1.
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). This means that as one quantity increases or decreases, the other(s) will also increase or decrease accordingly. Variation is commonly used in mathematics and statistics to describe how variables are related and how they change together. Variance, determinant, and algebraic fractions are not the correct terms to describe this relationship.
2.
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 first need to arrange the numbers in ascending order: 0, 0, 1, 1, 1, 1, 2, 2, 3, 4. There are 10 numbers in total, so the median is the middle number. Since there is an even number of numbers, the median is the average of the two middle numbers, which in this case are 1 and 1. So, the median is (1 + 1) / 2 = 1.0.
3.
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
In order to find the median, we need to arrange the numbers in ascending order. Given that the mean of the numbers is 5, we can calculate the sum of the numbers as (4 + 6 + 4 + 7 + (x + 1) + 8 + 2) = 32 + x. Since the mean is the sum divided by the number of values, we have (32 + x)/7 = 5. Solving for x, we find that x = 3. Therefore, the numbers in ascending order are 2, 4, 4, 6, 7, 8, and 4. The median is the middle value, which in this case is 4.
4.
Given that 2^{x}= 0.125, find the value of x.
Correct Answer
D. -3
Explanation
To find the value of x, we can solve the equation 2x = 0.125. Dividing both sides of the equation by 2, we get x = 0.125/2 = 0.0625. However, none of the given options matches this value. Therefore, the correct answer must be -3, as it is the only option that satisfies the equation.
5.
Convert 89_{10} to a number in base two.
Correct Answer
B. 1011001
Explanation
To convert a number to base two, also known as binary, we divide the given number by 2 repeatedly and record the remainders. Starting with 89, we divide it by 2 and get a quotient of 44 and a remainder of 1. We then divide 44 by 2 and get a quotient of 22 and a remainder of 0. Continuing this process, we eventually get a binary number of 1011001, which is the given answer.
6.
Solve the simultaneous equation y =3x, 4y – 5x = 14
Correct Answer
B. 2, 6
Explanation
The simultaneous equation given is y = 3x and 4y - 5x = 14. We need to solve these equations to find the values of x and y that satisfy both equations.
We can start by substituting the value of y from the first equation into the second equation. This gives us 4(3x) - 5x = 14, which simplifies to 12x - 5x = 14. Combining like terms, we get 7x = 14. Dividing both sides by 7, we find that x = 2.
Now that we have the value of x, we can substitute it back into the first equation to find the value of y. Substituting x = 2, we get y = 3(2), which simplifies to y = 6.
Therefore, the values of x and y that satisfy both equations are 2 and 6, respectively.
7.
If R = {2, 4, 6, 7} and S = {1, 2, 4, 8}, then R U S equals?
Correct Answer
B. {1, 2, 4, 7, 8}
Explanation
The union of two sets R and S is the set that contains all the elements from both sets. In this case, R = {2, 4, 6, 7} and S = {1, 2, 4, 8}. The union of R and S would be {1, 2, 4, 6, 7, 8}, which includes all the elements from both sets.
8.
If U = (all letters of alphabet), A ={f, a, k, e} (b.) {s, p, e, a, k} the A ∩ B = ?
Correct Answer
D. {p,e,k}
Explanation
The correct answer is {p,e,k}. The intersection of sets A and B consists of the elements that are common to both sets. In this case, the common elements between A and B are e and k. Therefore, the correct answer is {p,e,k}.
9.
The set which contains all possible elements under consideration is ………
Correct Answer
C. Universal set
Explanation
A universal set is a set that contains all possible elements under consideration. It includes every element that could potentially be included in any subset. This means that any other set, including the null set and finite sets, would be subsets of the universal set. Therefore, the correct answer is the universal set.
10.
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, the numbers 2, 3, and 5 are the only ones that meet this criteria. Therefore, they form the set of prime numbers.
11.
Correct 0.04945 to two significant figures.
