Q. What is the author's stance on the role of government in addressing inequalities?
A.
Governments should take a hands-off approach.
B.
Governments have a responsibility to intervene.
C.
Governments are the main cause of inequalities.
D.
Governments should focus on economic growth only.
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Solution
The passage indicates that the author believes governments should actively intervene to address inequalities.
Correct Answer:
B
— Governments have a responsibility to intervene.
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Q. What is the base of the decimal system?
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Solution
The decimal system is a base-10 numeral system.
Correct Answer:
C
— 10
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Q. What is the base of the logarithm if log_10(100) = 2?
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Solution
The base of the logarithm is 10, as log_10(100) = 2 means 10^2 = 100.
Correct Answer:
B
— 10
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Q. What is the base of the logarithm if log_2(8) = 3?
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Solution
Since 8 is 2 raised to the power of 3 (2^3 = 8), the base of the logarithm is 2.
Correct Answer:
A
— 2
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Q. What is the base of the logarithm if log_3(81) = 4?
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Solution
Since 81 is 3^4, the base of the logarithm is 3.
Correct Answer:
A
— 3
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Q. What is the base of the logarithm if log_b(1) = 0?
A.
Any positive number
B.
1
C.
0
D.
Undefined
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Solution
For any base b > 0, log_b(1) = 0, since b^0 = 1.
Correct Answer:
A
— Any positive number
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Q. What is the base of the octal numeral system?
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Solution
The octal numeral system is a base-8 system, using digits from 0 to 7.
Correct Answer:
B
— 8
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Q. What is the base-16 equivalent of the decimal number 255?
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Solution
To convert 255 to hexadecimal (base-16), divide by 16. 255 ÷ 16 = 15 remainder 15. The hexadecimal representation of 15 is F, so 255 in base-16 is FF.
Correct Answer:
A
— FF
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Q. What is the binary equivalent of the hexadecimal number 'A3'?
A.
10100011
B.
11010011
C.
10011011
D.
10111011
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Solution
The hexadecimal number 'A3' converts to binary as 10100011.
Correct Answer:
A
— 10100011
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Q. What is the common difference in the arithmetic sequence 10, 15, 20, 25? (2023)
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Solution
The common difference is found by subtracting any two consecutive terms: 15 - 10 = 5.
Correct Answer:
A
— 5
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Q. What is the decimal equivalent of the base-3 number '2101'?
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Solution
'2101' in base-3 = 2*3^3 + 1*3^2 + 0*3^1 + 1*3^0 = 54 + 9 + 0 + 1 = 64.
Correct Answer:
A
— 19
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Q. What is the decimal equivalent of the base-4 number '132'?
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Solution
'132' in base-4 is 1*16 + 3*4 + 2 = 26.
Correct Answer:
A
— 26
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Q. What is the decimal equivalent of the base-8 number '57'?
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Solution
'57' in base-8 is 5*8 + 7 = 40 + 7 = 47 in decimal.
Correct Answer:
A
— 47
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Q. What is the decimal equivalent of the binary number '1101'?
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Solution
'1101' in binary is calculated as 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8 + 4 + 0 + 1 = 13.
Correct Answer:
B
— 13
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Q. What is the decimal equivalent of the binary number 1010?
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Solution
The binary number 1010 is equivalent to the decimal number 10.
Correct Answer:
B
— 10
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Q. What is the decimal equivalent of the binary number 1011?
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Solution
The binary number 1011 is equal to 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8 + 0 + 2 + 1 = 11.
Correct Answer:
C
— 11
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Q. What is the difference between the amounts obtained by investing $1000 at 8% per annum for 2 years in simple interest and compound interest?
A.
$16
B.
$24
C.
$32
D.
$40
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Solution
SI = 1000 * 8/100 * 2 = $160. CI = 1000(1 + 0.08)^2 = $1166.4. Difference = $1166.4 - $160 = $24.
Correct Answer:
B
— $24
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Q. What is the difference between the compound interest and simple interest on a sum of $1000 at 5% per annum after 2 years? (2023)
A.
$10
B.
$20
C.
