which of the following options represents the mirror image of a shaded figure composed of squares?
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On which day was the highest rainfall recorded over a period of 7 days?
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Study Notes
Area of a Triangle
- A rectangle is divided into two congruent triangles; the length is twice the breadth.
- Given length of the rectangle is 16 cm, calculate the breadth as 8 cm.
- Area of the rectangle is 16 cm × 8 cm = 128 cm²; thus, each triangle has an area of 64 cm².
Data Handling
- For a data set of 10 values (12, 10, 6, 19, 15, 14, 9, 16, 6, 21), the median does not change when a specific value is added.
- Adding 14 to the data set maintains the median value.
Solid Shapes
- A solid shape drawn on isometric dot paper has a total of 10 faces.
Symmetry in Shapes
- The mirror image of a shaded figure can be visually determined from presented options.
- Understanding of symmetry is key in distinguishing shapes.
Rainfall Data
- The highest rainfall recorded was on Sunday, and the least was on Friday, indicating a significant variation of 15.2 mm.
Rotational Symmetry
- The letter that has only rotational symmetry is identified; S is one option.
Linear Equations
- Errors in solving equations can be traced back to specific steps; incorrect step identified in Hetal's solution is Step 3.
Mean Calculation
- The mean of 8 numbers is given as 10; excluding one number changes the mean to 9.
- The excluded number can be calculated, resulting in 17.
Area of Parallelogram
- Height of a parallelogram is noted to be 5 cm more than its base.
- Base measures 7 cm, and calculation leads to an area of 70 cm².
Investment and Interest
- At a 10% interest rate, the sum of money doubles in 10 years.
Volume Calculation of Cubes
- Cube-based model analysis reveals a total of 9 cubes from various views.
Integer Solution in Linear Equations
- Assessing the equation with variable ranges indicates an integer solution greater than -15.
Profit and Sale Price
- A pendant purchased for ₹1500 with a 15% profit results in a selling price of ₹1725.
Cross-sectional Shapes
- A horizontal cut to a party cap results in a specific shape that can be visualized.
Calculating Ribbon Length
- To decorate a semi-circular disc with a diameter of 35 cm, the circumference (and thus ribbon needed) calculates to 110 cm.
Quiz Competition Scores
- Usha’s highest score is 52, determined by the lowest score equation involving a multiple.
Equation Formation from Word Problem
- Formulating equations correctly from word problems is essential, as seen from Usha and Tanvi's score scenario.
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Description
This quiz focuses on applying percentages and geometric concepts to solve problems related to areas. It includes questions about shapes like rectangles and triangles, aiming to enhance understanding of area calculations. Perfect for students looking to reinforce their knowledge in mathematics.
