MATHEMATICS JSS 2

1. 58. If two or more numbers are added together, it's called ___

A. Difference

B. Sum

C. Product

D. Division

When two or more numbers are added together, the result is called the "sum" of the numbers. The sum is the total of all the numbers combined.

Explanation

When two or more numbers are added together, the result is called the "sum" of the numbers. The sum is the total of all the numbers combined.

2. 7. The following are polygons EXCEPT ___

A. Circle A. Circle

B. quadrilateral

C. hexagon

D. heptagon

Option 5

Option 6

A circle is not considered a polygon because it does not have straight sides. A polygon is defined as a closed figure with straight sides. Quadrilaterals, hexagons, and heptagons all have straight sides and are therefore polygons.

Explanation

A circle is not considered a polygon because it does not have straight sides. A polygon is defined as a closed figure with straight sides. Quadrilaterals, hexagons, and heptagons all have straight sides and are therefore polygons.

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

A. 0.3330

B. 0.3333

C. 0.3334

D. 0.4444

Option 5

Option 6

To convert 1/3 to a decimal fraction, we divide 1 by 3. The result is 0.3333, which is a recurring decimal that goes on indefinitely. Since the question asks for the answer to 4 decimal places, we round the recurring decimal to 0.3333.

Explanation

To convert 1/3 to a decimal fraction, we divide 1 by 3. The result is 0.3333, which is a recurring decimal that goes on indefinitely. Since the question asks for the answer to 4 decimal places, we round the recurring decimal to 0.3333.

4. 31. What is the value of 96²?

A. 6226

B. 7226

C. 9216

D. 7216

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Explanation

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5. 18, The probability of a student passing JSSCE Mathematics is 70/100. What is the probability that the student will fail?

A. 10/100

B. 30/100

C. 50/100

D. 70/100

The probability of passing is given as 70/100. Since the sum of the probabilities of all possible outcomes must equal 1, the probability of failing can be calculated by subtracting the probability of passing from 1. Therefore, the probability of failing is 1 - 70/100 = 30/100, which is equivalent to 3/10 or 0.3. Therefore, the correct answer is B. 30/100.

Explanation

The probability of passing is given as 70/100. Since the sum of the probabilities of all possible outcomes must equal 1, the probability of failing can be calculated by subtracting the probability of passing from 1. Therefore, the probability of failing is 1 - 70/100 = 30/100, which is equivalent to 3/10 or 0.3. Therefore, the correct answer is B. 30/100.

6. 28. 30% of N900

A. N270

B. N27

C. N90

D. 290A

30% of N900 is equal to 0.30 * N900 = N270.

Explanation

30% of N900 is equal to 0.30 * N900 = N270.

7. 14. Find the product of the square root of 16 and the square of 9 is

A. 3240

B. 1296

C. 324

D. 144C

The product of the square root of 16 and the square of 9 can be calculated as follows: √16 * 9^2 = 4 * 81 = 324. Therefore, the correct answer is C. 324.

Explanation

The product of the square root of 16 and the square of 9 can be calculated as follows: √16 * 9^2 = 4 * 81 = 324. Therefore, the correct answer is C. 324.

8. 25. Express 6561 in index form.

A. 93

B. 94

C. 95

D. 96

The correct answer is B. 94. In index form, a number is expressed as a base raised to a power. In this case, 6561 can be expressed as 9^4, which means 9 raised to the power of 4.

Explanation

The correct answer is B. 94. In index form, a number is expressed as a base raised to a power. In this case, 6561 can be expressed as 9^4, which means 9 raised to the power of 4.

9. 9. How many faces have a cylinder?

A. 1

B. 2

C. 3

D. 5

A cylinder has two faces. The two faces are the circular bases of the cylinder. These bases are congruent and parallel to each other.

Explanation

A cylinder has two faces. The two faces are the circular bases of the cylinder. These bases are congruent and parallel to each other.

10. 57.

Find the probability of choosing a vowel from 'KETU – LAGOS'.

A. 1/9

B. 2 /9

C. 1 /2

D. 4/9

The probability of choosing a vowel from the given set of letters can be found by counting the number of vowels (E, U, A, O) and dividing it by the total number of letters (9). There are 4 vowels and 9 total letters, so the probability is 4/9.

Explanation

The probability of choosing a vowel from the given set of letters can be found by counting the number of vowels (E, U, A, O) and dividing it by the total number of letters (9). There are 4 vowels and 9 total letters, so the probability is 4/9.

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

A. N2, 400

B. N4, 000

C. N950

D. N3, 200

The ratio of Jide's share to the total amount is 5/12 (5 parts out of 12 total parts). Therefore, Jide's share can be calculated by multiplying the total amount by the ratio: (5/12) * N9,600 = N4,000. Therefore, Jide's share is N4,000.

