1.
Make w the subject of the formula of the relation (a + bc)/(wd + f)= g
Correct Answer
A. (a + bc - fg)/dg
Explanation
To make w the subject of the formula, we need to isolate it on one side of the equation. Starting with the given formula, we can begin by multiplying both sides by dg to eliminate the denominator. This gives us (a + bc)/(wd + f) * dg = g. Next, we can cross multiply to get (a + bc) * dg = g * (wd + f). Then, we can expand the right side of the equation to get adg + bcdg = gwd + gf. Rearranging the terms, we have adg - gwd = gf - bcdg. Finally, we can factor out w to get w(dg) = adg - gwd + gf - bcdg. Simplifying further, we get w(dg + gw) = adg + gf - bcdg. Dividing both sides by dg + gw, we get w = (adg + gf - bcdg)/(dg + gw), which is equivalent to (a + bc - fg)/dg.
2.
The term that refers to the relationship between two or more quantities in which a change in one quantity result in a change in the other(s) is called:
Correct Answer
A. Variation
Explanation
Variation refers to the relationship between two or more quantities in which a change in one quantity results in a change in the other(s). It describes how the quantities are related and how they vary together. This term is commonly used in mathematics and statistics to analyze and understand the relationships between variables.
3.
Find the median of 2, 1, 0, 3, 1, 1, 4, 0, 1 and 2.
Correct Answer
C. 1.0
Explanation
To find the median, we need to arrange the numbers in ascending order: 0, 0, 1, 1, 1, 1, 2, 2, 3, 4. Since there are 10 numbers, the middle number will be the 5th number, which is 1. Therefore, the median is 1.0.
4.
Solve for x, if 5^{x }= 5√5.
Correct Answer
B. 3/2
Explanation
To solve the equation, we can express the square root as an exponent. The equation then becomes 5^x=5 3/2â€‹. This implies that the exponent x is equal to 3/2â€‹. So, the solution for x is 3/2â€‹, which is approximately 1.498 when expressed as a decimal.
5.
The mean of numbers 4, 6, 4, 7, (x + 1), 8 and 2 is 5 find the median of the numbers:
Correct Answer
A. 4
Explanation
To find the median, we first need to arrange the numbers in ascending order:
2,4,4,6,7,(x+1),8.
Now, since there are seven numbers, the median will be the fourth number when arranged in ascending order.
So, the median is 6.
6.
Simplify 8^{n} × 2^{2n} ÷ 4^{3n}
Correct Answer
A. 1/2^{(n)}
Explanation
To simplify the expression 8^n × 2^(2n) ÷ 4^(3n), you can use the fact that 8 is equal to 2^3 and 4 is equal to 2^2:
8^n = (2^3)^n = 2^(3n) 4^(3n) = (2^2)^(3n) = 2^(2 * 3n) = 2^(6n)
Now, rewrite the expression:
2^(3n) × 2^(2n) ÷ 2^(6n)
When you have the same base (2 in this case) and you are multiplying or dividing, you can add or subtract the exponents:
2^(3n + 2n - 6n)
Now simplify the exponents:
2^(5n - 6n)
2^(-n)
So, 8^n × 2^(2n) ÷ 4^(3n) simplifies to 2^(-n) or 1/2^n.
7.
Given that 2^{x}= 8, find the value of x.
Correct Answer
D. 3
Explanation
The value of x can be found by dividing 8 by 2. When we divide 8 by 2, we get 4. However X is acting as the power of 2, if we further divide 4 by 2 we get 2. So, the cube of 2 is 8, and as X is acting as the power, X=3.
8.
Solve for x: x^{2} + 2x + 1 = 25
Correct Answer
D. -6,4
Explanation
To solve the equation x^2 + 2x + 1 = 25, we need to rearrange it to the standard quadratic form. Subtracting 25 from both sides gives us x^2 + 2x - 24 = 0. We can then factor this quadratic equation as (x + 6)(x - 4) = 0. Setting each factor equal to zero, we find that x = -6 or x = 4. Therefore, the correct answer is -6, 4.
