Choose ONE of the options lettered A − D. Write the letter ONLY.

Question

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Here are the solutions to the questions:

1. Write 0.000283 in standard form.

Move the decimal point to the right until it is after the first non-zero digit.
$0.000283 \to 2.83$
Count the number of places the decimal point moved.
Since it moved 4 places to the right, the exponent of 10 is -4.
$0.000283 = 2.83 \times 10^{-4}$
The correct option is A.
$\boxed{\text{A. } 2.83 \times 10^{-4}}$
2. What is the next term in the sequence of 2, 5, 11, 23, 47,...?
Find the difference between consecutive terms.
$5 - 2 = 3$ $11 - 5 = 6$ $23 - 11 = 12$ $47 - 23 = 24$
Observe the pattern in the differences.
The differences are 3, 6, 12, 24, which is a geometric progression where each term is multiplied by 2. The next difference will be $24 \times 2 = 48$ .
Add the next difference to the last term in the sequence.
$47 + 48 = 95$
The correct option is D.
$\boxed{\text{D. } 95}$
3. Arrange the numbers -4, 0, -6 in descending order.
Descending order means arranging numbers from the largest to the smallest.
Compare the given numbers
0 is the largest, followed by -4, and then -6 is the smallest.
$0 > -4 > -6$
The correct order is 0, -4, -6.
The correct option is D.
$\boxed{\text{D. } 0, -4, -6}$
4. Find x, if $0.025 = \frac{1}{x}$ .
To solve for $x$ , take the reciprocal of both sides of the equation.
$x = \frac{1}{0.025}$
Convert the decimal to a fraction or perform the division.
$x = \frac{1}{\frac{25}{1000}} = \frac{1000}{25}$
Simplify the fraction.
$x = 40$
The correct option is D.
$\boxed{\text{D. } 40}$
5. If the exterior angles of a quadrilateral are $2x^\circ$ , $(x+15)^\circ$ , $(2x+5)^\circ$ and $(2x-10)^\circ$ , find the value of x.
The sum of the exterior angles of any convex polygon is $360^\circ$ .
Set up the equation.
$2x + (x+15) + (2x+5) + (2x-10) = 360$
Combine like terms.
$(2x+x+2x+2x) + (15+5-10) = 360$ $7x + 10 = 360$
Isolate the term with $x$ .
$7x = 360 - 10$ $7x = 350$
Solve for $x$ .
$x = \frac{350}{7}$ $x = 50$
The correct option is C.
$\boxed{\text{C. } 50^\circ}$
6. What is the value of $2p+3q$ , where $p=4$ and $q=5$ ?
Substitute the given values of $p$ and $q$ into the expression.
$2(4) + 3(5)$
Perform the multiplications.
$8 + 15$
Perform the addition.
$23$
The correct option is C.
$\boxed{\text{C. } 23}$
7. Evaluate $141^2 - 139^2$ .
Use the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$ .
Here, $a=141$ and $b=139$ .
$(141 - 139)(141 + 139)$
Perform the operations inside the parentheses.
$(2)(280)$
Perform the multiplication.
$560$
The correct option is D.
$\boxed{\text{D. } 560}$
8. What is the shape of the face of a cylinder?
A cylinder has two flat bases and a curved lateral surface.
The flat bases of a cylinder are circular.
The correct option is A.
$\boxed{\text{A. Circle}}$
9. Find the mean of the following sets of number 3, 6, 6, 7, 5, 3.
The mean is the sum of all numbers divided by the count of the numbers.
Count of numbers = 6.
Sum the numbers.
$\text{Sum} = 3 + 6 + 6 + 7 + 5 + 3 = 30$
Calculate the mean.
$\text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{30}{6} = 5$
The correct option is D.
$\boxed{\text{D. } 5}$
10. A father shared the sum of N500.00 among his three children Ayo, Dele and Segun in the ratio of 5:3:2. What is Dele's share?
Find the total number of ratio parts.
$\text{Total parts} = 5 + 3 + 2 = 10$
Determine Dele's share as a fraction of the total.
Dele's ratio is 3.
$\text{Dele's fraction} = \frac{3}{10}$
Calculate Dele's share by multiplying the fraction by the total sum.
$\text{Dele's share} = \frac{3}{10} \times N500.00 = N150.00$
The correct option is C.
$\boxed{\text{C. N150.00}}$
11. Solve the equation $\frac{3-y}{3} = 2$ .
Multiply both sides of the equation by 3.
$3-y = 2 \times 3$ $3-y = 6$
Subtract 3 from both sides.
$-y = 6 - 3$ $-y = 3$
Multiply both sides by -1 to solve for $y$ .
$y = -3$
The correct option is A.
$\boxed{\text{A. } -3}$
12. If 4 is added to 3 times a certain number, the result is 31. Find the number.
Let the certain number be $n$ .
Translate the problem into an algebraic equation.
"3 times a certain number" is $3n$ .
"4 is added to 3 times a certain number" is $3n + 4$ .
"the result is 31" means $3n + 4 = 31$ .
Subtract 4 from both sides of the equation.
$3n = 31 - 4$ $3n = 27$
Divide by 3 to solve for $n$ .
$n = \frac{27}{3}$ $n = 9$
The correct option is A.
$\boxed{\text{A. } 9}$
13. A shirt that was originally sold for N1,200.00 is now being sold for N1,300.00. What is the percentage increase in its price?
Calculate the increase in price.
$\text{Increase} = N1,300.00 - N1,200.00 = N100.00$
Calculate the percentage increase using the formula
$\frac{\text{Increase}}{\text{Original Price}} \times 100\%$ .
$\text{Percentage Increase} = \frac{N100.00}{N1,200.00} \times 100\%$
Simplify the expression.
$\text{Percentage Increase} = \frac{1}{12} \times 100\% \approx 8.33\%$
The closest option is 8%.
The correct option is C.
$\boxed{\text{C. } 8\%}$
14. What is the coefficient of x in the expression $(x-2)(x+9)$ ?
Expand the expression by multiplying the two binomials.
$(x-2)(x+9) = x(x+9) - 2(x+9)$ $= x^2 + 9x - 2x - 18$
Combine the like terms involving $x$ .
$= x^2 + (9-2)x - 18$ $= x^2 + 7x - 18$
Identify the coefficient of $x$ .
The coefficient of $x$ is 7.
The correct option is D.
$\boxed{\text{D. } 7}$
15. What is the multiplication inverse of $\frac{1}{2a}$ ?
The multiplicative inverse (or reciprocal) of a number is 1 divided by that number.
$\text{Multiplicative inverse of } \frac{1}{2a} = \frac{1}{\frac{1}{2a}}$
Simplify the complex fraction.
$= 1 \times \frac{2a}{1} = 2a$
The correct option is D.
$\boxed{\text{D. } 2a}$
16. If x varies directly as $y^2$ and $x=4$ when $y=2$ , find the relationship between x and y.
Write the direct variation relationship.
"x varies directly as $y^2$ " means $x = ky^2$ , where $k$ is the constant of proportionality.
Use the given values ( $x=4$ when $y=2$ ) to find the constant $k$ .
$4 = k(2^2)$ $4 = k(4)$
Solve for $k$ .
$k = \frac{4}{4}$ $k = 1$
Substitute the value of $k$ back into the direct variation equation to find the relationship between $x$ and $y$ .
$x = 1 \cdot y^2$ $x = y^2$
The correct option is C.
$\boxed{\text{C. } x = y^2}$