Explanation

The ratio of Jide's share to the total amount is 5/12 (5 parts out of 12 total parts). Therefore, Jide's share can be calculated by multiplying the total amount by the ratio: (5/12) * N9,600 = N4,000. Therefore, Jide's share is N4,000.

12. 44. Find the mean score of these scores: 2, 3, 0, 8, 7, 5, 9, 6

A. 3.75

B. 5.50

C. 5.00

D. 4.00

To find the mean score, we need to add up all the scores and then divide by the total number of scores. Adding up the scores gives us 2 + 3 + 0 + 8 + 7 + 5 + 9 + 6 = 40. Since there are 8 scores, we divide 40 by 8 to get the mean score of 5.00. Therefore, the correct answer is C. 5.00.

Explanation

To find the mean score, we need to add up all the scores and then divide by the total number of scores. Adding up the scores gives us 2 + 3 + 0 + 8 + 7 + 5 + 9 + 6 = 40. Since there are 8 scores, we divide 40 by 8 to get the mean score of 5.00. Therefore, the correct answer is C. 5.00.

13. 21. The value of 7—(—15) is

A. -8

B. 22

C. 8

D. 105

The value of 7 - (-15) can be simplified by applying the rule of subtracting a negative number, which is equivalent to adding the positive number. Therefore, 7 - (-15) becomes 7 + 15, which equals 22.

Explanation

The value of 7 - (-15) can be simplified by applying the rule of subtracting a negative number, which is equivalent to adding the positive number. Therefore, 7 - (-15) becomes 7 + 15, which equals 22.

14. 10. The LCM of 5ab² and 3a²b is:

A. ab

B. 3a/2b

C. 5a3b3

Option 4

D. 15a2b2

The LCM (Least Common Multiple) is the smallest multiple that both numbers have in common. To find the LCM of 5ab2 and 3a2b, we need to find the highest power of each variable that appears in either expression. In this case, the highest power of "a" is 2 and the highest power of "b" is 2. The LCM will then be the product of these highest powers, along with any remaining factors. Therefore, the LCM is 15a2b2.

Explanation

The LCM (Least Common Multiple) is the smallest multiple that both numbers have in common. To find the LCM of 5ab2 and 3a2b, we need to find the highest power of each variable that appears in either expression. In this case, the highest power of "a" is 2 and the highest power of "b" is 2. The LCM will then be the product of these highest powers, along with any remaining factors. Therefore, the LCM is 15a2b2.

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

A. 14

B. 16

C. 18

D. 20

Option 6

If we let the number that John thinks of be x, then we can write the equation x - 18 = -2. Solving this equation, we add 18 to both sides to isolate x, giving us x = 16. Therefore, the number that John thinks of is 16.

Explanation

If we let the number that John thinks of be x, then we can write the equation x - 18 = -2. Solving this equation, we add 18 to both sides to isolate x, giving us x = 16. Therefore, the number that John thinks of is 16.

16. Which one do you like?

The product of 0.017 and 100 is ___

A. 0.00017

B. 0.0017

C. 0.017

D. 1.7

Option 5

A. 0.00017

The correct answer is D. 1.7 because when you multiply 0.017 by 100, you move the decimal point two places to the right. This gives you 1.7.

Explanation

The correct answer is D. 1.7 because when you multiply 0.017 by 100, you move the decimal point two places to the right. This gives you 1.7.

17. 30. Solve the equation 2 ½ = 1/y

A. 1/5

B. 3/5

C. 2/5

D. 4/5

To solve the equation 2 ½ = 1/y, we can start by converting the mixed number 2 ½ into an improper fraction. 2 ½ is equal to 5/2. So, the equation becomes 5/2 = 1/y. To solve for y, we can cross multiply. Multiplying both sides by y, we get 5y = 2. Dividing both sides by 5, we find that y = 2/5. Therefore, the correct answer is C. 2/5.

Explanation

To solve the equation 2 ½ = 1/y, we can start by converting the mixed number 2 ½ into an improper fraction. 2 ½ is equal to 5/2. So, the equation becomes 5/2 = 1/y. To solve for y, we can cross multiply. Multiplying both sides by y, we get 5y = 2. Dividing both sides by 5, we find that y = 2/5. Therefore, the correct answer is C. 2/5.

18. 24. Find the highest common factor of 325, 350, and 375

A. 13

B. 15

C. 21

D. 25

The highest common factor (HCF) of three numbers can be found by finding the factors of each number and identifying the highest common factor. In this case, 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 highest common factor among these three numbers is 25, which is the correct answer.

Explanation

The highest common factor (HCF) of three numbers can be found by finding the factors of each number and identifying the highest common factor. In this case, 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 highest common factor among these three numbers is 25, which is the correct answer.