$30
D.
$40
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Solution
SI = 1000 * 5 * 2 / 100 = $100. CI = 1000[(1 + 0.05)^2 - 1] = $102.5. The difference is $2.5.
Correct Answer:
B
— $20
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Q. What is the distance between the points (1, 1) and (4, 5)?
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Solution
Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(4 - 1)² + (5 - 1)²] = √[3² + 4²] = √[9 + 16] = √25 = 5.
Correct Answer:
C
— 5
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Q. What is the distance between the points P(3, 4) and Q(7, 1) in the coordinate plane?
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Solution
Using the distance formula d = √((x2 - x1)² + (y2 - y1)²), we find d = √((7 - 3)² + (1 - 4)²) = √(16 + 9) = √25 = 5.
Correct Answer:
B
— 6
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Q. What is the distance between the points P(3, 4) and Q(7, 1)?
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Solution
Using the distance formula, d = √[(7-3)² + (1-4)²] = √[16 + 9] = √25 = 5.
Correct Answer:
A
— 5
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Q. What is the divisibility rule for 3?
A.
The last digit must be 0
B.
The sum of the digits must be divisible by 3
C.
The number must be even
D.
The number must end in 3 or 6
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Solution
A number is divisible by 3 if the sum of its digits is divisible by 3.
Correct Answer:
B
— The sum of the digits must be divisible by 3
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Q. What is the divisibility rule for 9?
A.
The number must be even
B.
The sum of the digits must be divisible by 9
C.
The last digit must be 0
D.
The number must be a multiple of 3
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Solution
A number is divisible by 9 if the sum of its digits is divisible by 9.
Correct Answer:
B
— The sum of the digits must be divisible by 9
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Q. What is the effect of a vertical stretch on the graph of a function?
A.
It compresses the graph towards the x-axis.
B.
It stretches the graph away from the x-axis.
C.
It shifts the graph to the left.
D.
It shifts the graph to the right.
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Solution
A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, causing the graph to stretch away from the x-axis.
Correct Answer:
B
— It stretches the graph away from the x-axis.
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Q. What is the effect of multiplying a function by a negative constant on its graph?
A.
It reflects the graph across the x-axis.
B.
It reflects the graph across the y-axis.
C.
It shifts the graph to the left.
D.
It stretches the graph vertically.
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Solution
Multiplying a function by a negative constant reflects the graph across the x-axis.
Correct Answer:
A
— It reflects the graph across the x-axis.
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Q. What is the equation of a line that passes through the origin and has a slope of 4?
A.
y = 4x
B.
y = x/4
C.
y = 4/x
D.
y = 1/4x
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Solution
The equation of a line in slope-intercept form is y = mx + b. Since it passes through the origin, b = 0, thus y = 4x.
Correct Answer:
A
— y = 4x
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Q. What is the GCF of 24 and 36?
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Solution
The GCF of 24 and 36 is 12, as it is the largest number that divides both without leaving a remainder.
Correct Answer:
B
— 12
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Q. What is the general term in the expansion of (x + y)^n?
A.
C(n, k)x^k y^(n-k)
B.
C(n, k)x^(n-k) y^k
C.
C(n, k)x^n y^k
D.
C(n, k)x^k y^n
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Solution
The general term in the expansion of (x + y)^n is given by C(n, k)x^k y^(n-k).
Correct Answer:
A
— C(n, k)x^k y^(n-k)
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Q. What is the geometric interpretation of the solution to a system of linear equations?
A.
The area enclosed by the lines
B.
The point of intersection of the lines
C.
The distance between the lines
D.
The angle between the lines
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Solution
The solution represents the point where the lines intersect, if they do.
Correct Answer:
B
— The point of intersection of the lines
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Q. What is the geometric interpretation of the solution to a system of linear equations in two variables?
A.
The point where the two lines intersect.
B.
The area enclosed by the lines.
C.
The distance between the lines.
D.
The slope of the lines.
Show solution
Solution
The solution to a system of linear equations in two variables is represented by the point where the two lines intersect.
Correct Answer:
A
— The point where the two lines intersect.
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