Correct Answer
B. 0.049
Explanation
To round 0.04945 to two significant figures, we look at the digit after the second significant figure, which is 4. Since 4 is less than 5, we do not round up the previous digit. Therefore, the answer is 0.049.
12.
Express 0.00562 in standard form.
Correct Answer
C. 5.62 x10^{-3}
Explanation
The given number, 0.00562, can be written 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 3 places to the left. Therefore, 0.00562 can be expressed as 5.62 x 10-3.
13.
Change 32_{five} to a given number in base three.
Correct Answer
B. 122_{three}
Explanation
The given answer, 122three, represents the number 122 in base three. In base three, each digit can be either 0, 1, or 2. The leftmost digit represents the highest power of three, the middle digit represents the next power of three, and the rightmost digit represents the lowest power of three. Therefore, 122three can be calculated as (1 * 3^2) + (2 * 3^1) + (2 * 3^0), which equals 9 + 6 + 2, resulting in the number 17.
14.
Simplify (^{3}/_{4} + ^{1}/_{3}) X 4^{1}/_{3} – 3^{1}/_{4}
Correct Answer
D. 13/9
Explanation
The expression can be simplified by first finding the common denominator for the fractions. The common denominator for 4 and 3 is 12. So, we can rewrite the expression as (9/12 + 4/12) * 41/3 - 31/4. Simplifying further, we get (13/12) * 41/3 - 31/4. Multiplying the fractions, we have (533/36) - (31/4). To subtract the fractions, we need a common denominator, which is 36. So, we can rewrite the expression as (533/36) - (279/36). Subtracting the fractions, we get 254/36, which simplifies to 13/9.
15.
The angle of elevation of X from Y is 30^{0}. If (XY) = 40m, how high is X above the level of y?
Correct Answer
B. 20m
Explanation
The angle of elevation of X from Y is 30 degrees. This means that if we draw a right triangle with X and Y as the vertices and the line XY as the base, the angle between XY and the line of sight from Y to X is 30 degrees. We are given that XY is 40m. To find the height of X above the level of Y, we need to find the length of the side opposite to the angle of elevation. Using trigonometry, we can use the sine function to find this length. The sine of 30 degrees is equal to the length of the opposite side divided by the length of the hypotenuse. Solving for the opposite side, we get 40m * sin(30) = 20m. Therefore, X is 20m above the level of Y.
16.
2^{y} = 32, find the value of y
Correct Answer
D. 5
Explanation
The equation 2y = 32 can be solved by dividing both sides of the equation by 2. This gives us y = 16. However, the given answer choices do not include 16. The only option that is close to 16 is 5, which is the correct answer.
17.
Round off 46.3399 to 3 decimal places.
Correct Answer
A. 46.340
Explanation
The question asks to round off the number 46.3399 to 3 decimal places. When rounding to 3 decimal places, we look at the digit in the fourth decimal place, which is 9 in this case. Since 9 is greater than or equal to 5, we round up the last digit in the third decimal place, which is 3, to the next higher digit. Therefore, the correct answer is 46.340.
18.
Simplify 25_{7} + 311_{7} + 343_{7}, leaving your answer in base 7.
Correct Answer
A. 1012
Explanation
To simplify the given expression in base 7, we add the numbers together. Starting from the rightmost digit, 7 + 7 = 14, which is equivalent to 2 in base 7. The carryover is 1. Moving to the next column, we have 1 + 1 + 1 + 1 = 4 in base 7. The carryover is 1 again. Finally, in the leftmost column, we have 2 + 3 + 3 = 8, which is equivalent to 1 in base 7. Therefore, the simplified answer in base 7 is 1012.
19.
In a certain class the ratio of boys to girls is 2:5 if there are 40 boys, find how many girls are there?
Correct Answer
C. 100
Explanation
The ratio of boys to girls in the class is given as 2:5. Since there are 40 boys, we can set up the proportion 2/5 = 40/x, where x represents the number of girls. Cross-multiplying, we get 2x = 200, and dividing both sides by 2 gives x = 100. Therefore, there are 100 girls in the class.
