JSS2 Mathematics Quiz Questions And Answers

1) If two numbers are added together, what it is called?

Sum

Division

Multiplication

Subtraction

In mathematics, when you combine or add two or more numbers together, the result is called the "sum." The term "sum" refers to the total obtained by adding numbers. Here's a simple example:

If you have the numbers 3, 5, and 7, and you add them together:

3+5+7=15

Here, 15 is the sum of the numbers 3, 5, and 7. The process of adding these numbers is called addition, and the result is the sum.

So, in general terms, when you add or combine numbers using the "+" symbol, the outcome is referred to as the sum.

Explanation

In mathematics, when you combine or add two or more numbers together, the result is called the "sum." The term "sum" refers to the total obtained by adding numbers. Here's a simple example:

If you have the numbers 3, 5, and 7, and you add them together:

3+5+7=15

Here, 15 is the sum of the numbers 3, 5, and 7. The process of adding these numbers is called addition, and the result is the sum.

So, in general terms, when you add or combine numbers using the "+" symbol, the outcome is referred to as the sum.

2) How many lines of symmetry have a square?

3

4

5

6

A square has 4 lines of symmetry. Each line passes through the midpoints of opposite sides or diagonally through opposite corners. These lines divide the square into two equal halves. Thus, the number of lines of symmetry for a square is 4.

Explanation

A square has 4 lines of symmetry. Each line passes through the midpoints of opposite sides or diagonally through opposite corners. These lines divide the square into two equal halves. Thus, the number of lines of symmetry for a square is 4.

3) The following are polygons EXCEPT ___.

Circle

Quadrilateral

Hexagon

Heptagon

A "Circle" is not considered a polygon. The other options, "quadrilateral," "hexagon," and "heptagon," are polygons because they have straight sides and are made up of line segments. In contrast, a circle is a curved shape with no straight sides, and it is not classified as a polygon.

Explanation

A "Circle" is not considered a polygon. The other options, "quadrilateral," "hexagon," and "heptagon," are polygons because they have straight sides and are made up of line segments. In contrast, a circle is a curved shape with no straight sides, and it is not classified as a polygon.

4) The probability of a student passing JSSCE Mathematics is 70/100. What is the probability that the student will fail?

10/100

30/100

50/100

70/100

The total probability of all outcomes must add up to 1 or 100%. The probability of passing is 70/100, so the probability of failing is the complement of this. Subtract the probability of passing from 1:
1 - 70/100 = 30/100.
Therefore, the probability that the student will fail is 30/100. The other options are incorrect because they do not represent the correct complement to the passing probability.

Explanation

The total probability of all outcomes must add up to 1 or 100%. The probability of passing is 70/100, so the probability of failing is the complement of this. Subtract the probability of passing from 1:
1 - 70/100 = 30/100.
Therefore, the probability that the student will fail is 30/100. The other options are incorrect because they do not represent the correct complement to the passing probability.

5) Find the Simple Interest on ₦500.00 for 2 years at 4%.

₦30.00

₦40.00

₦50.00

₦60.00

The correct answer is B. ₦40.00. The formula to calculate simple interest is Principal x Rate x Time. In this case, the principal is ₦500.00, the rate is 4%, and the time is 2 years. Plugging these values into the formula, we get ₦500.00 x 0.04 x 2 = ₦40.00. Therefore, the simple interest on ₦500.00 for 2 years at 4% is ₦40.00.

Explanation

The correct answer is B. ₦40.00. The formula to calculate simple interest is Principal x Rate x Time. In this case, the principal is ₦500.00, the rate is 4%, and the time is 2 years. Plugging these values into the formula, we get ₦500.00 x 0.04 x 2 = ₦40.00. Therefore, the simple interest on ₦500.00 for 2 years at 4% is ₦40.00.

6) Round off 3.9695 to 2 decimal places.

3.98

3.97

3.96

3.95

To round off 3.9695 to two decimal places, we first look at the third decimal place, which is 9. Since 9 is greater than or equal to 5, we round the second decimal place up by 1. Therefore, 3.9695 rounded to two decimal places becomes 3.97. The other options are incorrect because they either round too low or do not follow the proper rounding rules.

Explanation

To round off 3.9695 to two decimal places, we first look at the third decimal place, which is 9. Since 9 is greater than or equal to 5, we round the second decimal place up by 1. Therefore, 3.9695 rounded to two decimal places becomes 3.97. The other options are incorrect because they either round too low or do not follow the proper rounding rules.

7) What is the correct name for one thousand billion?

One hundred

One billion

One gazillion

One trillion

One thousand billion is equal to one trillion. In the American numbering system, a billion is 1,000,000,000 (10⁹), and a trillion is 1,000,000,000,000 (10¹²). Therefore, one thousand billion equals one trillion. The other options are incorrect because they don't correctly represent the value of one thousand billion. Thus, the correct name for one thousand billion is "one trillion."

Explanation

One thousand billion is equal to one trillion. In the American numbering system, a billion is 1,000,000,000 (10⁹), and a trillion is 1,000,000,000,000 (10¹²). Therefore, one thousand billion equals one trillion. The other options are incorrect because they don't correctly represent the value of one thousand billion. Thus, the correct name for one thousand billion is "one trillion."

8) Find the HCF of 36 and 60.

12

14

16

18

The HCF (Highest Common Factor) of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF of 36 and 60, we can list all the factors of both numbers and find the largest one they have in common. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The largest factor they have in common is 12, so the correct answer is option 1.