Choose ONE of the options lettered A - D. Write the letter ONLY.

Answer

Step-by-step solution

Move the decimal point to the right until it is after the first non-zero digit.

Count the number of places the decimal point moved.

Find the difference between consecutive terms.

Observe the pattern in the differences.

Add the next difference to the last term in the sequence.

Descending order means arranging numbers from the largest to the smallest.

Compare the given numbers

To solve for xxx, take the reciprocal of both sides of the equation.

Convert the decimal to a fraction or perform the division.

Simplify the fraction.

The sum of the exterior angles of any convex polygon is 360∘360^\circ360∘.

Combine like terms.

Isolate the term with xxx.

Solve for xxx.

Substitute the given values of ppp and qqq into the expression.

Perform the multiplications.

Perform the addition.

Use the difference of squares formula, a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b)a2−b2=(a−b)(a+b).

Perform the operations inside the parentheses.

Perform the multiplication.

A cylinder has two flat bases and a curved lateral surface.

The flat bases of a cylinder are circular.

The mean is the sum of all numbers divided by the count of the numbers.

Sum the numbers.

Calculate the mean.

Find the total number of ratio parts.

Determine Dele's share as a fraction of the total.

Calculate Dele's share by multiplying the fraction by the total sum.

Multiply both sides of the equation by 3.

Subtract 3 from both sides.

Multiply both sides by -1 to solve for yyy.

Let the certain number be nnn.

Subtract 4 from both sides of the equation.

Divide by 3 to solve for nnn.

Calculate the increase in price.

Calculate the percentage increase using the formula

Simplify the expression.

Expand the expression by multiplying the two binomials.

Combine the like terms involving xxx.

Identify the coefficient of xxx.

The multiplicative inverse (or reciprocal) of a number is 1 divided by that number.

Simplify the complex fraction.

Write the direct variation relationship.

Use the given values (x=4x=4x=4 when y=2y=2y=2) to find the constant kkk.

Solve for kkk.

Substitute the value of kkk back into the direct variation equation to find the relationship between xxx and yyy.

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More Mathematics Questions

To solve for $x$ , take the reciprocal of both sides of the equation.

The sum of the exterior angles of any convex polygon is $360^\circ$ .

Isolate the term with $x$ .

Solve for $x$ .

Substitute the given values of $p$ and $q$ into the expression.

Use the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$ .

Multiply both sides by -1 to solve for $y$ .

Let the certain number be $n$ .

Divide by 3 to solve for $n$ .

Combine the like terms involving $x$ .

Identify the coefficient of $x$ .

Use the given values ( $x=4$ when $y=2$ ) to find the constant $k$ .

Solve for $k$ .

Substitute the value of $k$ back into the direct variation equation to find the relationship between $x$ and $y$ .