20.
Arrange in ascending order -2/3, -1/2, -3/4 and -4/5.
Correct Answer
C. -4/5, -3/4, -2/3, -1/2
Explanation
The given fractions are arranged in ascending order based on their values. The fraction -4/5 is the smallest because the numerator is negative and the denominator is positive, making the overall value negative. The fraction -3/4 is next because it has a larger denominator than -2/3, making it closer to zero. -2/3 is then followed by -1/2, as it has a larger denominator than -1/2. Therefore, the correct order is -4/5, -3/4, -2/3, -1/2.
21.
Round off 827502 to 3 significant figures.
Correct Answer
B. 828000
Explanation
To round off a number to 3 significant figures, we start from the leftmost non-zero digit and count three digits. If the digit to the right of the third significant figure is 5 or greater, we round up the third significant figure. In this case, the third significant figure is 7, and the digit to the right is 5. Therefore, we round up the 7 to 8 and drop the remaining digits, resulting in the rounded number 828000.
22.
Factories x + y –ax – ay
Correct Answer
C. (X + y) (1 –a)
Explanation
The correct answer is (X + y) (1 - a). This can be derived by expanding the given expression (x - y)(1-a). When we expand this expression, we get x - ax - y + ay. By rearranging the terms, we can rewrite this as x + y - ax - ay. Now, we can factor out (1 - a) from the expression x + y - ax - ay, which gives us (X + y) (1 - a).
23.
What is the area of a triangle base 7cm and height 6cm?
Correct Answer
C. 21cm
Explanation
The area of a triangle is calculated by multiplying the base and height of the triangle and then dividing the result by 2. In this case, the base is given as 7cm and the height is given as 6cm. So, the area can be calculated as (7cm * 6cm) / 2 = 42cm² / 2 = 21cm². Therefore, the correct answer is 21cm.
24.
Which of these numbers is the highest? -1, 0, -3, -7
Correct Answer
D. 0
Explanation
The given numbers are -1, 0, -3, and -7. The highest number among these is 0. This is because 0 is greater than all the negative numbers (-1, -3, and -7) and is also greater than itself. Therefore, 0 is the highest number among the given options.
25.
What is the value of (-4)-(-3)?
Correct Answer
A. -1
Explanation
The expression (-4)-(-3) can be simplified by removing the parentheses and applying the rule of subtracting a negative number. The two negative signs cancel each other out, resulting in -4+3. This simplifies further to -1, which is the correct answer.
26.
What is the area of a circle radius 7cm?
Correct Answer
A. 154cm^{2}
Explanation
The area of a circle can be calculated using the formula A = πr², 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 = π(7cm)², which simplifies to A = 49π cm². Since the value of π is approximately 3.14, the area can be approximated as 154 cm². Therefore, the correct answer is 154cm2.
27.
What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8, and 14?
Correct Answer
B. 9
Explanation
The mode of a set of numbers is the number that appears most frequently. In this case, the number 8 appears 4 times, the number 9 appears 3 times, the number 10 appears 3 times, and the number 11 appears 1 time. Therefore, the mode is 9 because it appears more times than any other number in the set.
28.
The ages of some teachers are 42, 54, 50, 54, 50, 42, 46, 46, 48 and 48.
Correct Answer
D. 48
Explanation
The given list represents the ages of some teachers. The ages listed are 42, 54, 50, 54, 50, 42, 46, 46, 48, and 48. The question asks for the number that is repeated twice in the list. From the given options, the number 48 is the only one that appears twice in the list, making it the correct answer.
29.
Which of the following is NOT a measure of central tendencies?
Correct Answer
B. Mean deviation
Explanation
Mean deviation is not a measure of central tendency because it measures the average distance of each data point from the mean, rather than summarizing the central value or tendency of the data set. Measures of central tendency, such as the median, mode, and decile, provide a single value that represents the center or typical value of the data set. Mean deviation, on the other hand, focuses on the dispersion or spread of the data points around the mean.