Explanation

The HCF (Highest Common Factor) of two numbers is the largest number that divides both of them without leaving a remainder. To find the HCF of 36 and 60, we can list all the factors of both numbers and find the largest one they have in common. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The largest factor they have in common is 12, so the correct answer is option 1.

9) Express 18 as a product of its prime factors.

3x3=32

2x3x3=21x32

2x2x3x3 = 22x32

2x2x3=22x31

To find the prime factors of 18, divide it by the smallest prime number, 2: 18 ÷ 2 = 9. Next, divide 9 by 3: 9 ÷ 3 = 3. Divide again by 3: 3 ÷ 3 = 1. The prime factorization is 2 × 3 × 3 or 2¹ × 3².

Explanation

To find the prime factors of 18, divide it by the smallest prime number, 2: 18 ÷ 2 = 9. Next, divide 9 by 3: 9 ÷ 3 = 3. Divide again by 3: 3 ÷ 3 = 1. The prime factorization is 2 × 3 × 3 or 2¹ × 3².

10) What is the value of 96²?

62

72

91

81

The expression 9² represents 9 multiplied by itself. So, 9 × 9 = 81. This is the correct value of 9². The other options, 6226, 7226, 9216, and 7216, are incorrect as they do not match the result of 9², which is 81. Therefore, the correct answer is 81.

Explanation

The expression 9² represents 9 multiplied by itself. So, 9 × 9 = 81. This is the correct value of 9². The other options, 6226, 7226, 9216, and 7216, are incorrect as they do not match the result of 9², which is 81. Therefore, the correct answer is 81.

11) What is 30% of N900?

N270

N27

N90

N85

To find 30% of N900, multiply 900 by 0.30 (since 30% is the same as 30/100 or 0.30).

900 × 0.30 = 270.

Thus, 30% of N900 is N270. The other options are incorrect because they do not represent the correct calculation of 30% of N900.

Explanation

To find 30% of N900, multiply 900 by 0.30 (since 30% is the same as 30/100 or 0.30).

900 × 0.30 = 270.

Thus, 30% of N900 is N270. The other options are incorrect because they do not represent the correct calculation of 30% of N900.

12) Express 20% as a decimal number.

2.00

0.5

0.2

0.05

To express a percentage as a decimal number, you divide the percentage by 100. In this case, to express 20% as a decimal number, you divide 20 by 100, which equals 0.2. Therefore, the correct answer is option 3, 0.2.

Explanation

To express a percentage as a decimal number, you divide the percentage by 100. In this case, to express 20% as a decimal number, you divide 20 by 100, which equals 0.2. Therefore, the correct answer is option 3, 0.2.

13) Convert 1/3 to decimal fraction and give your answer to 4 decimal places.

0.3330

0.3333

0.3334

.

Explanation

.

14) The value of 7—(—15) is

-8

22

8

None of the above

.

Explanation

.

15) The LCM of 5ab² and 3a²b is:

Ab

3a/2b

5a3b3

15a2b2

The LCM (Least Common Multiple) of two numbers is the smallest number that is divisible by both numbers. In this case, the given numbers are 5ab2 and 3a2b. To find the LCM, we need to find the highest power of each variable that appears in either number. In this case, the highest power of 'a' is 2 and the highest power of 'b' is 2. Therefore, the LCM is 15a2b2, which is Option 4.

Explanation

The LCM (Least Common Multiple) of two numbers is the smallest number that is divisible by both numbers. In this case, the given numbers are 5ab2 and 3a2b. To find the LCM, we need to find the highest power of each variable that appears in either number. In this case, the highest power of 'a' is 2 and the highest power of 'b' is 2. Therefore, the LCM is 15a2b2, which is Option 4.

16) Express 0.000 000 000347 in standard form.

47 x 10-10

3.47 x 10-9

3.47 x 10-8

3.47 x 10-10

Explanation

17) Find the highest common factor of 325, 350, and 375

13

15

21

25

The highest common factor (HCF) of three numbers can be found by finding the factors of each number and then identifying the largest factor that is common to all three numbers. The factors of 325 are 1, 5, 13, 25, 65, and 325. The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350. The factors of 375 are 1, 3, 5, 15, 25, 75, and 375. The largest factor that is common to all three numbers is 25, so the correct answer is option D.

Explanation

The highest common factor (HCF) of three numbers can be found by finding the factors of each number and then identifying the largest factor that is common to all three numbers. The factors of 325 are 1, 5, 13, 25, 65, and 325. The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350. The factors of 375 are 1, 3, 5, 15, 25, 75, and 375. The largest factor that is common to all three numbers is 25, so the correct answer is option D.

18) John thinks of a number. 18 is subtracted from the number, the result gives – 2. What is the number?

14

16

18

20

Explanation

19) Complete the following sentence correctly. Vertically opposite angles ___.

Are equal

Add up to 1800

Are corresponding

Are alternate

Vertically opposite angles are equal. This is a basic property of intersecting lines, where two pairs of opposite angles are formed. These angles have the same measure and are considered congruent.

Explanation

Vertically opposite angles are equal. This is a basic property of intersecting lines, where two pairs of opposite angles are formed. These angles have the same measure and are considered congruent.

20) The product of 0.017 and 100 is ____________

0.00017

0.0017

0.017

1.7

To find the product of 0.017 and 100, you multiply the numbers. When you multiply 0.017 by 100, you shift the decimal point two places to the right, resulting in 1.7. The other options are incorrect because they either place the decimal in the wrong position or miscalculate the product. Therefore, the correct result of multiplying 0.017 by 100 is 1.7.

