Mathematics Ss 1 Lagos State Ministry Of Education (Edvi)

1) The set which contains all possible elements under consideration is ………

(A.) super set

(B.) null set

(C) universal set

(D.) finite set

The universal set is the set that contains all possible elements under consideration. It includes every element that could potentially be included in any other set. This set is often denoted by the symbol Ω. In this context, the universal set is the most appropriate choice as it encompasses all the elements that could be part of the set being discussed.

Explanation

The universal set is the set that contains all possible elements under consideration. It includes every element that could potentially be included in any other set. This set is often denoted by the symbol Ω. In this context, the universal set is the most appropriate choice as it encompasses all the elements that could be part of the set being discussed.

2) Which of these numbers is the highest? -1, 0, -3, -7

(A.) -7

(B.) -3

(C) -1

(D) 0

In this question, we are asked to identify the highest number among -1, 0, -3, and -7. Among these numbers, 0 is the highest because it is greater than all the other numbers listed.

Explanation

In this question, we are asked to identify the highest number among -1, 0, -3, and -7. Among these numbers, 0 is the highest because it is greater than all the other numbers listed.

3) 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

(A) Variation

(B) Variance

(C) Determinant

(D) Algebraic fractions

The term "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 the quantities are related and the change in one quantity directly affects the change in the other(s). Variance refers to the spread or dispersion of data, determinant is a mathematical concept used in linear algebra, and algebraic fractions are expressions that involve fractions with variables. Therefore, the correct answer is (A) Variation.

Explanation

The term "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 the quantities are related and the change in one quantity directly affects the change in the other(s). Variance refers to the spread or dispersion of data, determinant is a mathematical concept used in linear algebra, and algebraic fractions are expressions that involve fractions with variables. Therefore, the correct answer is (A) Variation.

4) The relationship consisting of two or more parts added together is called partial variation. TRUE or FALSE.

TRUE

False

Partial variation refers to a relationship in which two or more parts are added together. This means that as one part increases or decreases, the other part(s) also change accordingly. Therefore, the statement that the relationship consisting of two or more parts added together is called partial variation is true.

Explanation

Partial variation refers to a relationship in which two or more parts are added together. This means that as one part increases or decreases, the other part(s) also change accordingly. Therefore, the statement that the relationship consisting of two or more parts added together is called partial variation is true.

5) If U = (all letters of alphabet), A ={f, a, k, e} (B.) {s, p, e, a, k} the A ∩ B = ?

(A) {a,e,k}

(B.) {s,e,k}

(C.) {f,e, k}

(D.) {p,e,k}

The intersection of sets A and B is the set of elements that are common to both sets A and B. In this case, the common elements between set A and set B are 'a', 'e', and 'k'. Therefore, the correct answer is (A) {a, e, k}.

Explanation

The intersection of sets A and B is the set of elements that are common to both sets A and B. In this case, the common elements between set A and set B are 'a', 'e', and 'k'. Therefore, the correct answer is (A) {a, e, k}.

6) Round off 46.3399 to 3 decimal places

(A) 46.340

(B.) 46.339

(C.)50.330

(D.) 46.330

The correct answer is (A) 46.340 because when rounding off to 3 decimal places, we look at the fourth decimal place. If it is 5 or greater, we round the third decimal place up by 1. In this case, the fourth decimal place is 9, so we round the third decimal place (3) up to 4. Therefore, the rounded value is 46.340.

Explanation

The correct answer is (A) 46.340 because when rounding off to 3 decimal places, we look at the fourth decimal place. If it is 5 or greater, we round the third decimal place up by 1. In this case, the fourth decimal place is 9, so we round the third decimal place (3) up to 4. Therefore, the rounded value is 46.340.

7) Round off 827502 to 3 significant figures.

(A) 82700

(B) 828000

(C) 0 8380

(D) 842600

When rounding to 3 significant figures, we start from the leftmost non-zero digit and count three digits, including any zeros. In this case, the leftmost non-zero digit is 8. Counting three digits from the left, we have 827. The next digit is 5, which is greater than or equal to 5, so we round up. Therefore, the rounded number is 828,000.

Explanation

When rounding to 3 significant figures, we start from the leftmost non-zero digit and count three digits, including any zeros. In this case, the leftmost non-zero digit is 8. Counting three digits from the left, we have 827. The next digit is 5, which is greater than or equal to 5, so we round up. Therefore, the rounded number is 828,000.