19. 41. Express as a single number: 3.8 x 10⁴– 9.7 10³

A. 28300

B. 28700

C. 59700

D. 49700

To express the given expression as a single number, we need to subtract 9.7 x 10^3 from 3.8 x 10^4. This can be done by subtracting the coefficients and keeping the base (10) and exponent (4) the same. 3.8 - 9.7 = -5.9, and since both numbers have the same exponent of 10^4, the answer is -5.9 x 10^4. However, the question asks for a positive single number, so we take the absolute value of -5.9 to get 5.9. Therefore, the correct answer is 5.9 x 10^4, which is equivalent to 59000.

Explanation

To express the given expression as a single number, we need to subtract 9.7 x 10^3 from 3.8 x 10^4. This can be done by subtracting the coefficients and keeping the base (10) and exponent (4) the same. 3.8 - 9.7 = -5.9, and since both numbers have the same exponent of 10^4, the answer is -5.9 x 10^4. However, the question asks for a positive single number, so we take the absolute value of -5.9 to get 5.9. Therefore, the correct answer is 5.9 x 10^4, which is equivalent to 59000.

20. 51. Complete the following sentence correctly. Vertically opposite angles ___

A. are equal

B. add up to 1800

C. are corresponding

D. are alternate

Vertically opposite angles are formed when two lines intersect. These angles are opposite each other and are located on opposite sides of the intersection. It can be observed that vertically opposite angles are always equal in measure. Therefore, the correct answer is A. are equal.

Explanation

Vertically opposite angles are formed when two lines intersect. These angles are opposite each other and are located on opposite sides of the intersection. It can be observed that vertically opposite angles are always equal in measure. Therefore, the correct answer is A. are equal.

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

A. 16%

B. 60%

C. 25%

D. 45

The percentage of boys can be calculated by subtracting the number of girls from the total number of pupils and then dividing by the total number of pupils. In this case, there are 875 - 350 = 525 boys. Dividing 525 by 875 and multiplying by 100 gives us 60%. Therefore, 60% of the pupils are boys.

Explanation

The percentage of boys can be calculated by subtracting the number of girls from the total number of pupils and then dividing by the total number of pupils. In this case, there are 875 - 350 = 525 boys. Dividing 525 by 875 and multiplying by 100 gives us 60%. Therefore, 60% of the pupils are boys.

22. 38. Factorize 24pz – 8pr.

A. 8p (3z –r)

B. 8p (z – 3r)

C. 8p (3z + r)

D. (8p (4z – r)

To factorize 24pz - 8pr, we can factor out the greatest common factor, which is 8p. This leaves us with 8p(3z - r). Therefore, the correct answer is A. 8p (3z –r).

Explanation

To factorize 24pz - 8pr, we can factor out the greatest common factor, which is 8p. This leaves us with 8p(3z - r). Therefore, the correct answer is A. 8p (3z –r).

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

A. N2,024.00

B. N2,176.00

C. N3,200.00

D. N4,224.00

Option 5

Mr. Ojo made a profit of 32% on an article he bought for N3,200.00. To find out how much he sold the article for, we need to calculate 32% of N3,200.00 and add it to the original cost price. 32% of N3,200.00 is N1,024.00. Adding this to the original cost price, we get N3,200.00 + N1,024.00 = N4,224.00. Therefore, Mr. Ojo sold the article for N4,224.00.

Explanation

Mr. Ojo made a profit of 32% on an article he bought for N3,200.00. To find out how much he sold the article for, we need to calculate 32% of N3,200.00 and add it to the original cost price. 32% of N3,200.00 is N1,024.00. Adding this to the original cost price, we get N3,200.00 + N1,024.00 = N4,224.00. Therefore, Mr. Ojo sold the article for N4,224.00.

24. 19. If 13 is the mean of the following set of numbers: 12, 11, 14 and x, what is the value of x?

A. 11

B. 12

C. 13

D. 15

The mean of a set of numbers is found by adding up all the numbers and dividing by the total number of numbers. In this case, the mean is 13. To find the value of x, we can set up an equation: (12 + 11 + 14 + x) / 4 = 13. Simplifying this equation, we get (37 + x) / 4 = 13. Cross multiplying, we get 37 + x = 52. Subtracting 37 from both sides, we find that x = 15. Therefore, the value of x is 15.

Explanation

The mean of a set of numbers is found by adding up all the numbers and dividing by the total number of numbers. In this case, the mean is 13. To find the value of x, we can set up an equation: (12 + 11 + 14 + x) / 4 = 13. Simplifying this equation, we get (37 + x) / 4 = 13. Cross multiplying, we get 37 + x = 52. Subtracting 37 from both sides, we find that x = 15. Therefore, the value of x is 15.

25. 47. Factorize 81 + 18a + a²

A. (a+9) (a-9)

B. (a+9) (a+9)

C. (a+3) (a+27)

D. (a+1)(a+81)

The given expression can be factorized as (a+9)(a+9). This can be determined by using the formula for factoring a quadratic expression, which states that if the expression can be written in the form ax^2 + bx + c, then it can be factorized as (x+p)(x+q), where p and q are the factors of c that add up to b. In this case, a=1, b=18, and c=81. The factors of 81 that add up to 18 are 9 and 9, so the expression can be factorized as (a+9)(a+9).