Explanation

To find the product of 0.017 and 100, you multiply the numbers. When you multiply 0.017 by 100, you shift the decimal point two places to the right, resulting in 1.7. The other options are incorrect because they either place the decimal in the wrong position or miscalculate the product. Therefore, the correct result of multiplying 0.017 by 100 is 1.7.

21) The reciprocal of x²is ___.

X-2

X2-

X2

1-x

The reciprocal of x^2 is x^-2 because when we take the reciprocal of a number, we flip it upside down. In this case, we are taking the reciprocal of x^2, so we flip it to get 1/x^2. To simplify this expression, we can bring the x^2 to the denominator by changing the sign of the exponent, resulting in x^-2.

Explanation

The reciprocal of x^2 is x^-2 because when we take the reciprocal of a number, we flip it upside down. In this case, we are taking the reciprocal of x^2, so we flip it to get 1/x^2. To simplify this expression, we can bring the x^2 to the denominator by changing the sign of the exponent, resulting in x^-2.

22) Find the reciprocal of 2.5 ___.

0.0004

0.004

0.04

0.4

The reciprocal of 2.5 is found by dividing 1 by 2.5: 1 ÷ 2.5 = 0.4. To simplify, write 2.5 as a fraction: 1 ÷ (5/2). Multiplying by the reciprocal: 1 × (2/5) = 2/5 = 0.4. Converting the decimal 2.5 into a fraction enables easier calculations, ensuring accuracy in deriving the reciprocal. The result is 0.4.

Explanation

The reciprocal of 2.5 is found by dividing 1 by 2.5: 1 ÷ 2.5 = 0.4. To simplify, write 2.5 as a fraction: 1 ÷ (5/2). Multiplying by the reciprocal: 1 × (2/5) = 2/5 = 0.4. Converting the decimal 2.5 into a fraction enables easier calculations, ensuring accuracy in deriving the reciprocal. The result is 0.4.

23) The number of pupils in a school is 875. If 350 are girls, what percentage of the pupils are boys?

16%

60%

25%

45%

The correct answer is B. 60%. Since the total number of pupils is 875 and 350 of them are girls, the number of boys can be found by subtracting the number of girls from the total number of pupils: 875 - 350 = 525. To find the percentage of boys, divide the number of boys by the total number of pupils and multiply by 100: (525 / 875) * 100 = 60%.

Explanation

The correct answer is B. 60%. Since the total number of pupils is 875 and 350 of them are girls, the number of boys can be found by subtracting the number of girls from the total number of pupils: 875 - 350 = 525. To find the percentage of boys, divide the number of boys by the total number of pupils and multiply by 100: (525 / 875) * 100 = 60%.

24) Simplify ab (a – b)

A2b – ab2

Ab2 – ab

Ab – a2b2

A2b – ab

To simplify the expression, we use the distributive property:

ab (a – b) = ab * a – ab * b

This simplifies to a²b – ab²

Explanation

To simplify the expression, we use the distributive property:

ab (a – b) = ab * a – ab * b

This simplifies to a²b – ab²

25) If N9 600 was shared among three boys Ola, Tope, and Jide in the ratio 3: 4: 5, respectively, what is Jide's share?

N2,400

N4,000

N950

N3,200

Jide's share can be found by dividing the total amount shared (N9,600) in the ratio of 3:4:5. To find Jide's share, we need to find the fraction of the total amount that corresponds to his ratio. The fraction for Jide is 5 out of the total ratio of 3+4+5, which is 12. Therefore, Jide's share is (5/12) * N9,600 = N4,000.

Explanation

Jide's share can be found by dividing the total amount shared (N9,600) in the ratio of 3:4:5. To find Jide's share, we need to find the fraction of the total amount that corresponds to his ratio. The fraction for Jide is 5 out of the total ratio of 3+4+5, which is 12. Therefore, Jide's share is (5/12) * N9,600 = N4,000.

26) Number 1, 2, 3, 4, 5, 6 ___ are called.

Recurring decimal

Whole number

Natural number

Integers

Natural numbers are positive integers starting from 1 (1, 2, 3, …). These numbers are used for counting and exclude zero, fractions, and negative numbers. Unlike integers or whole numbers, natural numbers represent only positive, whole values without a zero. The set 1, 2, 3, etc., does not include negatives or decimals, making it distinct from other number groups. Since 1, 2, 3, etc., are part of this set, the correct classification is natural numbers.

Explanation

Natural numbers are positive integers starting from 1 (1, 2, 3, …). These numbers are used for counting and exclude zero, fractions, and negative numbers. Unlike integers or whole numbers, natural numbers represent only positive, whole values without a zero. The set 1, 2, 3, etc., does not include negatives or decimals, making it distinct from other number groups. Since 1, 2, 3, etc., are part of this set, the correct classification is natural numbers.

27) Simplify X⁶÷X³

X5

X4

X3

X2

The expression X6/X3 can be simplified by dividing the exponents. When dividing variables with the same base, you subtract the exponents. Therefore, X6/X3 is equal to X6-3, which simplifies to X3.

Explanation

The expression X6/X3 can be simplified by dividing the exponents. When dividing variables with the same base, you subtract the exponents. Therefore, X6/X3 is equal to X6-3, which simplifies to X3.