8) Find 2 3 7 + 4 0 5 in base 8

(A) 644

(B) 544

(C) 444

(D) 344

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Explanation

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9) Expand -5(4x+2)

A. -20x + 2

B. -20x - 10

C. -20x +10

D. -30x

The given expression is -5(4x+2). To expand it, we distribute the -5 to both terms inside the parentheses. This gives us -20x - 10. Therefore, the correct answer is B. -20x - 10.

Explanation

The given expression is -5(4x+2). To expand it, we distribute the -5 to both terms inside the parentheses. This gives us -20x - 10. Therefore, the correct answer is B. -20x - 10.

10) Solve the equation 2x - 1 = x + 9

(A) x = 5

(B) x = 6

(C) x = 9

(D) x = 10

To solve the equation 2x - 1 = x + 9, we need to isolate the variable x.
First, we can subtract x from both sides of the equation to eliminate it from the right side: 2x - x - 1 = x - x + 9.
This simplifies to x - 1 = 9.
Next, we can add 1 to both sides of the equation to isolate x: x - 1 + 1 = 9 + 1.
This simplifies to x = 10.
Therefore, the correct answer is (D) x = 10.

Explanation

To solve the equation 2x - 1 = x + 9, we need to isolate the variable x.
First, we can subtract x from both sides of the equation to eliminate it from the right side: 2x - x - 1 = x - x + 9.
This simplifies to x - 1 = 9.
Next, we can add 1 to both sides of the equation to isolate x: x - 1 + 1 = 9 + 1.
This simplifies to x = 10.
Therefore, the correct answer is (D) x = 10.

11) Express 0.00562 in standard form

(A.) 0.562 x 10-3

(B.) 5.62 x 10-2

(C) 5.62 x10-3

(D) 5.62 x 103

The given number, 0.00562, can be expressed in standard form by moving the decimal point to the right until there is only one non-zero digit to the left of the decimal point. This results in 5.62 x 10-3, which is the same as 5.62 multiplied by 10 raised to the power of -3.

Explanation

The given number, 0.00562, can be expressed in standard form by moving the decimal point to the right until there is only one non-zero digit to the left of the decimal point. This results in 5.62 x 10-3, which is the same as 5.62 multiplied by 10 raised to the power of -3.

12) Convert 89₁₀ to a number in base two

(A.) 1101001

(B) 1011001

(C.) 1001101

(D.) 101101

To convert a number to base two (binary), we divide the number by 2 repeatedly and record the remainders. Starting with 89, we divide it by 2 to get a quotient of 44 and a remainder of 1. We then divide 44 by 2 to get a quotient of 22 and a remainder of 0. Continuing this process, we get remainders of 1, 1, 0, 0, and 1. Reading the remainders from bottom to top, we get 1011001, which matches option (B).

Explanation

To convert a number to base two (binary), we divide the number by 2 repeatedly and record the remainders. Starting with 89, we divide it by 2 to get a quotient of 44 and a remainder of 1. We then divide 44 by 2 to get a quotient of 22 and a remainder of 0. Continuing this process, we get remainders of 1, 1, 0, 0, and 1. Reading the remainders from bottom to top, we get 1011001, which matches option (B).

13) Which of the following is equal to 72 125

A.

B.

C.

D.

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Explanation

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14) 2^y = 32, find the value of y

(A.) 2

(B.) 3,

(C.) 4

(D) 5

The equation 2y = 32 can be solved by dividing both sides of the equation by 2 to isolate y. This gives us y = 16. Therefore, the value of y is 16.

Explanation

The equation 2y = 32 can be solved by dividing both sides of the equation by 2 to isolate y. This gives us y = 16. Therefore, the value of y is 16.

15) What is the area of a circle radius 7cm?

(A) 154cm2

(B) 77cm2

(C) 22cm2

(D) 11cm2

The area of a circle can be calculated using the formula A = πr^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 = π(7^2) = 49π. The value of π is approximately 3.14. Multiplying 49 by 3.14 gives us approximately 154. Therefore, the area of the circle is approximately 154cm^2.