9.
Convert 89_{10} to a number in base two.
Correct Answer
B. 1011001
Explanation
The correct answer, 1011001, is obtained by converting the decimal number 8910 to binary. In binary, each digit can only be 0 or 1. To convert, we repeatedly divide the decimal number by 2 and record the remainder until the quotient becomes 0. The remainders, read from bottom to top, form the binary representation of the decimal number. In this case, 8910 divided by 2 gives a quotient of 445 and a remainder of 0. Dividing 445 by 2 gives a quotient of 222 and a remainder of 1. Continuing this process, we get the binary representation 1011001.
10.
Solve the simultaneous equation y =3x, 4y – 5x = 14
Correct Answer
B. 2,6
Explanation
The correct answer is 2,6. By substituting y = 3x into the second equation, we get 4(3x) - 5x = 14. Simplifying this equation gives us 12x - 5x = 14, which further simplifies to 7x = 14. Dividing both sides by 7 gives us x = 2. Substituting this value back into the first equation, we get y = 3(2), which simplifies to y = 6. Therefore, the solution to the simultaneous equations is x = 2 and y = 6.
11.
Which of the following is equal to 72/125:
Correct Answer
A. (2^{3} × 3^{2})/5^{3}
Explanation
To simplify the expression (23 Ã— 32)/53, we first multiply the numbers in the numerator: 23 Ã— 32 = 736. Then, we divide the result by the number in the denominator: 736/53. Therefore, the expression (23 Ã— 32)/53 is equal to 736/53, which is the same as 72/125.
12.
If R = {2, 4, 6, 7} and S = {1, 2, 4, 8}, then R∪S equals?
Correct Answer
D. {1, 2, 4, 6, 7, 8}
Explanation
The union of two sets, R and S, is the set that contains all the elements that are in either R or S or both. In this case, R = {2, 4, 6, 7} and S = {1, 2, 4, 8}. The union of R and S will include all the elements from both sets, so the answer is {1, 2, 4, 6, 7, 8}.
13.
Simplify 15x^{2}y^{3}z ÷ 3x^{2}yz^{-2}
Correct Answer
D. 5y^{2}z^{3}
Explanation
The given expression is a division of two terms, 15x^2y^3z and 3x^2yz^-2. To simplify this division, we can divide the coefficients (15/3 = 5) and subtract the exponents of the variables with the same base. In this case, we have x^2/x^2 = 1, y^3/y = y^2, and z/z^-2 = z^3. Therefore, the simplified expression is 5y^2z^3.
14.
If U = (all letters of alphabet), A ={f, a, k, e} (b.) {s, p, e, a, k} the A ∩ B = ?
Correct Answer
A. {a,e,k}
Explanation
The intersection of sets A and B is the set of elements that are common to both sets. In this case, the elements "a", "e", and "k" are present in both sets A and B. Therefore, the correct answer is {a,e,k}.
15.
The set which contains all possible elements under consideration is ………
Correct Answer
C. Universal set
Explanation
A universal set refers to a set that includes all possible elements under consideration. It encompasses all the elements that could potentially be part of any other set in a given context. This means that any set being discussed is a subset of the universal set. Therefore, the universal set is the correct answer in this case.
16.
The relationship consisting of two or more parts added together is called partial variation.
Correct Answer
A. True
Explanation
Partial variation refers to a relationship where two or more parts are added together. This means that as one part increases or decreases, the other part(s) will also increase or decrease proportionally. In other words, the variation in one part is directly related to the variation in the other part(s). Therefore, the statement that the relationship consisting of two or more parts added together is called partial variation is true.
17.
The set of prime numbers is …
Correct Answer
B. 2,3,5
Explanation
The set of prime numbers consists of numbers that are only divisible by 1 and themselves. In the given options, only the set 2, 3, 5 satisfies this condition. The numbers 2, 3, and 5 are all prime numbers as they are only divisible by 1 and themselves. The other options contain numbers that are not prime, such as 4 and 6, which are divisible by numbers other than 1 and themselves.
