1.
Express as a single number: 3.8 x 10^{4 }– 9.7 x 10
Correct Answer
A. 37903
2.
If two numbers are added together, it is called
Correct Answer
A. 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.
3.
The reciprocal of x^{2 }is ___
Correct Answer
A. 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.
4.
Mr. Ojo made a profit of 32% on an article he bought for N3,200.00. How much did he sell the article?
Correct Answer
D. 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 price. 32% of N3,200.00 is N1,024.00. Adding this to the original price, we get N3,200.00 + N1,024.00 = N4,224.00. Therefore, Mr. Ojo sold the article for N4,224.00.
5.
Number 1, 2, 3, 4, 5, 6 ___ are called
Correct Answer
C. Natural number
Explanation
The numbers 1, 2, 3, 4, 5, 6 are called natural numbers because they include all the positive integers (1, 2, 3, 4, 5, 6).
6.
If 2x^{0 }and 4x^{0 }are supplementary angles. What is the value of x?^{ }
Correct Answer
C. 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.
7.
Find the reciprocal of 2.5 ___
Correct Answer
D. 0.4
Explanation
The reciprocal of a number is obtained by dividing 1 by that number. In this case, the reciprocal of 2.5 would be 1/2.5, which is equal to 0.4.
8.
If 15 men dig a trench for 10 days, how many men will be required to dig the trench in 2 days?
Correct Answer
B. 75 men
9.
Express 675 000 000 in a standard form
Correct Answer
A. 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.
10.
A trader buys a gallon of palm oil for N1,500.00 and sells it at a profit of 10%. Calculate the selling price
Correct Answer
B. N1,650.00
Explanation
The selling price can be calculated by adding the profit to the cost price. The profit is 10% of N1,500.00, which is N150.00. Therefore, the selling price is N1,500.00 + N150.00 = N1,650.00.
11.
Find the mean score of these scores: 2, 3, 0, 8, 7, 5, 9, 6
Correct Answer
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.
12.
Find the HCF of 36 and 60
Correct Answer
A. 12
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.
13.
How many lines of symmetry have a square?
Correct Answer
B. 4
Explanation
A square has 4 lines of symmetry. Each line of symmetry divides the square into two equal halves, and there are 4 ways to do this in a square.
14.
Round off 23 456 713 500 145 to 3 significant figures and write your answer in words
Correct Answer
C. Twenty – three trillion and five hundred billion
15.
Simplify (-4 X -2 X -3)/(-2 X 6)
Correct Answer
D. 2
Explanation
When multiplying negative numbers, the result is always positive. So, (-4) X (-2) X (-3) = -24. Similarly, (-2) X 6 = -12. Therefore, (24)/(-12) = -2.
16.
Simplify ab (a – b)
Correct Answer
A. A^{2}b – ab^{2}
Explanation
The expression ab (a - b) can be simplified by distributing the ab to both terms inside the parentheses. This results in a^2b - ab^2, which matches Option A.
17.
Express 18 as a product of its prime factors.
Correct Answer
B. 2x3x3=2^{1}x3^{2 }
Explanation
The prime factors of 18 are 2 and 3. Therefore, the product of its prime factors is 2 x 3 x 3, which is equal to 18.
18.
Factorize 81 + 18a + a
Correct Answer
B. (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).
19.
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 ___
Correct Answer
B. -1
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.
20.
Numbers that cannot be expressed as fractions are called ___
Correct Answer
C. Irrational numbers
Explanation
The correct answer is C. Irrational numbers. Irrational numbers are numbers that cannot be expressed as fractions or ratios of two integers. They are non-repeating and non-terminating decimals. Decimal numbers (option B) is a broad term that includes both rational and irrational numbers. Rational numbers (option D) are numbers that can be expressed as fractions or ratios of two integers. Recurring numbers (option A) are numbers that have a repeating pattern in their decimal representation, which is a characteristic of rational numbers.
21.