Explanation

The area of a circle can be calculated using the formula A = πr^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 = π(7^2) = 49π. The value of π is approximately 3.14. Multiplying 49 by 3.14 gives us approximately 154. Therefore, the area of the circle is approximately 154cm^2.

16) What is the value of (-4)-(-3)?

(A) -1

(B.) -7

(C) -12

(D) 12

To find the value of (-4)-(-3), we can simplify it by removing the parentheses. When we subtract a negative number, it is the same as adding its positive counterpart. So (-4)-(-3) becomes -4 + 3. Adding -4 and 3 gives us -1. Therefore, the value of (-4)-(-3) is -1.

Explanation

To find the value of (-4)-(-3), we can simplify it by removing the parentheses. When we subtract a negative number, it is the same as adding its positive counterpart. So (-4)-(-3) becomes -4 + 3. Adding -4 and 3 gives us -1. Therefore, the value of (-4)-(-3) is -1.

17) Simplify ^x/₂ + ^x/₃

A. x/3

B. x/6

C. 5x/6

D. 3x/5

To simplify the expression x/2 + x/3, we need to find a common denominator. The least common multiple of 2 and 3 is 6. So, we can rewrite the expression as (3x/6) + (2x/6). Combining the like terms, we get (3x + 2x)/6, which simplifies to 5x/6. Therefore, the correct answer is C. 5x/6.

Explanation

To simplify the expression x/2 + x/3, we need to find a common denominator. The least common multiple of 2 and 3 is 6. So, we can rewrite the expression as (3x/6) + (2x/6). Combining the like terms, we get (3x + 2x)/6, which simplifies to 5x/6. Therefore, the correct answer is C. 5x/6.

18) Find the median of 2,1,0,3,1,1,4,0,1 and 2.

(A) 0.0

(B) 0.5

(C) 1.0

(D) 1.5

The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are 0, 0, 1, 1, 1, 1, 2, 2, 3, and 4. There are 10 numbers, so the middle value is the 5th number, which is 1. Therefore, the median is 1.0.

Explanation

The median is the middle value in a set of numbers when they are arranged in order. In this case, the numbers are 0, 0, 1, 1, 1, 1, 2, 2, 3, and 4. There are 10 numbers, so the middle value is the 5th number, which is 1. Therefore, the median is 1.0.

19) Given that 2^x= 0.125, find the value of x

(A.) 0

(B.) -1

(C.) -2

(D) -3

The equation given is 2x = 0.125. To find the value of x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 2. Dividing 0.125 by 2 gives us 0.0625. So, x = 0.0625. However, none of the answer choices match this value. Therefore, the correct answer is not available.

Explanation

The equation given is 2x = 0.125. To find the value of x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 2. Dividing 0.125 by 2 gives us 0.0625. So, x = 0.0625. However, none of the answer choices match this value. Therefore, the correct answer is not available.

20) 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

Given that the ratio of boys to girls is 2:5, and there are 40 boys, we can set up a proportion to find the number of girls.

Let x be the number of girls.

2/5 = 40/x

Cross multiplying, we get:

2x = 40 * 5

2x = 200

Dividing both sides by 2, we find:

x = 100

Therefore, there are 100 girls in the class.

Explanation

Given that the ratio of boys to girls is 2:5, and there are 40 boys, we can set up a proportion to find the number of girls.

Let x be the number of girls.

2/5 = 40/x

Cross multiplying, we get:

2x = 40 * 5

2x = 200

Dividing both sides by 2, we find:

x = 100

Therefore, there are 100 girls in the class.

21) If R = {2, 4, 6, 7} and S = {1, 2, 4, 8}, then R∪S equals?

(A.) {2, 4}

(B.) {1, 2, 4, 7, 8}

(C.) {2, 6, 7}

(D) {1, 2, 4, 6, 7, 8}

The union of two sets, R and S, is the set that contains all elements that are in either set R or set S, or both. In this case, set R contains the elements {2, 4, 6, 7} and set S contains the elements {1, 2, 4, 8}. The union of R and S would then be the set that contains all these elements, resulting in {1, 2, 4, 6, 7, 8}. Therefore, the correct answer is (D) {1, 2, 4, 6, 7, 8}.