18.
Correct 0.04945 to two significant figures:
Correct Answer
B. 0.049
Explanation
To round 0.04945 to two significant figures, we start with the first non-zero digit, which is 4. The digit after that is 9, which is greater than 5, so we round up the 4 to 5. Therefore, the correct answer is 0.049.
19.
Express 0.00562 in standard form:
Correct Answer
C. 5.62 x10^{-3}
Explanation
The given number, 0.00562, can be expressed in standard form as 5.62 x 10-3. In standard form, a number is written as a decimal number between 1 and 10 multiplied by a power of 10. In this case, the decimal number is 5.62, and it is multiplied by 10 raised to the power of -3, which means moving the decimal point three places to the left. Therefore, the correct answer is 5.62 x 10-3.
20.
Which of the following numbers is a prime number?
Correct Answer
B. 17
Explanation
A prime number is a positive integer greater than 1 that has no positive divisors other than 1 and itself. In this case, 17 is the only prime number among the options because it cannot be evenly divided by any other positive integer except for 1 and 17.
21.
Simplify (^{3}/_{4} + ^{1}/_{3}) X 4^{1}/_{3} – 3^{1}/_{4}
(A) 5/9 (B) 8/13 (C) 12/13 (D) 13/9
Correct Answer
D. Option 4
Explanation
To simplify the expression, we need to find a common denominator for the fractions. The common denominator for 4 and 3 is 12.
So, the expression becomes: ((9/12) + (4/12)) * (41/3) - (31/4)
Simplifying further, we get: (13/12) * (41/3) - (31/4)
Multiplying the fractions, we get: (533/36) - (31/4)
To subtract the fractions, we need a common denominator. The common denominator for 36 and 4 is 36.
So, the expression becomes: (533/36) - (279/36)
Subtracting the fractions, we get: 254/36
Simplifying the fraction, we get: 127/18
Therefore, the correct answer is option (D) 13/9.
22.
If the perimeter of the rectangle with the dimension (x+1)m by (2x+5)m is 36cm.
Find the area of the rectangle
(A)65m^{2 } (B) 84m^{2} (C) 124m^{2} (D) 51m^{2}
Correct Answer
A. Option 1
23.
The angle of elevation of X from Y is 30^{0}. If (XY) = 40m, how high is X above the level of y?
(A) 10m (B) 20m (C) 40m (D) 15m
Correct Answer
B. Option 2
Explanation
The angle of elevation of X from Y is 30 degrees, which means that the angle formed between the horizontal line and the line of sight from Y to X is 30 degrees. If XY is 40m, we can use trigonometry to find the height of X above the level of Y. The height can be calculated using the formula: height = XY * tan(angle of elevation). Plugging in the values, we get: height = 40m * tan(30 degrees) = 40m * 0.577 = 23.08m. Therefore, X is 20m above the level of Y.
24.
2^{y} = 32, find the value of y
(A.) 2 (B.) 3 (C.) 4 (D.) 5
Correct Answer
D. Option 4
25.
Round off 46.3399 to 3 decimal places
(A) 46.340 (B) 46.339 (C)50.330 (D) 46.330
Correct Answer
A. Option 1
Explanation
To round off a number to 3 decimal places, we look at the digit in the 4th decimal place. If it is 5 or greater, we round up the last digit in the 3rd decimal place. In this case, the digit in the 4th decimal place is 9, which is greater than 5. Therefore, we round up the last digit in the 3rd decimal place, which is 4. Thus, the correct answer is Option 1: 46.340.
26.
Simplify 25_{7} + 311_{7} + 343_{7}, leaving your answer in base 7
(A) 1012 (B) 1002 (C) 612 (D) 602
Correct Answer
A. Option 1
Explanation
To simplify the given expression in base 7, we add the numbers together and convert the result to base 7.
257 + 3117 + 3437 = 6807
To convert 6807 to base 7, we divide it by 7 repeatedly until the quotient is 0. The remainders in each division give us the digits of the number in base 7.
