Q. A trapezium has bases of lengths 10 cm and 6 cm, and a height of 4 cm. What is the area of the trapezium?
A.
32 cm²
B.
40 cm²
C.
36 cm²
D.
28 cm²
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Solution
Area of a trapezium = (1/2) × (base1 + base2) × height = (1/2) × (10 + 6) × 4 = 32 cm².
Correct Answer:
A
— 32 cm²
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Q. A triangle has a base of 12 cm and a height of 5 cm. What is the area of the triangle?
A.
30 cm²
B.
60 cm²
C.
24 cm²
D.
12 cm²
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Solution
Area = (1/2) × base × height = (1/2) × 12 × 5 = 30 cm².
Correct Answer:
A
— 30 cm²
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Q. A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the triangle?
A.
24 cm²
B.
30 cm²
C.
36 cm²
D.
20 cm²
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Solution
Using Heron's formula, s = (6 + 8 + 10)/2 = 12. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12 × 6 × 4 × 2] = 24 cm².
Correct Answer:
A
— 24 cm²
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Q. A triangle has sides of lengths 7 cm, 24 cm, and 25 cm. What is the area of the triangle? (2021)
A.
84 cm²
B.
96 cm²
C.
120 cm²
D.
168 cm²
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Solution
The triangle is a right triangle (7² + 24² = 25²). The area is (1/2) * base * height = (1/2) * 7 * 24 = 84 cm².
Correct Answer:
A
— 84 cm²
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Q. A wholesaler sells a batch of goods for $1200, which includes a profit of 20%. What was the cost price of the goods?
A.
$1000
B.
$1100
C.
$1200
D.
$1300
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Solution
Let the cost price be x. Selling Price = x + 20% of x = 1.2x. Thus, 1.2x = 1200, so x = 1000.
Correct Answer:
A
— $1000
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Q. A wholesaler sells a product to a retailer at a price of $400, which includes a profit margin of 25%. What was the cost price for the wholesaler?
A.
$300
B.
$320
C.
$350
D.
$360
Show solution
Solution
Let the cost price be x. Selling Price = Cost Price + Profit = x + 0.25x = 1.25x. Setting this equal to $400 gives 1.25x = $400, so x = $400 / 1.25 = $320.
Correct Answer:
A
— $300
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Q. A wholesaler sells a product to a retailer at a price that includes a 20% profit margin. If the retailer sells it at a 10% loss, what is the retailer's selling price if the cost price for the wholesaler is $200?
A.
$180
B.
$200
C.
$220
D.
$240
Show solution
Solution
Wholesaler's selling price = Cost Price + 20% of Cost Price = $200 + $40 = $240. Retailer's selling price = $240 - 10% of $240 = $240 - $24 = $216.
Correct Answer:
A
— $180
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Q. A wholesaler sells a product to a retailer for $200, which is a 20% profit on the cost price. What is the cost price of the product?
A.
$160
B.
$180
C.
$200
D.
$220
Show solution
Solution
Let the cost price be x. Selling Price = x + (20% of x) = 1.2x. Therefore, 1.2x = $200, x = $200 / 1.2 = $166.67.
Correct Answer:
A
— $160
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Q. According to the passage, what is one major consequence of ignoring social inequalities? (2023)
A.
Increased economic growth.
B.
Social unrest and instability.
C.
Improved community relations.
D.
Greater individual success.
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Solution
The passage warns that neglecting social inequalities can lead to social unrest and instability, highlighting the urgency of addressing these issues.
Correct Answer:
B
— Social unrest and instability.
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Q. According to the passage, what is the significance of the vertex in a quadratic function?
A.
It represents the function's maximum or minimum value.
B.
It is the point where the function crosses the y-axis.
C.
It indicates the function's slope.
D.
It is the point of discontinuity.
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Solution
The vertex of a quadratic function is crucial as it represents the maximum or minimum point of the graph.
Correct Answer:
A
— It represents the function's maximum or minimum value.
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Q. According to the passage, which of the following is a common misconception about inequalities?
A.
Inequalities are only a recent phenomenon.
B.
Inequalities affect only certain demographics.
C.
Inequalities can be easily measured.
D.
Inequalities are always visible.
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Solution
The passage suggests that many believe inequalities are a recent issue, which is a misconception.
Correct Answer:
A
— Inequalities are only a recent phenomenon.
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Q. According to the passage, which of the following is a common misconception about inequality?
A.
It is only an economic issue.
B.
It affects everyone equally.
C.
It can be easily solved.
D.
It is a global issue.
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Solution
The passage clarifies that inequality is multifaceted and not limited to economic factors.
Correct Answer:
A
— It is only an economic issue.
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Q. According to the passage, which of the following is a significant barrier to achieving equality?
A.
Lack of awareness about inequalities.
B.
Cultural differences among communities.
C.
Resistance to change from those in power.
D.
Insufficient funding for education.
Show solution
Solution
The passage highlights resistance from those in power as a major barrier to achieving equality.
Correct Answer:
C
— Resistance to change from those in power.
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Q. Arrange the following numbers in ascending order based on their factors: 15, 12, 18, 10. (2023)
A.
10, 12, 15, 18
B.
12, 10, 15, 18
C.
15, 10, 12, 18
D.
18, 15, 12, 10
Show solution
Solution
The number of factors for each is: 10 (4), 12 (6), 15 (4), 18 (6). Arranging them gives 10, 12, 15, 18.