Explanation

The union of two sets, R and S, is the set that contains all elements that are in either set R or set S, or both. In this case, set R contains the elements {2, 4, 6, 7} and set S contains the elements {1, 2, 4, 8}. The union of R and S would then be the set that contains all these elements, resulting in {1, 2, 4, 6, 7, 8}. Therefore, the correct answer is (D) {1, 2, 4, 6, 7, 8}.

22) Simplify 15x²y³z ÷ 3x²yz^-2

(A) 5xy2z

(B) 5x2yz

(C) 5x2z

(D) 5y2z3

To simplify the given expression, we divide the coefficients and subtract the exponents of the variables. In this case, the coefficient 15 is divided by 3 to give 5. The variable x has an exponent of 2 in the numerator and an exponent of 2 in the denominator, so they cancel out. The variable y has an exponent of 3 in the numerator and an exponent of 1 in the denominator, so we subtract 1 from 3 to get an exponent of 2. The variable z has an exponent of 1 in the numerator and an exponent of -2 in the denominator, so we subtract -2 from 1 to get an exponent of 3. Therefore, the simplified expression is 5y2z3.

Explanation

To simplify the given expression, we divide the coefficients and subtract the exponents of the variables. In this case, the coefficient 15 is divided by 3 to give 5. The variable x has an exponent of 2 in the numerator and an exponent of 2 in the denominator, so they cancel out. The variable y has an exponent of 3 in the numerator and an exponent of 1 in the denominator, so we subtract 1 from 3 to get an exponent of 2. The variable z has an exponent of 1 in the numerator and an exponent of -2 in the denominator, so we subtract -2 from 1 to get an exponent of 3. Therefore, the simplified expression is 5y2z3.

23) What is the area of a triangle base 7cm and height 6cm?

(A.) 42cm

(B.) 40cm

(C) 21cm

(D.) 14cm

The area of a triangle is calculated by multiplying the base 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 (7 * 6) / 2 = 42 / 2 = 21cm.

Explanation

The area of a triangle is calculated by multiplying the base 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 (7 * 6) / 2 = 42 / 2 = 21cm.

24) Change 32_five to a given number in base three

(A) 221three

(B) 122three

(C) 121three

(D) 101three

To convert 32five to base three, we need to divide 32 by 3 repeatedly until the quotient is 0. The remainders in each division will give us the digits in the base three representation. Starting with 32, we have 32 divided by 3 equals 10 with a remainder of 2. We then divide 10 by 3 to get 3 with a remainder of 1. Finally, we divide 3 by 3 to get 1 with a remainder of 0. Therefore, the base three representation of 32five is 122three.

Explanation

To convert 32five to base three, we need to divide 32 by 3 repeatedly until the quotient is 0. The remainders in each division will give us the digits in the base three representation. Starting with 32, we have 32 divided by 3 equals 10 with a remainder of 2. We then divide 10 by 3 to get 3 with a remainder of 1. Finally, we divide 3 by 3 to get 1 with a remainder of 0. Therefore, the base three representation of 32five is 122three.

25) 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)

The given expression represents the result of subtracting the product of a and x from the sum of x and y. The correct answer (C) (X + y) (1 - a) matches this expression as it represents the sum of x and y multiplied by the difference of 1 and a.

Explanation

The given expression represents the result of subtracting the product of a and x from the sum of x and y. The correct answer (C) (X + y) (1 - a) matches this expression as it represents the sum of x and y multiplied by the difference of 1 and a.

26) Solve for x ,

A. 31/2

B. 11/2

C. 3/4

D. 1/4

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Explanation

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27) Make w the subject of the formula of the relation

A.

B.

C.

D.

The correct answer is A because it states to make "w" the subject of the formula of the relation. This means that we need to rearrange the formula so that "w" is isolated on one side of the equation.

Explanation

The correct answer is A because it states to make "w" the subject of the formula of the relation. This means that we need to rearrange the formula so that "w" is isolated on one side of the equation.

28) Simplify 8ⁿ x 2²ⁿ ÷ 4³ⁿ

A. 2-n

B. 21-n

C. 2n

D. 2n+1

The given expression can be simplified by using the laws of exponents. When dividing two numbers with the same base, we subtract the exponents. In this case, 8n divided by 43n can be simplified to 8n-3n, which equals 2n. Then, when multiplying two numbers with the same base, we add the exponents. Therefore, 2n multiplied by 22n can be simplified to 2n+n, which equals 3n. So, the final simplified expression is 3n divided by 43n, which can be further simplified to 3n-n, which equals 2-n.