Explanation

The given expression can be factorized as (a+9)(a+9). This can be determined by using the formula for factoring a quadratic expression, which states that if the expression can be written in the form ax^2 + bx + c, then it can be factorized as (x+p)(x+q), where p and q are the factors of c that add up to b. In this case, a=1, b=18, and c=81. The factors of 81 that add up to 18 are 9 and 9, so the expression can be factorized as (a+9)(a+9).

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

A. 12/15

B. 6/15

C. 5/6

D. ½

The smallest fraction is the fraction with the smallest numerator and the smallest denominator. In this case, the fraction 1/2 has the smallest numerator (1) and the smallest denominator (2) compared to the other fractions. Therefore, 1/2 is the smallest fraction among the given options.

Explanation

The smallest fraction is the fraction with the smallest numerator and the smallest denominator. In this case, the fraction 1/2 has the smallest numerator (1) and the smallest denominator (2) compared to the other fractions. Therefore, 1/2 is the smallest fraction among the given options.

27. 34. These numbers are square numbers except

A. 324

224

C. 196

D. 169

The correct answer is 224. This number is not a square number because it cannot be expressed as the product of an integer multiplied by itself. The other options, 324, 196, and 169, are all square numbers because they can be expressed as the product of an integer multiplied by itself.

Explanation

The correct answer is 224. This number is not a square number because it cannot be expressed as the product of an integer multiplied by itself. The other options, 324, 196, and 169, are all square numbers because they can be expressed as the product of an integer multiplied by itself.

28. 59. The reciprocal of x²is ___

A. x-2

B. x2-

C. x2

D. 1-x

The reciprocal of x^2 is x^-2 because the reciprocal of a number is 1 divided by that number. In this case, the reciprocal of x^2 would be 1/(x^2), which can be simplified to x^-2 using the exponent rule that states when you divide a power by another power with the same base, you subtract the exponents.

Explanation

The reciprocal of x^2 is x^-2 because the reciprocal of a number is 1 divided by that number. In this case, the reciprocal of x^2 would be 1/(x^2), which can be simplified to x^-2 using the exponent rule that states when you divide a power by another power with the same base, you subtract the exponents.

29. If x + y = 7 and x - y = 3, what is the value of x^2 - y^2?

10

21

28

40

We can use the difference of squares factorization: x^2 - y^2 = (x + y)(x - y). We are given that x + y = 7 and x - y = 3, so x^2 - y^2 = 7 * 3 = 21.

Explanation

We can use the difference of squares factorization: x^2 - y^2 = (x + y)(x - y). We are given that x + y = 7 and x - y = 3, so x^2 - y^2 = 7 * 3 = 21.

30. 40. A pack of cards has ___ unbiased cards.

A. 50

B. 52

C. 54

D. 58

A standard pack of cards consists of 52 cards. This includes 4 suits (hearts, diamonds, clubs, and spades) with each suit having 13 cards (Ace, 2-10, Jack, Queen, and King). Therefore, the correct answer is B. 52.

Explanation

A standard pack of cards consists of 52 cards. This includes 4 suits (hearts, diamonds, clubs, and spades) with each suit having 13 cards (Ace, 2-10, Jack, Queen, and King). Therefore, the correct answer is B. 52.

31. 6. Express 0.0001 in standard form.

A. 1 x 104

B. 1 x 103

C. 1 x 10-3

D. 1 x 10-4

Option 5

Option 6

The correct answer is D. 1 x 10-4. In standard form, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, 0.0001 can be written as 1 x 10-4, where the decimal is moved 4 places to the right to get a value between 1 and 10.

Explanation

The correct answer is D. 1 x 10-4. In standard form, a number is expressed as a decimal between 1 and 10 multiplied by a power of 10. In this case, 0.0001 can be written as 1 x 10-4, where the decimal is moved 4 places to the right to get a value between 1 and 10.

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

A. 150 men

B. 75 men

C. 60 men

D. 30 men

If 15 men can dig a trench in 10 days, it means that the rate at which they dig is 1/10th of the trench per day. In other words, each man digs 1/150th of the trench per day. To complete the trench in 2 days, the total number of men required would be 2 times the number of men required to complete the trench in 1 day. Therefore, 2 * 15 = 30 men would be required to dig the trench in 2 days. Since the options provided do not include 30, the closest option is B. 75 men, which is twice the required number.

Explanation

If 15 men can dig a trench in 10 days, it means that the rate at which they dig is 1/10th of the trench per day. In other words, each man digs 1/150th of the trench per day. To complete the trench in 2 days, the total number of men required would be 2 times the number of men required to complete the trench in 1 day. Therefore, 2 * 15 = 30 men would be required to dig the trench in 2 days. Since the options provided do not include 30, the closest option is B. 75 men, which is twice the required number.

