Answer all questions correctly. Use computer to write but make sure all math is in math formation. Don’t focus on writing and explaining your process unless the question asks you to explain. Only show the necessary steps needed to answer the problem. If you are writing unnecessarily the grader might be confused on what to grade. Please focus on simply solving the problems, I don’t need you to explain.
Problem 1: Solve the equation for x: 3x – 7 = 14.
To solve for x, add 7 to both sides of the equation: 3x = 14 + 7 = 21. Now, divide both sides by 3 to isolate x: x = 21 / 3 = 7.
Problem 2: Find the area of a rectangle with length 8 cm and width 5 cm.
The area (A) of a rectangle is given by the formula A = length × width. Substitute the values: A = 8 cm × 5 cm = 40 square cm.
Problem 3: Calculate the square root of 144.
The square root (√) of 144 is 12 because 12 × 12 = 144.
Problem 4: Evaluate the expression: 2(3^2) + 4(5) – 6.
First, calculate the exponent: 3^2 = 9. Now, substitute the values into the expression: 2(9) + 4(5) – 6. Perform the operations: 18 + 20 – 6 = 32.
Problem 5: Find the circumference of a circle with a radius of 5 cm.
The circumference (C) of a circle is given by the formula C = 2πr, where r is the radius. Substitute the radius: C = 2π × 5 cm ≈ 31.42 cm (rounded to two decimal places).
Problem 6: Solve the equation for y: 2y + 3 = 11.
To solve for y, subtract 3 from both sides of the equation: 2y = 11 – 3 = 8. Now, divide both sides by 2 to isolate y: y = 8 / 2 = 4.
Problem 7: Calculate the product of 7 and 9.
The product of 7 and 9 is 63 because 7 × 9 = 63.
Problem 8: Find the area of a triangle with base 6 cm and height 10 cm.
The area (A) of a triangle is given by the formula A = (1/2) × base × height. Substitute the values: A = (1/2) × 6 cm × 10 cm = 30 square cm.
Problem 9: Evaluate the expression: 4 + 2 × 6 – 5.
Perform the operations from left to right: 4 + 12 – 5 = 16 – 5 = 11.
Problem 10: Calculate the volume of a rectangular prism with length 4 cm, width 3 cm, and height 5 cm.
The volume (V) of a rectangular prism is given by the formula V = length × width × height. Substitute the values: V = 4 cm × 3 cm × 5 cm = 60 cubic cm.
Frequently Asked Questions (FAQs)
Q1: What is the formula for calculating the area of a triangle?
A1: The formula for calculating the area (A) of a triangle is (1/2) × base × height.
Q2: How do you solve a quadratic equation?
A2: To solve a quadratic equation in the form ax^2 + bx + c = 0, you can use the quadratic formula: x = (-b ± √(b^2 – 4ac)) / (2a).
Q3: What is the perimeter of a rectangle?
A3: The perimeter (P) of a rectangle is calculated as P = 2(length + width).
Q4: How do you find the mean (average) of a set of numbers?
A4: To find the mean of a set of numbers, add all the numbers together and then divide by the total number of values in the set.
Q5: What is the Pythagorean Theorem?
A5: The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.