Explanation

The given expression can be simplified by using the laws of exponents. When dividing two numbers with the same base, we subtract the exponents. In this case, 8n divided by 43n can be simplified to 8n-3n, which equals 2n. Then, when multiplying two numbers with the same base, we add the exponents. Therefore, 2n multiplied by 22n can be simplified to 2n+n, which equals 3n. So, the final simplified expression is 3n divided by 43n, which can be further simplified to 3n-n, which equals 2-n.

29) Solve the simultaneous equation y =3x, 4y – 5x = 14

(A.) -2, -6

(B) 2,6

(C.) 2,-6

(D.) -1,-3

The correct answer is (B) 2,6. To solve the simultaneous equations, we can substitute the value of y from the first equation into the second equation. Substituting y = 3x into 4y - 5x = 14 gives 4(3x) - 5x = 14. Simplifying this equation gives 12x - 5x = 14, which simplifies further to 7x = 14. Dividing both sides by 7 gives x = 2. Substituting this value back into the first equation gives y = 3(2) = 6. Therefore, the solution to the simultaneous equations is x = 2 and y = 6.

Explanation

The correct answer is (B) 2,6. To solve the simultaneous equations, we can substitute the value of y from the first equation into the second equation. Substituting y = 3x into 4y - 5x = 14 gives 4(3x) - 5x = 14. Simplifying this equation gives 12x - 5x = 14, which simplifies further to 7x = 14. Dividing both sides by 7 gives x = 2. Substituting this value back into the first equation gives y = 3(2) = 6. Therefore, the solution to the simultaneous equations is x = 2 and y = 6.

30) Correct 0.04945 to two significant figures

(A.) 0.040

(B) 0.049

(C.) 0.0495

(D.) 0.050

To round 0.04945 to two significant figures, we look at the first two digits after the decimal point. Since the digit after 4 is 5, which is greater than 5, we round up the 4 to 5. Therefore, the correct answer is 0.049.

Explanation

To round 0.04945 to two significant figures, we look at the first two digits after the decimal point. Since the digit after 4 is 5, which is greater than 5, we round up the 4 to 5. Therefore, the correct answer is 0.049.

31) The angle of elevation of X from Y is 30⁰. If (XY) = 40m, how high is X above the level of y?

(A) 10m

(B) 20m

(C) 40m

(D) 15m

The angle of elevation of X from Y is 30°. This means that the angle formed between the horizontal line passing through Y and the line of sight from Y to X is 30°. Since the length of XY is given as 40m, we can use trigonometry to find the height of X above the level of Y. By using the sine function, we can set up the equation sin(30°) = height/40m. Solving for height, we get height = 40m * sin(30°) = 20m. Therefore, X is 20m above the level of Y.

Explanation

The angle of elevation of X from Y is 30°. This means that the angle formed between the horizontal line passing through Y and the line of sight from Y to X is 30°. Since the length of XY is given as 40m, we can use trigonometry to find the height of X above the level of Y. By using the sine function, we can set up the equation sin(30°) = height/40m. Solving for height, we get height = 40m * sin(30°) = 20m. Therefore, X is 20m above the level of Y.

32) 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

The given fractions are -2/3, -1/2, -3/4, and -4/5. To arrange them in ascending order, we need to find the smallest fraction first. Since all the fractions are negative, the smallest fraction will have the largest denominator. Therefore, -4/5 is the smallest fraction. Next, we compare the remaining fractions. -3/4 is smaller than -2/3, and -2/3 is smaller than -1/2. Therefore, the correct order is -4/5, -3/4, -2/3, -1/2.

Explanation

The given fractions are -2/3, -1/2, -3/4, and -4/5. To arrange them in ascending order, we need to find the smallest fraction first. Since all the fractions are negative, the smallest fraction will have the largest denominator. Therefore, -4/5 is the smallest fraction. Next, we compare the remaining fractions. -3/4 is smaller than -2/3, and -2/3 is smaller than -1/2. Therefore, the correct order is -4/5, -3/4, -2/3, -1/2.