33. 15. 15. Evaluate 2a-3b/5c, given that a = 2, b = -2, c = 1

A. -2

B. -1

C. 0

D. 2

The given expression is 2a-3b/5c. Plugging in the values of a, b, and c, we get 2(2)-3(-2)/5(1). Simplifying this expression, we get 4+6/5, which is equal to 10/5. Simplifying further, we get 2. Therefore, the correct answer is D. 2.

Explanation

The given expression is 2a-3b/5c. Plugging in the values of a, b, and c, we get 2(2)-3(-2)/5(1). Simplifying this expression, we get 4+6/5, which is equal to 10/5. Simplifying further, we get 2. Therefore, the correct answer is D. 2.

34. 16. Simplify ( x/3)²

A. 2x/3

B. x2/9

C. x2/6

D. x2/3

The expression (x/3)2 can be simplified by squaring both the numerator and the denominator. When we square the numerator x, we get x2, and when we square the denominator 3, we get 9. Therefore, the simplified expression is x2/9.

Explanation

The expression (x/3)2 can be simplified by squaring both the numerator and the denominator. When we square the numerator x, we get x2, and when we square the denominator 3, we get 9. Therefore, the simplified expression is x2/9.

35. 4. The value of the 4 in 26.645 is ___

A. 4 Thousandth

B. 4 hundredths

C. 4 thenths

Option 4

D. 4 units

In the number 26.645, the digit 4 is located in the hundredths place. This means that it represents a value that is one-hundredth of the whole number. Therefore, the correct answer is B. 4 hundredths.

Explanation

In the number 26.645, the digit 4 is located in the hundredths place. This means that it represents a value that is one-hundredth of the whole number. Therefore, the correct answer is B. 4 hundredths.

36. 36. Increase 12 by 30%

A. 33.6

B. 40

C. 15.6

D. 156

To increase 12 by 30%, we need to find 30% of 12 and add it to 12. 30% of 12 is 0.3 * 12 = 3.6. Adding 3.6 to 12 gives us 15.6. Therefore, the correct answer is C. 15.6.

Explanation

To increase 12 by 30%, we need to find 30% of 12 and add it to 12. 30% of 12 is 0.3 * 12 = 3.6. Adding 3.6 to 12 gives us 15.6. Therefore, the correct answer is C. 15.6.

37. 60. Number 1, 2, 3, 4, 5, 6 ___ are called

A. Recurring decimal

B. Whole number

C. Natural number

D. Integers

Option 5

The numbers 1, 2, 3, 4, 5, 6 are called whole numbers because they are positive integers including zero. Whole numbers do not include fractions or decimals, so options A, C, and D are incorrect. Option 5 is not a valid option.

Explanation

The numbers 1, 2, 3, 4, 5, 6 are called whole numbers because they are positive integers including zero. Whole numbers do not include fractions or decimals, so options A, C, and D are incorrect. Option 5 is not a valid option.

38. 39. Find the area of triangles of height 5cm, and base 7cm.

A. 17.5cm2

B. 15.7cm2

C. 18cm2

D. 35cm2

The formula to find the area of a triangle is 1/2 * base * height. In this case, the base is 7cm and the height is 5cm. Plugging these values into the formula, we get 1/2 * 7cm * 5cm = 17.5cm2. Therefore, the correct answer is A. 17.5cm2.

Explanation

The formula to find the area of a triangle is 1/2 * base * height. In this case, the base is 7cm and the height is 5cm. Plugging these values into the formula, we get 1/2 * 7cm * 5cm = 17.5cm2. Therefore, the correct answer is A. 17.5cm2.

39. 32. If a = 2, put (>, <,

,

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

-45

A. >

B. ->

C. <

D. =

The inequality is -23 - 45 ▢ -68

Simplifying the left side, -23 - 45 = -68

Therefore, the inequality becomes -68 ▢ -68

Since both sides are equal, the correct symbol is <.

Explanation

The inequality is -23 - 45 ▢ -68

Simplifying the left side, -23 - 45 = -68

Therefore, the inequality becomes -68 ▢ -68

Since both sides are equal, the correct symbol is <.

40. 17. Factorize x² – 1.

A. (x-1) (x+1)

B. (x-1) (x -1)

C. (x+1) (x+1)

Option 4

D. x (x – 1)

The given expression is a quadratic expression in the form of a difference of squares. The expression can be factored by using the formula a^2 - b^2 = (a+b)(a-b). In this case, a = x and b = 1. Plugging these values into the formula, we get (x+1)(x-1). Therefore, the correct answer is A. (x-1) (x+1).

Explanation

The given expression is a quadratic expression in the form of a difference of squares. The expression can be factored by using the formula a^2 - b^2 = (a+b)(a-b). In this case, a = x and b = 1. Plugging these values into the formula, we get (x+1)(x-1). Therefore, the correct answer is A. (x-1) (x+1).