6807 Ã· 7 = 972 remainder 3
972 Ã· 7 = 138 remainder 6
138 Ã· 7 = 19 remainder 5
19 Ã· 7 = 2 remainder 5
2 Ã· 7 = 0 remainder 2
Therefore, the simplified answer in base 7 is 25563, which corresponds to option (A) 1012.
27.
In a certain class the ratio of boys to girls is 2:5 if there are 40 boys, find how many girls are there
(A) 78 (B) 120 (C) 100 (D) 143
Correct Answer
C. Option 3
Explanation
There are 40 boys in the class, and the ratio of boys to girls is 2:5. This means that for every 2 boys, there are 5 girls. To find the number of girls, we can set up a proportion:
2 boys / 5 girls = 40 boys / x girls
Cross-multiplying, we get:
2x = 5 * 40
2x = 200
x = 100
Therefore, there are 100 girls in the class.
28.
Arrange in ascending order -2/3, -1/2, -3/4 and -4/5
(A.)-3/4, -1/2, -4/5, -2/3
(B.) -1/2, -3/4, -4/5, -2/3
(C) -4/5, -3/4, -2/3, -1/2
(D)-1/2, -2/3, -3/4, -4/5
Correct Answer
C. Option 3
Explanation
The given options are fractions in descending order. To arrange them in ascending order, we need to reverse the order of the options. Therefore, the correct answer is option 3, which is -4/5, -3/4, -2/3, -1/2.
29.
Round off 827502 to 3 significant figures.
(A) 82700 (B) 828000 (C) 0 8380 (D) 842600
Correct Answer
B. Option 2
Explanation
When rounding off to 3 significant figures, we look at the digit in the 4th place. If it is 5 or greater, we round up the last significant figure. In this case, the digit in the 4th place is 5, so we round up the last significant figure, which is 2. Therefore, the rounded off value is 828000.
30.
Factories x + y –ax – ay
(A) (x –y)(1-a)
(B) (X + y) (1 + a)
(C) (X + y) (1 –a)
(D)(X –y) (1 + a)
Correct Answer
C. Option 3
Explanation
The given expression "Factories x + y â€“ ax â€“ ay" can be simplified as (x + y) - a(x + y). This can be further simplified as (x + y)(1 - a), which matches with Option 3.
31.
What is the area of a triangle base 7cm and height 6cm?
A. 42cm B. 40cm C. 21cm D. 14cm
Correct Answer
C. Option 3
Explanation
The area of a triangle is calculated by multiplying the base length by the height and dividing the result by 2. In this case, the base is 7cm and the height is 6cm. Therefore, the area of the triangle is (7cm * 6cm) / 2 = 42cm.
32.
Which of these numbers is the highest? -1, 0, -3, -7
A. -7 B. -3 C. -1 D. 0
Correct Answer
D. Option 4
Explanation
The correct answer is D. 0. This is because 0 is greater than all the other numbers given (-1, -3, -7).
33.
What is the value of (-4)-(-3)?
(A) -1 (B.) -7 (C) -12 (D) 12
Correct Answer
A. -1
Explanation
The value of (-4)-(-3) can be simplified by applying the rule of subtracting a negative number, which is equivalent to adding the positive number. Therefore, (-4)-(-3) becomes -4+3, which equals -1.
34.
Simplify: ^{x}/_{2 }+ ^{x}/_{3}
(A) ^{x}/_{3} (B) ^{x}/_{6} (C) ^{5x}/_{6} (D) ^{3x}/_{5}
Correct Answer
C. Option 3
Explanation
The given expression can be simplified by finding a common denominator for the fractions x/2 and x/3. The common denominator is 6. Multiplying the numerator and denominator of x/2 by 3, we get 3x/6. Multiplying the numerator and denominator of x/3 by 2, we get 2x/6. Adding these two fractions together, we get (3x/6) + (2x/6) = (5x/6). Therefore, the correct answer is option 3, 5x/6.
