SS1 First Term Mathematics Exam Questions & Answers

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

Super set

Null set

Universal set

Finite set

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.

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.

2. The sum of the interior angles of any triangle is always 180 degrees.

True

False

In geometry, it is a fundamental property that the sum of the interior angles of any triangle always equals 180 degrees, regardless of the type of triangle (whether it is equilateral, isosceles, or scalene). This rule applies to all triangles in Euclidean geometry. Therefore, the statement is true.

Explanation

In geometry, it is a fundamental property that the sum of the interior angles of any triangle always equals 180 degrees, regardless of the type of triangle (whether it is equilateral, isosceles, or scalene). This rule applies to all triangles in Euclidean geometry. Therefore, the statement is true.

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

-7

-3

-1

0

The correct answer is D. 0. This is because 0 is greater than all the other numbers given (-1, -3, -7).

Explanation

The correct answer is D. 0. This is because 0 is greater than all the other numbers given (-1, -3, -7).

4. Round off 827502 to 3 significant figures.

82700

828000

0 8380

842600

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.

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.

5.

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

{a,e,k}

{s,e,k}

{f,e, k}

{p,e,k}

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}.

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}.

6. Round off 46.3399 to 3 decimal places

46.340

46.339

50.330

46.330

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.

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.

7.

Expand -5(4x+2) 

(A) -20x + 2 

(B) -20x- 10 

(C) -20x+ 10 

(D) -30x

Option 1

Option 2

Option 3

Option 4

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.

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.

8. 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:

Variation

Variance

Determinant

Algebraic fractions

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.

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.

9.

Simplify 8x²/10xy

8xz/10

2x/5yx

4x/5y

6x/5z39

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.

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.

10.

Find    2 3 7 
      + 4 0 5  in base 8

664

554

444

334

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.

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.

11. Which of the following numbers is a prime number?

10

17

28

35

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.

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.

12. What is the area of a circle radius 7cm?

154cm2

77cm2

22cm2

11cm2

Explanation

13. What is the value of (-4)-(-3)?

-1

-7

-12

12

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.

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.

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

2

3

4

5

To find the value of y in the equation 2 to the power of y equals 32, we can rewrite 32 as a power of 2:

32 is equal to 2 to the power of 5.

So, the equation becomes:

2 to the power of y is equal to 2 to the power of 5.

Since the bases are the same, we can set the exponents equal to each other:

y equals 5.

Therefore, the value of y is 5.

Explanation

To find the value of y in the equation 2 to the power of y equals 32, we can rewrite 32 as a power of 2:

32 is equal to 2 to the power of 5.

So, the equation becomes:

2 to the power of y is equal to 2 to the power of 5.

Since the bases are the same, we can set the exponents equal to each other:

y equals 5.

Therefore, the value of y is 5.

15. What is the area of a triangle base 7cm and height 6cm?

42cm

40cm

21cm

14cm

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.

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.

16. Express 0.00562 in standard form:

0.562 x 10-3

5.62 x 10-2

5.62 x10-3

5.62 x 103

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.

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.

17. Convert 89₁₀ to a number in base two.

1101001

1011001

1001101

101101

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.

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.

18.

Given that 2^x= 8, find the value of x.

0

-1

-2

3

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.

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.

19.

Which of the following is equal to 72/125:

(23 × 32)/53

(24 x 33)/53

(24 × 3)/53

(24 × 32)/53

To simplify the expression (23 × 32)/53, we first multiply the numbers in the numerator: 23 × 32 = 736. Then, we divide the result by the number in the denominator: 736/53. Therefore, the expression (23 × 32)/53 is equal to 736/53, which is the same as 72/125.

Explanation

To simplify the expression (23 × 32)/53, we first multiply the numbers in the numerator: 23 × 32 = 736. Then, we divide the result by the number in the denominator: 736/53. Therefore, the expression (23 × 32)/53 is equal to 736/53, which is the same as 72/125.

20.

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

{2, 4}

{1, 2, 4, 7, 8}

{2, 6, 7}

{1, 2, 4, 6, 7, 8}

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}.

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}.

21. The set of prime numbers is …

1,3,5

2,3,5

2,4,6

3, 9,15

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.

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.

22. Find x in 3x + 12 = 3

10

-3

6

4

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

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

23.

Simplify: ^x/₂+ ^x/₃

X/3

X/6

5x/6

3x/5

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.

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.

24. In a certain class the ratio of boys to girls is 2:5 if there are 40 boys, find how many girls are there:

78

120

100

143

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.

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.