28) If a = 2, put (>, <,

,

or =) in the box for the inequality below: -23___ -45

>

≥

<

=

When a = 2, the inequality is -23 compared to -45. Since -23 is greater than -45 on the number line, the correct symbol to place between -23 and -45 is ">". This means that -23 is indeed greater than -45. Therefore, the correct symbol is ">", indicating that -23 is larger than

Explanation

When a = 2, the inequality is -23 compared to -45. Since -23 is greater than -45 on the number line, the correct symbol to place between -23 and -45 is ">". This means that -23 is indeed greater than -45. Therefore, the correct symbol is ">", indicating that -23 is larger than

29) Express as a single number: 3.8 x 10⁴– 9.7 x 10

37903

28700

59700

49700

Explanation

30) Find the mean score of these scores: 2, 3, 0, 8, 7, 5, 9, 6

3.75

5.50

5.00

4.00

The mean score is calculated by adding all the scores together and then dividing the sum by the total number of scores. In this case, the sum of the scores is 2+3+0+8+7+5+9+6=40. Since there are 8 scores, the mean score is 40/8=5.00. Therefore, the correct answer is C. 5.00.

Explanation

The mean score is calculated by adding all the scores together and then dividing the sum by the total number of scores. In this case, the sum of the scores is 2+3+0+8+7+5+9+6=40. Since there are 8 scores, the mean score is 40/8=5.00. Therefore, the correct answer is C. 5.00.

31) Express 6561 in index form.

93

94

95

96

To express 6561 in index form, we need to find a number that, when raised to a power, results in 6561. By trial or calculation, we find that 9 raised to the power of 4 gives 6561 (9 × 9 × 9 × 9 = 6561). Therefore, the correct index form of 6561 is 9⁴. This demonstrates how powers work to express repeated multiplication in a simpler form.

Explanation

To express 6561 in index form, we need to find a number that, when raised to a power, results in 6561. By trial or calculation, we find that 9 raised to the power of 4 gives 6561 (9 × 9 × 9 × 9 = 6561). Therefore, the correct index form of 6561 is 9⁴. This demonstrates how powers work to express repeated multiplication in a simpler form.

32) Simplify ( x/3)²

2x/3

X2/9

X2/6

X2/3

To simplify (x/3)², you square both the numerator and denominator. The numerator, x, squared is x², and the denominator, 3, squared is 9. Therefore, the simplified expression becomes x²/9. This shows how exponents apply to both the numerator and denominator separately, resulting in the final simplified form.

Explanation

To simplify (x/3)², you square both the numerator and denominator. The numerator, x, squared is x², and the denominator, 3, squared is 9. Therefore, the simplified expression becomes x²/9. This shows how exponents apply to both the numerator and denominator separately, resulting in the final simplified form.

33) Find the probability of choosing a vowel from ‘KETU–LAGOS’.

1/9

2/9

1/2

4/9

The given question asks for the probability of choosing a vowel from the given word "KETU-LAGOS". To find the probability, we need to count the number of vowels in the word and divide it by the total number of letters in the word. The word "KETU-LAGOS" has a total of 10 letters, out of which there are 4 vowels (E, U, A, O). Therefore, the probability of choosing a vowel from the given word is 4/10, which simplifies to 2/5 or 4/9.

Explanation

The given question asks for the probability of choosing a vowel from the given word "KETU-LAGOS". To find the probability, we need to count the number of vowels in the word and divide it by the total number of letters in the word. The word "KETU-LAGOS" has a total of 10 letters, out of which there are 4 vowels (E, U, A, O). Therefore, the probability of choosing a vowel from the given word is 4/10, which simplifies to 2/5 or 4/9.

34)

Which of the following fractions is the smallest fraction: 3/4, 5/6, 1/2 and 12/15?

12/15

1/2

5/6

3/4

To compare fractions, we need to find a common denominator. The least common denominator for 4, 6, 2, and 15 is 60. Converting each fraction to have a denominator of 60, we get:

3/4 = 45/60

5/6 = 50/60

1/2 = 30/60

12/15 = 48/60

The smallest fraction is the one with the smallest numerator, which is 1/2.

Explanation

To compare fractions, we need to find a common denominator. The least common denominator for 4, 6, 2, and 15 is 60. Converting each fraction to have a denominator of 60, we get:

3/4 = 45/60

5/6 = 50/60

1/2 = 30/60

12/15 = 48/60

The smallest fraction is the one with the smallest numerator, which is 1/2.

35) If a rectangle has a length of 10 cm and a width of 5 cm, what is the perimeter of the rectangle?

15 cm

30 cm

25 cm

20 cm

Explanation

36) Solve the equation 2 ½ = 1/y

1/5

3/5

2/5

4/5

The equation 2 ½ = 1/y can be solved by multiplying both sides of the equation by y. This eliminates the fraction on the left side of the equation. The equation becomes 2y = 1. To isolate y, divide both sides of the equation by 2. This gives y = 1/2. However, this is not one of the answer options provided. Therefore, the correct answer is not available.

Explanation

The equation 2 ½ = 1/y can be solved by multiplying both sides of the equation by y. This eliminates the fraction on the left side of the equation. The equation becomes 2y = 1. To isolate y, divide both sides of the equation by 2. This gives y = 1/2. However, this is not one of the answer options provided. Therefore, the correct answer is not available.

37) Express 0.0001 in standard form.

1 x 104

1 x 103

1 x 10-3

1 x 10-4

In standard form, a number is written as a coefficient between 1 and 10, multiplied by a power of 10. For 0.0001, we move the decimal point four places to the right, making it 1 x 10⁻⁴. This represents the number in standard form. The other options are incorrect because they do not correctly reflect the position of the decimal point for 0.0001.

Explanation

In standard form, a number is written as a coefficient between 1 and 10, multiplied by a power of 10. For 0.0001, we move the decimal point four places to the right, making it 1 x 10⁻⁴. This represents the number in standard form. The other options are incorrect because they do not correctly reflect the position of the decimal point for 0.0001.