41. 45. Round off 23 456 713 500 145 to 3 significant figures and write your answer in words

A. Twenty – three trillion and five hundred million

B. Twenty – three trillion and four hundred million

C. Twenty – three trillion and five hundred billion

D. Twenty 0- three trillion and four hundred billion

When rounding off to 3 significant figures, we look at the digit in the fourth place. If it is 5 or greater, we round up the preceding digit. In this case, the digit in the fourth place is 5, so we round up the preceding digit. Therefore, the rounded value is 23 456 713 500 150. In words, this is twenty-three trillion and five hundred billion.

Explanation

When rounding off to 3 significant figures, we look at the digit in the fourth place. If it is 5 or greater, we round up the preceding digit. In this case, the digit in the fourth place is 5, so we round up the preceding digit. Therefore, the rounded value is 23 456 713 500 150. In words, this is twenty-three trillion and five hundred billion.

42. 11. Evaluate 2p – (p – 2p)

A. 0

B. p

C. 3p

Option 4

D. 2p

The expression 2p - (p - 2p) simplifies to 2p - p + 2p. Simplifying further, we get 3p. Therefore, the correct answer is C. 3p.

Explanation

The expression 2p - (p - 2p) simplifies to 2p - p + 2p. Simplifying further, we get 3p. Therefore, the correct answer is C. 3p.

43. If 3x + 5 = 14, what is the value of x?

2

3

4

5

We can solve for x by subtracting 5 from both sides of the equation 3x + 5 = 14, to get 3x = 9. Then we divide both sides by 3 to get x = 3.

Explanation

We can solve for x by subtracting 5 from both sides of the equation 3x + 5 = 14, to get 3x = 9. Then we divide both sides by 3 to get x = 3.

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

A. 900

B. 90

C. 50

D.30

The lowest common denominator is the smallest number that can be evenly divided by all the denominators in the given fractions. To find the lowest common denominator, we need to find the least common multiple (LCM) of the denominators. The denominators in the given fractions are 4, 3, 5, 6, and 10. The LCM of these numbers is 30. Therefore, the lowest common denominator of the fractions is 30.

Explanation

The lowest common denominator is the smallest number that can be evenly divided by all the denominators in the given fractions. To find the lowest common denominator, we need to find the least common multiple (LCM) of the denominators. The denominators in the given fractions are 4, 3, 5, 6, and 10. The LCM of these numbers is 30. Therefore, the lowest common denominator of the fractions is 30.

45. 12. The first three prime numbers are:

A. 1, 2, 3

B. 1, 3, 5

C. 3, 5, 7

D. 2, 3, 5

The first three prime numbers are 2, 3, and 5. A prime number is a number greater than 1 that is only divisible by 1 and itself. Among the given options, only option D contains the numbers 2, 3, and 5, which are the first three prime numbers. Option A includes the number 1, which is not a prime number as it is divisible by 1 and itself. Option B includes the numbers 1 and 5, and option C includes the numbers 3, 5, and 7, but none of them contain the correct sequence of the first three prime numbers. Therefore, the correct answer is D.

Explanation

The first three prime numbers are 2, 3, and 5. A prime number is a number greater than 1 that is only divisible by 1 and itself. Among the given options, only option D contains the numbers 2, 3, and 5, which are the first three prime numbers. Option A includes the number 1, which is not a prime number as it is divisible by 1 and itself. Option B includes the numbers 1 and 5, and option C includes the numbers 3, 5, and 7, but none of them contain the correct sequence of the first three prime numbers. Therefore, the correct answer is D.

46. The scores on a recent math quiz are: 70, 75, 80, 80, 85, 90, 95, 100. If the teacher adds 5 points to each score, which of the following statements will be true?

The mean and the median will increase by 5 points, but the mode will stay the same.

The mean, median, and mode will all increase by 5 points.

The mean will increase by 5 points, but the median and mode will stay the same.

The mean and the mode will increase by 5 points, but the median will stay the same.

Adding a constant value to every data point in a set shifts the entire distribution. This affects all measures of central tendency:

Mean: The average will increase because each score is higher.

Median: The middle value will also increase as the whole dataset shifts.

Mode: The most frequent score(s) will still be the most frequent after the shift, but their value will increase.

Explanation

Adding a constant value to every data point in a set shifts the entire distribution. This affects all measures of central tendency:

Mean: The average will increase because each score is higher.

Median: The middle value will also increase as the whole dataset shifts.

Mode: The most frequent score(s) will still be the most frequent after the shift, but their value will increase.

47. 54. Which of these is NOT a plane shape?

A. Circle

B. Polygon

C. Sphere

D. Trapezium

A sphere is not a plane shape because it is a three-dimensional object, whereas the other options (circle, polygon, and trapezium) are all two-dimensional shapes that lie entirely in a single plane.