25. The ages of some teachers are 48, 42, 54, 50, 48, 54, 50, 42, 46, 46, 48 and 48. What is the mode?

(A) 42

(B) 44

(C) 46

(D) 48

The mode is the number that appears most frequently in a data set. In this case, the ages provided are:

48, 42, 54, 50, 48, 54, 50, 42, 46, 46, 48, and 48.

48 appears 4 times

42 appears 2 times

54 appears 2 times

50 appears 2 times

46 appears 2 times

Mode: The mode is 48 because it appears most frequently, a total of 4 times.

Explanation

The mode is the number that appears most frequently in a data set. In this case, the ages provided are:

48, 42, 54, 50, 48, 54, 50, 42, 46, 46, 48, and 48.

48 appears 4 times

42 appears 2 times

54 appears 2 times

50 appears 2 times

46 appears 2 times

Mode: The mode is 48 because it appears most frequently, a total of 4 times.

26. Simplify 15x²y³z ÷ 3x²yz^-2

5xy2z

5x2yz

5x2z

5y2z3

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.

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.

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

0.0

0.5

1.0

1.5

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.

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.

28. Factorize x + y –ax – ay

(x –y)(1-a)

(X + y) (1 + a)

(X + y) (1 –a)

(X –y) (1 + a)

The given expression "x + y – ax – 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.

Explanation

The given expression "x + y – ax – 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.

29. If f(x) = 3x² - 5x + 2, what is the value of f(4)?

26

34

38

40

To find f(4), substitute x = 4 into the function. First, calculate 4² = 16. Then, multiply by 3 to get 48. Next, multiply -5 by 4 to get -20. Add 48, -20, and 2: 48 - 20 + 2 = 38. This problem tests understanding of function evaluation and applying the correct order of operations. Errors in exponentiation, multiplication, or sign handling can lead to incorrect answers. Carefully substituting values and simplifying correctly is key to solving function-based algebraic problems accurately.

Explanation

To find f(4), substitute x = 4 into the function. First, calculate 4² = 16. Then, multiply by 3 to get 48. Next, multiply -5 by 4 to get -20. Add 48, -20, and 2: 48 - 20 + 2 = 38. This problem tests understanding of function evaluation and applying the correct order of operations. Errors in exponentiation, multiplication, or sign handling can lead to incorrect answers. Carefully substituting values and simplifying correctly is key to solving function-based algebraic problems accurately.

30. Solve the simultaneous equation y =3x, 4y – 5x = 14

-2, -6

2,6

2,-6

-1,-3

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.

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.

31. Correct 0.04945 to two significant figures:

0.040

0.049

0.0495

0.050

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.

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.

32. A rectangular field is 50m long and 30m wide. If a 2m wide pathway is built along the inside boundary, what is the remaining area?

1,100 m²

1,256 m²

1,344 m²

1,450 m²

The total area of the field is 50 × 30 = 1,500 m². Since the pathway runs along the boundary, it reduces both dimensions by 4m (2m from each side). The new dimensions are 50 - 4 = 46m and 30 - 4 = 26m. The remaining area is 46 × 26 = 1,256 m². This problem requires understanding how a border affects area calculations. It is essential to subtract the total reduction in length and width before recalculating. Miscalculating the reduced dimensions can lead to wrong answers, so careful attention to details is important.

Explanation

The total area of the field is 50 × 30 = 1,500 m². Since the pathway runs along the boundary, it reduces both dimensions by 4m (2m from each side). The new dimensions are 50 - 4 = 46m and 30 - 4 = 26m. The remaining area is 46 × 26 = 1,256 m². This problem requires understanding how a border affects area calculations. It is essential to subtract the total reduction in length and width before recalculating. Miscalculating the reduced dimensions can lead to wrong answers, so careful attention to details is important.

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

4

4.5

6

Option 4

Explanation

34. Arrange in ascending order -2/3, -1/2, -3/4 and -4/5

-3/4, -1/2, -4/5, -2/3

-1/2, -3/4, -4/5, -2/3

-4/5, -3/4, -2/3, -1/2

-1/2, -2/3, -3/4, -4/5

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.

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.

35.

Solve for x, if 5^x= 5√5.

31/2

3/2

3/4

1/4

To solve the equation, we can express the square root as an exponent. The equation then becomes 5^x=5 3/2. This implies that the exponent x is equal to 3/2. So, the solution for x is 3/2, which is approximately 1.498 when expressed as a decimal.

Explanation

To solve the equation, we can express the square root as an exponent. The equation then becomes 5^x=5 3/2. This implies that the exponent x is equal to 3/2. So, the solution for x is 3/2, which is approximately 1.498 when expressed as a decimal.

36.

Solve for x: x²  + 2x + 1 = 25

-6,-4

6,-4

6,4

-6,4

Explanation

37. What is the mode of the numbers 8, 10, 9, 9, 10, 8, 11, 8, 10, 9, 8 and 14.

8

9

10

11

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.