38) Mr. Ojo made a profit of 32% on an article he bought for N3,200.00. How much did he sell the article?

N2,024.00

N2,176.00

N3,200.00

N4,224.00

Explanation

39) If 13 is the mean of the following set of numbers: 12, 11, 14, and x, what is the value of x?

11

12

13

15

Option iii: (1/4x + 2) is the correct answer. This is because (x+8)/4 can be simplified as (1/4)x + (8/4), which is equal to (1/4x + 2). Option i: 1/4(x + 8) is incorrect because it expands the expression instead of simplifying it. Option ii: (x + 2) is also incorrect because it does not include the division by 4.

Explanation

Option iii: (1/4x + 2) is the correct answer. This is because (x+8)/4 can be simplified as (1/4)x + (8/4), which is equal to (1/4x + 2). Option i: 1/4(x + 8) is incorrect because it expands the expression instead of simplifying it. Option ii: (x + 2) is also incorrect because it does not include the division by 4.

40) Express 675 000 000 in a standard form.

6.75 x 108

6.75 x 107

6.75 x 106

6.75 x 105

The correct answer is A. 6.75 x 10^8. This is because in standard form, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. So, 675,000,000 can be written as 6.75 multiplied by 100,000,000, which can be further simplified to 6.75 x 10^8.

Explanation

The correct answer is A. 6.75 x 10^8. This is because in standard form, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. So, 675,000,000 can be written as 6.75 multiplied by 100,000,000, which can be further simplified to 6.75 x 10^8.

41) A trader buys a gallon of palm oil for N1,500.00 and sells it at a profit of 10%. Calculate the selling price.

N1,750.00

N1,650.00

N1,550.00

N1,450.00

Selling price = cost price + profit. Profit = cost price × profit %. Here, profit = 1500 × 10/100 = 150. Add this to the cost price: 1500 + 150 = 1650. The calculation breaks into two steps: determining the profit and adding it to the cost. Thus, the selling price is 1650.

Explanation

Selling price = cost price + profit. Profit = cost price × profit %. Here, profit = 1500 × 10/100 = 150. Add this to the cost price: 1500 + 150 = 1650. The calculation breaks into two steps: determining the profit and adding it to the cost. Thus, the selling price is 1650.

42) These numbers are square numbers except.

324

224

196

169

The given numbers are 324, 224, 196, and 169. To determine which number is not a square number, we need to find the square root of each number. The square root of 324 is 18, the square root of 224 is not a whole number, the square root of 196 is 14, and the square root of 169 is 13. Since the square root of 224 is not a whole number, it is not a square number.

Explanation

The given numbers are 324, 224, 196, and 169. To determine which number is not a square number, we need to find the square root of each number. The square root of 324 is 18, the square root of 224 is not a whole number, the square root of 196 is 14, and the square root of 169 is 13. Since the square root of 224 is not a whole number, it is not a square number.

43) If 15 men dig a trench for 10 days, how many men will be required to dig the trench in 2 days?

150 men

75 men

60 men

30 men

Explanation

44) Factorize 24pz – 8pr.

8p (3z –r)

8p (z – 3r)

8p (3z + r)

(8p (4z – r)

The given expression can be factorized as 8p(3z - r). This can be done by factoring out the greatest common factor, which is 8p, from both terms in the expression. The remaining terms inside the parentheses are (3z - r), which cannot be simplified further. Therefore, the correct factorization is 8p(3z - r).

Explanation

The given expression can be factorized as 8p(3z - r). This can be done by factoring out the greatest common factor, which is 8p, from both terms in the expression. The remaining terms inside the parentheses are (3z - r), which cannot be simplified further. Therefore, the correct factorization is 8p(3z - r).

45) The value of the 4 in 26.645 is ___

4 thousandth

4 hundredths

4 tenths

Option 4

The value of the 4 in 26.645 is 4 hundredths. This is because the digit 4 is in the hundredths place, which is two places to the right of the decimal point. In decimal notation, each place value to the right of the decimal point represents a fraction of the whole number. Therefore, the digit 4 in this number represents 4 out of 100, or 0.04.

Explanation

The value of the 4 in 26.645 is 4 hundredths. This is because the digit 4 is in the hundredths place, which is two places to the right of the decimal point. In decimal notation, each place value to the right of the decimal point represents a fraction of the whole number. Therefore, the digit 4 in this number represents 4 out of 100, or 0.04.

46) Factorize 81 + 18a + a.

(a+9) (a-9)

(a+9) (a+9)

(a+3) (a+27)

(a+1)(a+81)

To factorize the given expression, 81 + 18a + a^2, we need to find two binomials that, when multiplied, produce the given expression.

Let's consider the given options:

(a+9)(a-9): When multiplied, this would result in a^2 - 81, which is different from the given expression.

(a+9)(a+9): When multiplied, this would result in a^2 + 18a + 81, which matches the given expression.

(a+3)(a+27): When multiplied, this would result in a^2 + 30a + 81, which is different from the given expression.

(a+1)(a+81): When multiplied, this would result in a^2 + 82a + 81, which is different from the given expression.

Therefore, the correct factorization of 81 + 18a + a^2 is (a+9)(a+9).

Explanation

To factorize the given expression, 81 + 18a + a^2, we need to find two binomials that, when multiplied, produce the given expression.

Let's consider the given options:

(a+9)(a-9): When multiplied, this would result in a^2 - 81, which is different from the given expression.

(a+9)(a+9): When multiplied, this would result in a^2 + 18a + 81, which matches the given expression.

(a+3)(a+27): When multiplied, this would result in a^2 + 30a + 81, which is different from the given expression.

