Mathematics JSS 2

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.

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.

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.

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.

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

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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

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.

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 <.

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.

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.

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.

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.

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".

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.