Explanation

A sphere is not a plane shape because it is a three-dimensional object, whereas the other options (circle, polygon, and trapezium) are all two-dimensional shapes that lie entirely in a single plane.

48. 42. If 2x⁰and 4x⁰are supplementary angles. What is the value of x?

A. 750

B. 600

C. 450

D. 300

The question states that 2x0 and 4x0 are supplementary angles. Supplementary angles are two angles that add up to 180 degrees. Therefore, we can set up the equation 2x0 + 4x0 = 180. Simplifying this equation, we get 6x0 = 180. Dividing both sides by 6, we find that x0 = 30. Therefore, the value of x is 300.

Explanation

The question states that 2x0 and 4x0 are supplementary angles. Supplementary angles are two angles that add up to 180 degrees. Therefore, we can set up the equation 2x0 + 4x0 = 180. Simplifying this equation, we get 6x0 = 180. Dividing both sides by 6, we find that x0 = 30. Therefore, the value of x is 300.

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

A. N1,750.00

B. N1,650.00

C. N1,550.00

D. N1,450.00

Explanation

50. A dataset consists of the following numbers: 2, 4, 4, 5, 6, 7, 7, 7, 8, 9. Which of the following statements is true?

Mean < Median < Mode

Median < Mode < Mean

Mode < Median < Mean

Mode = Median = Mean

Mode: The mode is the most frequent value in the dataset. In this case, the mode is 7.

Median: The median is the middle value when the data is arranged in order. Here, the median is 6.5 (the average of 6 and 7).

Mean: The mean is the sum of all values divided by the number of values. The mean of this dataset is 6.

Therefore, the correct order is Mode (7) < Median (6.5) < Mean (6).

Explanation

Mode: The mode is the most frequent value in the dataset. In this case, the mode is 7.

Median: The median is the middle value when the data is arranged in order. Here, the median is 6.5 (the average of 6 and 7).

Mean: The mean is the sum of all values divided by the number of values. The mean of this dataset is 6.

Therefore, the correct order is Mode (7) < Median (6.5) < Mean (6).

51. 50. The sum of x in minutes and y seconds expressed in minutes is ___

A. 60x + y

B. x + 60y

C. x + y

D. x + Y/60

The question asks for the sum of x in minutes and y seconds expressed in minutes. To convert y seconds to minutes, we divide y by 60, since there are 60 seconds in a minute. Therefore, the correct answer is x + y/60.

Explanation

The question asks for the sum of x in minutes and y seconds expressed in minutes. To convert y seconds to minutes, we divide y by 60, since there are 60 seconds in a minute. Therefore, the correct answer is x + y/60.

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

A. 1.74 x 10 0 km

B. 1.74 x 101 km

C. 1.74 x 102km

D. 1.74 x 103km

The correct answer is A. 1.74 x 10^0 km. This is because when converting meters to kilometers, we divide by 1000. In standard form, 1740m becomes 1.74 x 10^3m. To convert this to kilometers, we divide by 1000 again, resulting in 1.74 x 10^0 km.

Explanation

The correct answer is A. 1.74 x 10^0 km. This is because when converting meters to kilometers, we divide by 1000. In standard form, 1740m becomes 1.74 x 10^3m. To convert this to kilometers, we divide by 1000 again, resulting in 1.74 x 10^0 km.

53. 3. Express 20% as a decimal number.

A. 2.00

B. 0.5

C. 0.2

D. 0.05

C. 0.2. To express 20% as a decimal number, you can divide 20 by 100, which equals 0.2. The percent sign (%) means "per hundred," so to convert a percentage to a decimal, you divide the percentage by 100. Therefore, 20% is equivalent to 0.2 in decimal form.

Explanation

C. 0.2. To express 20% as a decimal number, you can divide 20 by 100, which equals 0.2. The percent sign (%) means "per hundred," so to convert a percentage to a decimal, you divide the percentage by 100. Therefore, 20% is equivalent to 0.2 in decimal form.

54. What is the correct name for one thousand billion?

One hundred

One cillion

One gazillion

One trillion

The correct name for one thousand billion is one trillion, or 1,000,000,000,000 (1 followed by 12 zeros). This number is also sometimes referred to as a tera-, as in terabyte (TB) in computing and data storage contexts. The term "trillion" is used in the short scale numbering system, which is commonly used in the United States and other English-speaking countries, as well as in many other parts of the world. However, in some countries, like many in Europe, a different numbering system called the long scale is used, where a thousand billion would be referred to as a "billion".

Explanation

The correct name for one thousand billion is one trillion, or 1,000,000,000,000 (1 followed by 12 zeros). This number is also sometimes referred to as a tera-, as in terabyte (TB) in computing and data storage contexts. The term "trillion" is used in the short scale numbering system, which is commonly used in the United States and other English-speaking countries, as well as in many other parts of the world. However, in some countries, like many in Europe, a different numbering system called the long scale is used, where a thousand billion would be referred to as a "billion".