(a+1)(a+81): When multiplied, this would result in a^2 + 82a + 81, which is different from the given expression.

Therefore, the correct factorization of 81 + 18a + a^2 is (a+9)(a+9).

47) Find the product of the square root of 16 and the square of 9 is

3240

1296

324

144

The square root of 16 is 4, and the square of 9 is 81. Multiplying these results gives 4 * 81 = 324. Therefore, the correct answer is 324. The other options are incorrect as they do not match the correct product of 4 and 81.

Explanation

The square root of 16 is 4, and the square of 9 is 81. Multiplying these results gives 4 * 81 = 324. Therefore, the correct answer is 324. The other options are incorrect as they do not match the correct product of 4 and 81.

48) How many faces have a cylinder?

1

2

3

5

A cylinder has two circular faces, one at the top and one at the bottom. These are the flat surfaces of the cylinder. The curved surface that wraps around the sides is not considered a face in the context of counting faces.

Explanation

A cylinder has two circular faces, one at the top and one at the bottom. These are the flat surfaces of the cylinder. The curved surface that wraps around the sides is not considered a face in the context of counting faces.

49) Find the area of triangles of height 5cm, and base 7cm.

17.5cm2

15.7cm2

18cm2

35cm2

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 length is 7cm and the height is 5cm. So, the area of the triangle is (7 * 5) / 2 = 17.5cm2.

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 length is 7cm and the height is 5cm. So, the area of the triangle is (7 * 5) / 2 = 17.5cm2.

50) In bisecting any line, the following are required.

A ruler and a pair of dividers

A ruler and protractor

A ruler and a pair of compasses

A ruler and pencil

To bisect any line, a ruler and a pair of compasses are required. A ruler is needed to measure the length of the line accurately, while a pair of compasses is used to draw arcs that intersect the line at two points. The midpoint of the line is then determined by drawing a straight line connecting the two points of intersection. A protractor is not necessary for bisecting a line, as it is used for measuring angles. A pencil is a common tool used for drawing, but it is not specifically required for bisecting a line.

Explanation

To bisect any line, a ruler and a pair of compasses are required. A ruler is needed to measure the length of the line accurately, while a pair of compasses is used to draw arcs that intersect the line at two points. The midpoint of the line is then determined by drawing a straight line connecting the two points of intersection. A protractor is not necessary for bisecting a line, as it is used for measuring angles. A pencil is a common tool used for drawing, but it is not specifically required for bisecting a line.

51) A pack of cards has ___ unbiased cards.

50

52

54

58

A standard deck of playing cards contains 52 unbiased cards. This means that the deck is designed and manufactured to ensure that each card in the deck is equally likely to be drawn or dealt, with no preference or bias towards any particular card. The deck is carefully arranged to have a balanced distribution of suits (hearts, diamonds, clubs, and spades) and face values (numbered cards and face cards like kings, queens, and jacks).

Explanation

A standard deck of playing cards contains 52 unbiased cards. This means that the deck is designed and manufactured to ensure that each card in the deck is equally likely to be drawn or dealt, with no preference or bias towards any particular card. The deck is carefully arranged to have a balanced distribution of suits (hearts, diamonds, clubs, and spades) and face values (numbered cards and face cards like kings, queens, and jacks).

52) The lowest common denominator of 1/4, 2/3, 4/5, 5/6 and 5/10 and is ___.

900

90

50

60

The lowest common denominator of a set of fractions is the smallest number that each denominator can divide into evenly. In this case, the denominators are 4, 3, 5, 6, and 10. The lowest common denominator for these numbers is 60, as it is the smallest number that all of these denominators can divide into evenly.

Explanation

The lowest common denominator of a set of fractions is the smallest number that each denominator can divide into evenly. In this case, the denominators are 4, 3, 5, 6, and 10. The lowest common denominator for these numbers is 60, as it is the smallest number that all of these denominators can divide into evenly.

53) Numbers that cannot be expressed as fractions are called ___

Recurring numbers

Decimal numbers

Irrational numbers

Rational numbers

Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have decimal representations that neither terminate nor repeat. Some famous examples of irrational numbers include pi (π) and the square root of 2.

Explanation

Irrational numbers are numbers that cannot be expressed as a fraction of two integers. They have decimal representations that neither terminate nor repeat. Some famous examples of irrational numbers include pi (π) and the square root of 2.

54) Factorize x² – 1.

(x-1) (x+1)

(x-1) (x -1)

(x+1) (x+1)

X (x – 1)

The expression x² - 1 is a difference of squares, and it can be factored using the formula a² - b² = (a - b)(a + b). In this case, x² - 1 can be factored as (x - 1)(x + 1), which is the correct factorization. The other options are incorrect because they don't follow the difference of squares rule. Thus, the factorization of x² - 1 is (x - 1)(x + 1).

Explanation

The expression x² - 1 is a difference of squares, and it can be factored using the formula a² - b² = (a - b)(a + b). In this case, x² - 1 can be factored as (x - 1)(x + 1), which is the correct factorization. The other options are incorrect because they don't follow the difference of squares rule. Thus, the factorization of x² - 1 is (x - 1)(x + 1).

55) The first three prime numbers are:

1, 2, 3

1, 3, 5

3, 5, 7

2, 3, 5

The value of the 4 in 26.645 is 4 hundredths. This is because the digit 4 is in the hundredths place, which is two places to the right of the decimal point. In decimal notation, each place value to the right of the decimal point represents a fraction of the whole number. Therefore, the digit 4 in this number represents 4 out of 100, or 0.04.