Express 0.000 000 000347 in standard form
Correct Answer
D. 3.47 x 10^{-10}
Explanation
The given number, 0.000 000 000347, can be expressed in standard form as 3.47 x 10-10. This is because we move the decimal point 10 places to the right to get the number 3.47, and then multiply it by 10 raised to the power of -10.
22.
Find the Simple Interest on ₦500.00 for 2 years at 4%.
Correct Answer
B. ₦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.
23.
Solve the equation 2 ½ = 1/y
Correct Answer
C. 2/5
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.
24.
If the sum of three consecutive even integers is 114, what is the largest of these integers?
Correct Answer
C. 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.
25.
Simplify X^{6}÷X^{3}
Correct Answer
C. X^{3 }
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.
26.
Find the highest common factor of 325, 350, and 375
Correct Answer
D. 25
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.
27.
Express 6561 in index form.
Correct Answer
B. 9^{4} ^{ }
28.
What is the value of 96^{2}?
Correct Answer
C. 9216
29.
Simplify ( x/3)^{2}
Correct Answer
B. X^{2}/9
Explanation
The expression (x/3)^2 can be simplified by squaring both the numerator and denominator separately. Squaring the numerator x gives x^2, and squaring the denominator 3 gives 9. Therefore, the simplified expression is x^2/9, which matches with Option 2.
30.
If a = 2, put (>, <, , or =) in the box for the inequality below: -23___ -45
Correct Answer
A. >
Explanation
When a = 2, the inequality -23 > -45 is true because -23 is greater than -45.
31.
The number of pupils in a school is 875. If 350 are girls, what percentage of the pupils are boys?
Correct Answer
B. 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%.
32.
The lowest common denominator of 1/4, 2/3, 4/5, 5/6 and 5/10 and is ___
Correct Answer
D. 60
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.
33.
These numbers are square numbers except
Correct Answer
B. 224
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.
34.
Solve 5m/6=31⁄3
Correct Answer
D. 12.4
35.
The sum of x in minutes and y seconds expressed in minutes is ___
Correct Answer
D. X + y/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.
36.
If N9 600 was shared among three boys Ola, Tope, and Jide in the ratio 3: 4: 5, respectively, what is Jide’s share?
Correct Answer
B. 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.
37.
Complete the following sentence correctly. Vertically opposite angles ___
Correct Answer
A. Are equal
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.
38.
John thinks of a number. 18 is subtracted from the number, the result gives – 2. What is the number?
Correct Answer
B. 16
Explanation
18 is subtracted from the number, and the result is -2. To find the original number, we need to add 18 to -2. Adding 18 to -2 gives us 16. Therefore, the number John is thinking of is 16.
39.
Find the probability of choosing a vowel from ‘KETU–LAGOS’.
Correct Answer
D. 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.
40.
Increase 12 by 30%
Correct Answer
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.
41.
How many faces have a cylinder?
Correct Answer
C. 3
Explanation
A cylinder has three faces: two circular faces at the top and bottom, and one curved face that wraps around the sides.
42.
Factorize x^{2} – 1.
Correct Answer
A. (x-1) (x+1)
Explanation
The given expression can be factored as the difference of squares, which is (x-1)(x+1).
43.
The point where the x-axis crosses the y-axis in a graph is called ___
Correct Answer
C. Origin
Explanation
The point where the x axis crosses the y axis in a graph is called the origin.
44.
The product of 0.017 and 100 is ____________
Correct Answer
D. 1.7
Explanation
The product of 0.017 and 100 is 1.7 because when you multiply 0.017 by 100, you move the decimal point two places to the right, resulting in 1.7.
45.
What is the correct name for one thousand billion?
Correct Answer
D. One trillion
46.
Factorize 24pz – 8pr.
Correct Answer
A. 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).
47.
Express 1740m in km, leaving your answer in standard form.
Correct Answer
A. 1.74 x 10 ^{0} km
48.
The least number by which 112 must be multiplied to give a perfect square is __
Correct Answer
C. 7
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.
49.
Express 20% as a decimal number.
Correct Answer
C. 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.
50.
The LCM of 5ab^{2} and 3a^{2}b is:
Correct Answer
D. 15a^{2}b^{2}
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.