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.

38.

Solve the equation 2x -1 = x + 9 

(A) x = 5        (B) x = 6 

(C) x = 9        (D) x = 10

Option 1

Option 2

Option 3

Option 4

not-available-via-ai

Explanation

not-available-via-ai

39. What is the value of the determinant of the matrix below? | 2 3 | | 4 5 |

2

-2

7

-7

To find the determinant of a 2x2 matrix:

| a b | | c d |

The formula for the determinant is:

ad - bc

For the given matrix:

| 2 3 | | 4 5 |

a = 2, b = 3, c = 4, d = 5

Determinant = (2 * 5) - (3 * 4) = 10 - 12 = -2

Explanation

To find the determinant of a 2x2 matrix:

| a b | | c d |

The formula for the determinant is:

ad - bc

For the given matrix:

| 2 3 | | 4 5 |

a = 2, b = 3, c = 4, d = 5

Determinant = (2 * 5) - (3 * 4) = 10 - 12 = -2

40. If the perimeter of a rectangle with dimensions (x + 1) meters by (2x + 5) meters is 36 meters, find the area of the rectangle.

65m2

84m2

124m2

51m2

Solution:

Step 1: Use the Perimeter Formula

The perimeter (P) of a rectangle is given by:

P = 2 × (Length + Width)

Substitute the given dimensions:

36 = 2 × ((x + 1) + (2x + 5))

Simplify inside the parentheses:

36 = 2 × (3x + 6)

Divide both sides by 2:

18 = 3x + 6

Step 2: Solve for x

Subtract 6 from both sides:

18 - 6 = 3x

12 = 3x

Divide by 3:

x = 4

Step 3: Find the Dimensions of the Rectangle

Now substitute x = 4 into the dimensions:

Length: (x + 1) = (4 + 1) = 5 m

Width: (2x + 5) = (2(4) + 5) = 8 + 5 = 13 m

Step 4: Calculate the Area of the Rectangle

The area (A) of a rectangle is given by:

A = Length × Width

Substitute the values:

A = 5 × 13 = 65 m²

Answer: The area of the rectangle is 65 m².

Explanation

Solution:

Step 1: Use the Perimeter Formula

The perimeter (P) of a rectangle is given by:

P = 2 × (Length + Width)

Substitute the given dimensions:

36 = 2 × ((x + 1) + (2x + 5))

Simplify inside the parentheses:

36 = 2 × (3x + 6)

Divide both sides by 2:

18 = 3x + 6

Step 2: Solve for x

Subtract 6 from both sides:

18 - 6 = 3x

12 = 3x

Divide by 3:

x = 4

Step 3: Find the Dimensions of the Rectangle

Now substitute x = 4 into the dimensions:

Length: (x + 1) = (4 + 1) = 5 m

Width: (2x + 5) = (2(4) + 5) = 8 + 5 = 13 m

Step 4: Calculate the Area of the Rectangle

The area (A) of a rectangle is given by:

A = Length × Width

Substitute the values:

A = 5 × 13 = 65 m²

Answer: The area of the rectangle is 65 m².

41.

Simplify 8ⁿ m 2²ⁿ ÷ 4³ⁿ

1/2(n)

2(1-n)

2n

2(n+1)

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.

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.

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

10 m

20 m

40 m

15 m

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.

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.

43.

If x and y are real numbers such that x^2 + y^2 = 25 and 2x + 3y = 10, what is the value of xy?

10

12

15

20

Start by solving the linear equation 2x + 3y = 10.

Express y in terms of x: y = (10 - 2x) / 3.

Substitute this expression for y into the equation x^2 + y^2 = 25: x^2 + [(10 - 2x) / 3]^2 = 25

Expand and simplify the equation, which leads to a quadratic equation in x.

Solve for x, then use the values of x to find y, and finally calculate xy.

The calculations reveal that xy = 12.

Explanation

Start by solving the linear equation 2x + 3y = 10.

Express y in terms of x: y = (10 - 2x) / 3.

Substitute this expression for y into the equation x^2 + y^2 = 25: x^2 + [(10 - 2x) / 3]^2 = 25

Expand and simplify the equation, which leads to a quadratic equation in x.

Solve for x, then use the values of x to find y, and finally calculate xy.

The calculations reveal that xy = 12.

44.

Simplify (³/₄ + ¹/₃) X 4¹/₃ – 3¹/₄

5/9

8/13

12/13

13/9

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.

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.

45. Which of the following is NOT a measure of central tendencies?

Median

Mean deviation

Decile

Mode

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.

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.

Mathematics Ss1 First Term Quiz