Explanation

The value of the 4 in 26.645 is 4 hundredths. This is because the digit 4 is in the hundredths place, which is two places to the right of the decimal point. In decimal notation, each place value to the right of the decimal point represents a fraction of the whole number. Therefore, the digit 4 in this number represents 4 out of 100, or 0.04.

56)

Increase 12 by 30%.

33.6

40

15.6

156

To increase a number by a certain percentage, you can multiply the number by 1 plus the percentage as a decimal. In this case, to increase 12 by 30%, you would calculate 12 * (1 + 0.30) = 12 * 1.30 = 15.6. Therefore, the correct answer is option C, 15.6.

Explanation

To increase a number by a certain percentage, you can multiply the number by 1 plus the percentage as a decimal. In this case, to increase 12 by 30%, you would calculate 12 * (1 + 0.30) = 12 * 1.30 = 15.6. Therefore, the correct answer is option C, 15.6.

57) Evaluate 2p – (p – 2p).

0

P

3p

2p

Explanation

58) The least number by which 112 must be multiplied to give a perfect square is __

2

3

7

5

To find the least number by which 112 must be multiplied to give a perfect square, we need to find the prime factors of 112. The prime factorization of 112 is 2 * 2 * 2 * 2 * 7. In order for the number to be a perfect square, each prime factor must have an even exponent. The exponent of 2 is already even, but the exponent of 7 is 1, which is odd. Therefore, we need to multiply 112 by 7 to make the exponent of 7 even. Hence, the correct answer is option C.

Explanation

To find the least number by which 112 must be multiplied to give a perfect square, we need to find the prime factors of 112. The prime factorization of 112 is 2 * 2 * 2 * 2 * 7. In order for the number to be a perfect square, each prime factor must have an even exponent. The exponent of 2 is already even, but the exponent of 7 is 1, which is odd. Therefore, we need to multiply 112 by 7 to make the exponent of 7 even. Hence, the correct answer is option C.

59) Evaluate (2a-3b)/5c, given that
a = 2, b = -2, c = 1

-2

-1

0

Option 4

Substituting the given values into the expression, we get:

(2(2) - 3(-2)) / 5(1) = (4 + 6) / 5 = 10 / 5 = 2.

Thus, the correct answer is 2. The other options are incorrect because they do not match the result of the calculation.

Explanation

Substituting the given values into the expression, we get:

(2(2) - 3(-2)) / 5(1) = (4 + 6) / 5 = 10 / 5 = 2.

Thus, the correct answer is 2. The other options are incorrect because they do not match the result of the calculation.

60) If 2x⁰and 4x⁰are supplementary angles. What is the value of x?

10

20

30

40

If two angles are supplementary, it means that the sum of their measures is 180 degrees.

In this case, you have two angles: 2x and 4x.

So, you can write the equation:

2x + 4x = 180

Combine like terms:

6x = 180

Now, divide both sides by 6 to solve for x:

6x/6 = 180/6

x = 30

So, the value of x is 30.

Explanation

If two angles are supplementary, it means that the sum of their measures is 180 degrees.

In this case, you have two angles: 2x and 4x.

So, you can write the equation:

2x + 4x = 180

Combine like terms:

6x = 180

Now, divide both sides by 6 to solve for x:

6x/6 = 180/6

x = 30

So, the value of x is 30.

61) Which of these is NOT a plane shape?

Circle

Polygon

Sphere

Trapezium

A plane shape is a two-dimensional figure that lies flat on a plane, such as a circle, polygon, or trapezium. A sphere, however, is a three-dimensional object with volume and surface area. It does not lie flat on a plane and, therefore, is not a plane shape. The other options (circle, polygon, and trapezium) are all plane shapes because they exist in two dimensions. Thus, the correct answer is a sphere, which is a 3D shape.

Explanation

A plane shape is a two-dimensional figure that lies flat on a plane, such as a circle, polygon, or trapezium. A sphere, however, is a three-dimensional object with volume and surface area. It does not lie flat on a plane and, therefore, is not a plane shape. The other options (circle, polygon, and trapezium) are all plane shapes because they exist in two dimensions. Thus, the correct answer is a sphere, which is a 3D shape.

62)

Simplify (-4  X -2  X -3)/(-2 X  6)

-1/2

-2

-3

2

First, calculate the numerator: (-4) × (-2) × (-3) = -24. Then, calculate the denominator: (-2) × 6 = -12. Divide: (-24) ÷ (-12) = -2. The negative signs cancel out during division. Thus, the simplified value is -2.

Explanation

First, calculate the numerator: (-4) × (-2) × (-3) = -24. Then, calculate the denominator: (-2) × 6 = -12. Divide: (-24) ÷ (-12) = -2. The negative signs cancel out during division. Thus, the simplified value is -2.

63) If the sum of three consecutive even integers is 114, what is the largest of these integers?

36

38

40

42

Let's call the first even integer x. Since they are consecutive even integers, the second integer would be x+2 and the third integer would be x+4. The sum of these three integers is 114. So the equation would be:

x + (x+2) + (x+4) = 114 3x + 6 = 114 3x = 108 x = 36 (dividing both sides by 3) The largest of these integers would be x+4 which is equal to x+4=36+4=40. Therefore the largest integer is 40.

Explanation

Let's call the first even integer x. Since they are consecutive even integers, the second integer would be x+2 and the third integer would be x+4. The sum of these three integers is 114. So the equation would be:

x + (x+2) + (x+4) = 114 3x + 6 = 114 3x = 108 x = 36 (dividing both sides by 3) The largest of these integers would be x+4 which is equal to x+4=36+4=40. Therefore the largest integer is 40.