Correct Answer:
A
— 10, 12, 15, 18
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Q. Based on the passage, which of the following actions is least likely to reduce social inequalities? (2023)
A.
Implementing progressive taxation.
B.
Enhancing access to quality education.
C.
Promoting economic growth without regulation.
D.
Increasing social welfare programs.
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Solution
Promoting economic growth without regulation is least likely to address social inequalities, as it may lead to greater disparities.
Correct Answer:
C
— Promoting economic growth without regulation.
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Q. Based on the passage, which of the following is a potential consequence of ignoring social inequalities?
A.
Increased social cohesion.
B.
Worsening economic conditions.
C.
Greater access to education for all.
D.
Enhanced community engagement.
Show solution
Solution
Ignoring social inequalities can lead to worsening economic conditions, as highlighted in the passage.
Correct Answer:
B
— Worsening economic conditions.
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Q. Based on the passage, which of the following is NOT a factor contributing to social inequalities?
A.
Economic status.
B.
Access to education.
C.
Cultural background.
D.
Personal choice.
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Solution
The passage discusses systemic factors rather than individual choices as contributors to social inequalities.
Correct Answer:
D
— Personal choice.
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Q. Based on the passage, which of the following is NOT a reason given for the persistence of inequalities?
A.
Historical injustices
B.
Lack of education
C.
Government negligence
D.
Cultural beliefs
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Solution
The passage does not mention government negligence as a reason for the persistence of inequalities.
Correct Answer:
C
— Government negligence
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Q. Based on the passage, which of the following is NOT a suggested method for addressing inequalities?
A.
Implementing progressive taxation.
B.
Increasing access to quality education.
C.
Promoting economic growth without regulation.
D.
Enhancing social welfare programs.
Show solution
Solution
The passage does not support the idea of promoting unregulated economic growth as a method to address inequalities.
Correct Answer:
C
— Promoting economic growth without regulation.
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Q. Based on the passage, which of the following is NOT a suggested solution to combat inequalities? (2023)
A.
Implementing progressive taxation.
B.
Enhancing access to education.
C.
Promoting free market policies.
D.
Increasing minimum wage.
Show solution
Solution
The passage does not advocate for free market policies as a solution to inequalities.
Correct Answer:
C
— Promoting free market policies.
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Q. Based on the passage, which of the following statements about the graph of a quadratic function is true?
A.
It can have at most one x-intercept.
B.
It is always increasing.
C.
It is a parabola that opens upwards or downwards.
D.
It has no maximum or minimum points.
Show solution
Solution
A quadratic function is represented by a parabola, which can open upwards or downwards depending on the coefficient of the squared term.
Correct Answer:
C
— It is a parabola that opens upwards or downwards.
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Q. For a number to be divisible by 10, which of the following must be true?
A.
It must end in 0
B.
It must be a two-digit number
C.
It must be a prime number
D.
It must be even
Show solution
Solution
A number is divisible by 10 if it ends in 0.
Correct Answer:
A
— It must end in 0
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Q. For a number to be divisible by 11, which of the following must be true?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
B.
The number must be even
C.
The number must end in 1
D.
The sum of the digits must be divisible by 11
Show solution
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.
Correct Answer:
A
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
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Q. For a number to be divisible by 8, what must be true about its last three digits?
A.
They must be divisible by 8
B.
They must be even
C.
They must be a multiple of 10
D.
They must be prime
Show solution
Solution
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Correct Answer:
A
— They must be divisible by 8
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Q. From a group of 8 people, how many ways can a team of 4 be selected?
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Solution
The number of ways to choose 4 people from 8 is given by 8C4 = 70.
Correct Answer:
B
— 56
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Q. How does the author illustrate the concept of digital sum? (2023)
A.
By providing historical examples.
B.
Through mathematical equations.
C.
By using real-world applications.
D.
By comparing it to other mathematical concepts.
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Solution
The author illustrates the concept of digital sum through real-world applications, making it relatable and understandable.
Correct Answer:
C
— By using real-world applications.
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Q. How does the author structure the argument about digital sum?
A.
Chronologically, detailing its history.
B.
By comparing it with other mathematical concepts.
C.
Through examples and case studies.
D.
By outlining its benefits and challenges.
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Solution
The author presents a structured argument by outlining both the benefits and challenges associated with digital sum, providing a balanced view.
Correct Answer:
D
— By outlining its benefits and challenges.
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Q. How does the author support the claim about the efficiency of digital sum? (2023)
A.
By providing statistical data.
B.
By citing historical examples.
C.
By discussing its computational advantages.
D.
By comparing it to other methods.
Show solution
Solution
The author supports the claim about the efficiency of digital sum by discussing its computational advantages in various applications.
Correct Answer:
C
— By discussing its computational advantages.
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Q. How does the author support the claims made about digital sum? (2023)
A.
By providing historical examples.
B.
By citing recent technological advancements.
C.
By referencing mathematical theories.
D.
By discussing personal experiences.
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Solution
The author supports the claims about digital sum by citing recent technological advancements that utilize this concept.
Correct Answer:
B
— By citing recent technological advancements.
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Q. How many different ways can 3 men and 2 women be seated in a row?
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Solution
The number of arrangements of 5 people (3 men + 2 women) is 5! = 120.
Correct Answer:
B
— 120
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