33) Find x

A. 10

(B.) 8

(C) 6

(D.) 4

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Explanation

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34) Solve for x: x² + 2x + 1 = 25

(A.) -6, -4

(B.) 6. - 4

(C.) 6, 4

(D) -6, 4

To solve the equation x^2 + 2x + 1 = 25, we first subtract 25 from both sides to get x^2 + 2x - 24 = 0. Then, we factor the quadratic equation to get (x + 6)(x - 4) = 0. Setting each factor equal to zero, we find x = -6 and x = 4. Therefore, the correct answer is (D) -6, 4.

Explanation

To solve the equation x^2 + 2x + 1 = 25, we first subtract 25 from both sides to get x^2 + 2x - 24 = 0. Then, we factor the quadratic equation to get (x + 6)(x - 4) = 0. Setting each factor equal to zero, we find x = -6 and x = 4. Therefore, the correct answer is (D) -6, 4.

35) The mean of numbers 4, 6, 4, 7, (x + 1), 8 and 2 is 5 find the median of the numbers

(A) 4

(B.) 4.5

(C.) 5

(D.) 5.5

The mean of a set of numbers is found by adding up all the numbers and then dividing by the total number of numbers. In this case, the sum of the numbers 4, 6, 4, 7, (x + 1), 8, and 2 is 31 + (x + 1). To find the mean, we divide this sum by 7 (since there are 7 numbers in the set). So, the mean is (31 + (x + 1))/7 = 5. Multiplying both sides by 7 gives us 31 + (x + 1) = 35. Simplifying, we get x = 2.

Now that we know x = 2, we can substitute it back into the set of numbers and find the median. The numbers are 4, 6, 4, 7, (2 + 1), 8, and 2. When arranged in ascending order, the set becomes 2, 4, 4, 6, 7, 8, and 3. The median is the middle number, which is 4. Therefore, the correct answer is (A) 4.

Explanation

The mean of a set of numbers is found by adding up all the numbers and then dividing by the total number of numbers. In this case, the sum of the numbers 4, 6, 4, 7, (x + 1), 8, and 2 is 31 + (x + 1). To find the mean, we divide this sum by 7 (since there are 7 numbers in the set). So, the mean is (31 + (x + 1))/7 = 5. Multiplying both sides by 7 gives us 31 + (x + 1) = 35. Simplifying, we get x = 2.

Now that we know x = 2, we can substitute it back into the set of numbers and find the median. The numbers are 4, 6, 4, 7, (2 + 1), 8, and 2. When arranged in ascending order, the set becomes 2, 4, 4, 6, 7, 8, and 3. The median is the middle number, which is 4. Therefore, the correct answer is (A) 4.

36) Simplify (³/₄ + ¹/₃) X 4¹/₃ – 3¹/₄

(A) 5/9

(B) 8/13

(C) 12/13

(D) 13/9

To simplify the given expression, we first need to find the common denominator for the fractions. The common denominator for 4 and 3 is 12.

Next, we can add the fractions (3/4 + 1/3) by converting them to have the common denominator of 12.

(3/4) * (3/3) = 9/12
(1/3) * (4/4) = 4/12

Now, we can add these fractions together:
9/12 + 4/12 = 13/12

Next, we multiply this sum by 41/3:
(13/12) * (41/3) = (13 * 41) / (12 * 3) = 533/36

Finally, we subtract 31/4 from this result:
(533/36) - (31/4) = (533/36) - (279/36) = 254/36 = 127/18

Therefore, the simplified expression is 127/18, which is equivalent to 13/9.

Explanation

To simplify the given expression, we first need to find the common denominator for the fractions. The common denominator for 4 and 3 is 12.

Next, we can add the fractions (3/4 + 1/3) by converting them to have the common denominator of 12.

(3/4) * (3/3) = 9/12
(1/3) * (4/4) = 4/12

Now, we can add these fractions together:
9/12 + 4/12 = 13/12

Next, we multiply this sum by 41/3:
(13/12) * (41/3) = (13 * 41) / (12 * 3) = 533/36

Finally, we subtract 31/4 from this result:
(533/36) - (31/4) = (533/36) - (279/36) = 254/36 = 127/18

Therefore, the simplified expression is 127/18, which is equivalent to 13/9.

37) The set of prime numbers is ……….