64) What is the sum of the first 20 odd numbers?

200

400

600

800

The first 20 odd numbers form an arithmetic progression with the first term being 1, the common difference being 2, and the number of terms being 20. The sum 'S' of an arithmetic progression is given by S = n/2 [2a + (n-1)d], where 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference. 1 Substituting these values into the formula gives S = 20/2 [2(1) + (20-1)2] = 10 (2 + 38) = 10 (40) = 400.

Explanation

The first 20 odd numbers form an arithmetic progression with the first term being 1, the common difference being 2, and the number of terms being 20. The sum 'S' of an arithmetic progression is given by S = n/2 [2a + (n-1)d], where 'n' is the number of terms, 'a' is the first term, and 'd' is the common difference. 1 Substituting these values into the formula gives S = 20/2 [2(1) + (20-1)2] = 10 (2 + 38) = 10 (40) = 400.

65) What is the value of x in the equation 3x + 5 = 14?

2

3

4

5

The equation 3x + 5 = 14 is a linear equation with one variable, x. To solve for x, we need to isolate it on one side of the equation. First, subtract 5 from both sides to get 3x = 9. Then, divide both sides by 3 to get x = 3. Therefore, the value of x that satisfies the equation is 3.

Explanation

The equation 3x + 5 = 14 is a linear equation with one variable, x. To solve for x, we need to isolate it on one side of the equation. First, subtract 5 from both sides to get 3x = 9. Then, divide both sides by 3 to get x = 3. Therefore, the value of x that satisfies the equation is 3.

66) The sum of x in minutes and y seconds expressed in minutes is ___.

60x + y

X + 60y

X + y

X + y/60

The correct answer is D. x + y/60. This is because when converting seconds to minutes, we divide the number of seconds by 60. So, to express the sum of x minutes and y seconds in minutes, we add x to the quotient of y divided by 60.

Explanation

The correct answer is D. x + y/60. This is because when converting seconds to minutes, we divide the number of seconds by 60. So, to express the sum of x minutes and y seconds in minutes, we add x to the quotient of y divided by 60.

67) The point where the x-axis crosses the y-axis in a graph is called ___

Cartesian

Intersection

Origin

Ordered pairs

The point where the x-axis crosses the y-axis in a graph is called the origin. In a coordinate plane, the origin is represented by the coordinates (0, 0), where both x and y are zero. This is the point of intersection of the x-axis and y-axis. The other options are incorrect, as "Cartesian" refers to the coordinate system, "intersection" is a general term, and "ordered pairs" refer to coordinates.

Explanation

The point where the x-axis crosses the y-axis in a graph is called the origin. In a coordinate plane, the origin is represented by the coordinates (0, 0), where both x and y are zero. This is the point of intersection of the x-axis and y-axis. The other options are incorrect, as "Cartesian" refers to the coordinate system, "intersection" is a general term, and "ordered pairs" refer to coordinates.

68) The difference between the median and the mode of the following set of numbers: 7, 4, 9, 5, 6, 7, 8, 7, 4,6, 5 is ___.

-2

-1

0

1

To find the median, we first need to arrange the numbers in ascending order: 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 9. There are 11 numbers in this set, which is an odd number, so the median is the middle value, which is 6. The mode is the number that appears most frequently in the set. In this case, the number 7 appears three times, which is more frequent than any other number in the set. Now, let's calculate the difference between the median and the mode:

Median (6) - Mode (7) = 6 - 7 = -1

So, the difference between the median and the mode of the given set of numbers is -1, which corresponds to option B.

Explanation

To find the median, we first need to arrange the numbers in ascending order: 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 9. There are 11 numbers in this set, which is an odd number, so the median is the middle value, which is 6. The mode is the number that appears most frequently in the set. In this case, the number 7 appears three times, which is more frequent than any other number in the set. Now, let's calculate the difference between the median and the mode:

Median (6) - Mode (7) = 6 - 7 = -1

So, the difference between the median and the mode of the given set of numbers is -1, which corresponds to option B.

69) Express 1740m in km, leaving your answer in standard form.

1.74 x 10 to the power of 0 km

1.74 x 10 to the power of 1 km

1.74 x 10 to the power of 2 km

1.74 x 10 to the power of 3 km

To convert meters to kilometers, divide by 1000 because 1 kilometer equals 1000 meters.

1740 divided by 1000 equals 1.74 kilometers.

In standard form, numbers between 1 and 10 are written as a number multiplied by 10 to the power of 0.

So, 1.74 kilometers = 1.74 x 10 to the power of 0 kilometers.

Explanation

To convert meters to kilometers, divide by 1000 because 1 kilometer equals 1000 meters.

1740 divided by 1000 equals 1.74 kilometers.

In standard form, numbers between 1 and 10 are written as a number multiplied by 10 to the power of 0.

So, 1.74 kilometers = 1.74 x 10 to the power of 0 kilometers.

70) What is the slope of the line represented by the equation y = 2x - 4?

2

-4

1/2

-2

The equation y = 2x - 4 is in the form y = mx + c, where 'm' represents the slope and 'c' represents the y-intercept. This form is known as the slope-intercept form because it directly shows the slope and y-intercept of the line. By comparing the given equation with the slope-intercept form, we can see that the coefficient of x is 2, which is the slope of the line.

Explanation

The equation y = 2x - 4 is in the form y = mx + c, where 'm' represents the slope and 'c' represents the y-intercept. This form is known as the slope-intercept form because it directly shows the slope and y-intercept of the line. By comparing the given equation with the slope-intercept form, we can see that the coefficient of x is 2, which is the slope of the line.

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