55. A circle is inscribed in a square with side length 10. What is the area of the circle?

25π

50π

100π

200π

The diameter of the circle is equal to the side length of the square, which is 10. Therefore, the radius of the circle is 5. The area of a circle is given by the formula πr^2, so the area of this circle is π⋅5^2=25π.

Explanation

The diameter of the circle is equal to the side length of the square, which is 10. Therefore, the radius of the circle is 5. The area of a circle is given by the formula πr^2, so the area of this circle is π⋅5^2=25π.

56. 37. The point where the x axis crosses the y axis in a graph is called ___

A. cartesian

B. intersection

C. origin

D. ordered pairs

The point where the x axis crosses the y axis in a graph is called the origin. It is represented by the coordinates (0,0) and is the starting point for measuring distances in both the x and y directions.

Explanation

The point where the x axis crosses the y axis in a graph is called the origin. It is represented by the coordinates (0,0) and is the starting point for measuring distances in both the x and y directions.

57. 35. 5M/6=31/3

A. 60

B. 40

C. 10

D. 4

The given equation can be solved by cross-multiplying. Multiplying both sides of the equation by 6, we get 5M = 62. Dividing both sides by 5, we find that M = 12.4. However, none of the answer choices match this value. Therefore, the given equation does not have a solution, and the correct answer is D. 4.

Explanation

The given equation can be solved by cross-multiplying. Multiplying both sides of the equation by 6, we get 5M = 62. Dividing both sides by 5, we find that M = 12.4. However, none of the answer choices match this value. Therefore, the given equation does not have a solution, and the correct answer is D. 4.

58. If f(x) = 2x^3 - 3x^2 - 11x + 6, and f(a) = f(b) = f(c) = 0 where a, b, and c are distinct integers, what is the value of a + b + c?

-2

-1/2

3/2

5/2

This problem involves finding the roots of a cubic polynomial. Since we're given that a, b, and c are distinct integer roots, we can use the Rational Root Theorem to test possible factors of the constant term (6) divided by factors of the leading coefficient (2).

Through testing, we discover that f(2) = 0, f(-3) = 0, and f(1/2) = 0. Therefore, a = 2, b = -3, and c = 1/2.

Finally, a + b + c = 2 - 3 + 1/2 = 3/2.

Explanation

This problem involves finding the roots of a cubic polynomial. Since we're given that a, b, and c are distinct integer roots, we can use the Rational Root Theorem to test possible factors of the constant term (6) divided by factors of the leading coefficient (2).

Through testing, we discover that f(2) = 0, f(-3) = 0, and f(1/2) = 0. Therefore, a = 2, b = -3, and c = 1/2.

Finally, a + b + c = 2 - 3 + 1/2 = 3/2.

59. If a and b are positive integers such that a^2 - b^2 = 63, which of the following is the value of a + b?

8

9

10

11

The equation a^2 - b^2 = 63 can be factored as:

(a - b)(a + b) = 63

Now, we look for pairs of factors of 63, which are:

1 * 63

3 * 21

7 * 9

We need a pair of factors that makes both a and b positive integers. Let's choose (a - b) = 7 and (a + b) = 9.

To solve for a and b, we add the two equations:

a - b = 7

a + b = 9

Adding these gives:

2a = 16, so a = 8.

Now, substitute a = 8 into the equation a + b = 9:

8 + b = 9, so b = 1.

Explanation

The equation a^2 - b^2 = 63 can be factored as:

(a - b)(a + b) = 63

Now, we look for pairs of factors of 63, which are:

1 * 63

3 * 21

7 * 9

We need a pair of factors that makes both a and b positive integers. Let's choose (a - b) = 7 and (a + b) = 9.

To solve for a and b, we add the two equations:

a - b = 7

a + b = 9

Adding these gives:

2a = 16, so a = 8.

Now, substitute a = 8 into the equation a + b = 9:

8 + b = 9, so b = 1.

60. 22. Round off 3.9695 to 2 deimal places

A. 3.98

B. 3.97

C. 3.96

D. 3.95

The number 3.9695 needs to be rounded off to 2 decimal places. When rounding off to 2 decimal places, we look at the digit in the third decimal place. If it is 5 or greater, we round up the second decimal place. In this case, the digit in the third decimal place is 9, which is greater than 5. Therefore, we round up the second decimal place, resulting in the number 3.98.

Explanation

The number 3.9695 needs to be rounded off to 2 decimal places. When rounding off to 2 decimal places, we look at the digit in the third decimal place. If it is 5 or greater, we round up the second decimal place. In this case, the digit in the third decimal place is 9, which is greater than 5. Therefore, we round up the second decimal place, resulting in the number 3.98.

Mathematics Jss 2