(A) 1,3,5

(B) 2,3,5

(C) 2,4,6

(D) 3, 9,15

The set of prime numbers only contains numbers that are divisible by 1 and themselves. In the given options, only option B (2,3,5) consists of numbers that are prime. Option A (1,3,5) includes 1, which is not a prime number. Option C (2,4,6) includes 4 and 6, which are not prime numbers. Option D (3,9,15) includes 9 and 15, which are not prime numbers. Therefore, the correct answer is option B (2,3,5).

Explanation

The set of prime numbers only contains numbers that are divisible by 1 and themselves. In the given options, only option B (2,3,5) consists of numbers that are prime. Option A (1,3,5) includes 1, which is not a prime number. Option C (2,4,6) includes 4 and 6, which are not prime numbers. Option D (3,9,15) includes 9 and 15, which are not prime numbers. Therefore, the correct answer is option B (2,3,5).

38) If the perimeter of the rectangle with the dimension x+1m by 2x+5m is 36cm. Find the area of the rectangle

(A) 65m2

(B.) 84m2

(C.) 124m2

(D.) 51m2

The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter is given as 36cm. The dimensions of the rectangle are given as x+1m and 2x+5m. To find the perimeter, we add these dimensions together: (x+1m) + (2x+5m) + (x+1m) + (2x+5m) = 36cm. Simplifying this equation gives us 6x + 12m = 36cm. Solving for x gives us x = 4cm. Substituting this value back into the dimensions, we get the length as 5m and the width as 13m. The area of a rectangle is calculated by multiplying the length and width, which gives us 5m * 13m = 65m2. Therefore, the correct answer is (A) 65m2.

Explanation

The perimeter of a rectangle is equal to the sum of all its sides. In this case, the perimeter is given as 36cm. The dimensions of the rectangle are given as x+1m and 2x+5m. To find the perimeter, we add these dimensions together: (x+1m) + (2x+5m) + (x+1m) + (2x+5m) = 36cm. Simplifying this equation gives us 6x + 12m = 36cm. Solving for x gives us x = 4cm. Substituting this value back into the dimensions, we get the length as 5m and the width as 13m. The area of a rectangle is calculated by multiplying the length and width, which gives us 5m * 13m = 65m2. Therefore, the correct answer is (A) 65m2.

39) Simplify 25₇ + 311₇ + 343₇, leaving your answer in base 7

(A) 1012

(B.) 1002

(C.) 612

(D.) 602

To simplify the given expression in base 7, we need to add the numbers together and then convert the sum to base 7.

Adding 257, 3117, and 3437 gives us 6808.

To convert this sum to base 7, we divide it by 7 repeatedly and record the remainders.

6808 divided by 7 is 972 remainder 4.
972 divided by 7 is 138 remainder 6.
138 divided by 7 is 19 remainder 5.
19 divided by 7 is 2 remainder 5.
2 divided by 7 is 0 remainder 2.

Reading the remainders in reverse order gives us 25156 in base 7.

Therefore, the simplified answer in base 7 is 1012, which matches option (A).

Explanation

To simplify the given expression in base 7, we need to add the numbers together and then convert the sum to base 7.

Adding 257, 3117, and 3437 gives us 6808.

To convert this sum to base 7, we divide it by 7 repeatedly and record the remainders.

6808 divided by 7 is 972 remainder 4.
972 divided by 7 is 138 remainder 6.
138 divided by 7 is 19 remainder 5.
19 divided by 7 is 2 remainder 5.
2 divided by 7 is 0 remainder 2.

Reading the remainders in reverse order gives us 25156 in base 7.

Therefore, the simplified answer in base 7 is 1012, which matches option (A).

40) Simplify 8x²/10xy

A. 8xz/10

B. 2x/5yx

C. 4x/5y

D. 6x/5z

The expression 8x^2/10xy can be simplified by canceling out common factors. In this case, we can cancel out the 8 and the 10 to get 1/5. Additionally, we can cancel out one of the x's from the numerator and denominator to get x/1. Finally, we are left with z in the numerator and y in the denominator. Therefore, the simplified expression is 8xz/10 = 4xz/5.

Explanation

The expression 8x^2/10xy can be simplified by canceling out common factors. In this case, we can cancel out the 8 and the 10 to get 1/5. Additionally, we can cancel out one of the x's from the numerator and denominator to get x/1. Finally, we are left with z in the numerator and y in the denominator. Therefore, the simplified expression is 8xz/10 = 4xz/5.