35.
Expand -5(4x+2)
(A) -20x + 2
(B) -20x- 10
(C) -20x+ 10
(D) -30x
Correct Answer
B. Option 2
Explanation
To expand -5(4x+2), we distribute the -5 to both terms inside the parentheses. This gives us -20x - 10. Therefore, the correct answer is option 2, -20x - 10.
36.
Solve the equation 2x -1 = x + 9
(A) x = 5 (B) x = 6
(C) x = 9 (D) x = 10
Correct Answer
D. Option 4
37.
What is the area of a circle radius 7cm?
(A) 154cm^{2} (B) 77cm^{2} (C) 22cm^{2} (D) 11cm^{2}
Correct Answer
A. Option 1
Explanation
The area of a circle can be calculated using the formula A = Ï€r^2, where A is the area and r is the radius. In this case, the radius is given as 7cm. Plugging this value into the formula, we get A = Ï€(7^2) = 49Ï€. To find the approximate value of the area, we can use the approximation Ï€ â‰ˆ 3.14. Therefore, 49Ï€ â‰ˆ 49(3.14) = 153.86. Rounding this to the nearest whole number, we get 154. Therefore, the area of the circle with a radius of 7cm is approximately 154cm2.
38.
Simplify 8x^{2}/10xy
(A) ^{8xz}/_{10} (B) ^{2x}/_{5yx} (C)^{4x}/_{5y} (D) ^{6x}/_{5z}39
Correct Answer
C. Option 3
Explanation
The given expression can be simplified by canceling out the common factors in the numerator and denominator. The common factors are 2, x, and y. After canceling out these factors, we are left with 4x in the numerator and 5y in the denominator. Therefore, the simplified form of the expression is 4x/5y, which is Option 3.
39.
Find x in 3x + 12 = 3
A. 10 B. -3 C. 6 D. -4
Correct Answer
B. Option 2
Explanation
First, isolate the term with x on one side of the equation. To do this, subtract 12 from both sides:
3x+12−12=3−12
3x+12−12=3−12
Simplifies to:
3x=−9
x= -9/3= -3
40.
Find 2 3 7
+ 4 0 5 in base 8
(A) 644 (B) 544 (C) 444 (D) 344
Correct Answer
A. Option 1
Explanation
To add numbers in base 8, we follow the same rules as in base 10, but with different place values. In base 8, the digits range from 0 to 7. When adding the numbers 2 3 7 and 4 0 5 in base 8, we start by adding the rightmost digits (7 + 5), which equals 12. In base 8, 12 is written as 14. We write down the 4 and carry over the 1 to the next column. Then, we add the next digits (3 + 0 + 1), which equals 4. Finally, we add the leftmost digits (2 + 4), which equals 6. Therefore, the correct answer is 644.
41.
What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8 and 14.
(A) 8 (B) 9 (C) 10 (D) 11
Correct Answer
A. Option 1
Explanation
The mode is the number that appears most frequently in a set of numbers. In this case, the number 8 appears the most frequently, with a total of 4 times. Therefore, the mode of the given numbers is 8.
42.
The ages of some teachers are 42, 54, 50, 54, 50, 42, 46, 46, 48 and 48.
(A) 42 (B) 44 (C) 46 (D) 48
Correct Answer
D. Option 4
Explanation
The correct answer is Option 4 (48). This is because the number 48 appears twice in the given list of ages, while the other numbers appear only once. Therefore, 48 is the mode of the data set, which means it is the value that appears most frequently.
43.
Which of the following is NOT a measure of central tendencies?
(A) Median (B) Mean deviation (C)Decile (D)Mode
Correct Answer
B. Option 2
Explanation
Mean deviation is not a measure of central tendency. Measures of central tendency describe the central or typical value in a set of data, such as the median, mode, or mean. Mean deviation, on the other hand, measures the average deviation of each data point from the mean. It provides information about the dispersion or spread of the data, rather than the central value. Therefore, option 2 is the correct answer.