WVGSA Mathematics — Questions and Answers
Question 1: What is the value of x in the equation 2x + 4 = 12?
- x = 4
- x = 2 (Correct answer)
- x = 6
- x = 8
Correct answer: x = 2
To solve the equation 2x + 4 = 12, first subtract 4 from both sides to isolate the term with x, resulting in 2x = 8. Next, divide both sides by 2 to find the value of x. This calculation yields x = 4.
Question 2: What is the perimeter of a rectangle with length 5 cm and width 3 cm?
- 16 cm
- 15 cm
- 14 cm (Correct answer)
- 18 cm
Correct answer: 14 cm
The perimeter of a rectangle is found by adding the lengths of all four sides, or by using the formula P = 2(length + width). For a rectangle with a length of 5 cm and a width of 3 cm, the perimeter is calculated as 2(5 cm + 3 cm). This simplifies to 2(8 cm), resulting in a perimeter of 16 cm.
Question 3: What is the area of a triangle with base 6 cm and height 4 cm?
- 24 cm²
- 12 cm² (Correct answer)
- 18 cm²
- 30 cm²
Correct answer: 12 cm²
The area of a triangle is calculated using the formula A = (1/2) × base × height. For a triangle with a base of 6 cm and a height of 4 cm, the area is (1/2) × 6 cm × 4 cm. This calculation results in (1/2) × 24 cm², which equals 12 cm².
Question 4: What is the value of 3²?
- 6
- 9 (Correct answer)
- 12
- 18
Correct answer: 9
The expression 3² represents 3 raised to the power of 2, which means multiplying 3 by itself. Therefore, 3² is calculated as 3 × 3. This operation results in a value of 9.
Question 5: Which of the following is an example of a prime number?
- 6
- 7 (Correct answer)
- 8
- 9
Correct answer: 7
A prime number is a whole number greater than 1 that has only two positive divisors: 1 and itself. Among the given options, 7 fits this definition perfectly, as its only divisors are 1 and 7. Numbers like 6, 8, and 9 have additional divisors, making them composite numbers.
Question 6: What is the value of 7 × 8?
- 54
- 56 (Correct answer)
- 63
- 64
Correct answer: 56
The value of 7 × 8 is a basic multiplication fact. Multiplying the number 7 by 8 means adding 7 to itself 8 times, or 8 to itself 7 times. This fundamental arithmetic operation directly results in the product of 56.
Question 7: What is the value of the expression 2 + 3 × 4?
- 14 (Correct answer)
- 20
- 24
- 12
Correct answer: 14
To evaluate the expression 2 + 3 × 4, one must follow the order of operations (PEMDAS/BODMAS), which dictates that multiplication should be performed before addition. First, calculate 3 × 4, which equals 12. Then, add this result to 2, so 2 + 12, yielding a final value of 14.
Question 8: What is the greatest common divisor (GCD) of 12 and 18?
- 2
- 3 (Correct answer)
- 6
- 9
Correct answer: 3
To find the greatest common divisor (GCD) of 12 and 18, list all positive divisors for each number. The divisors of 12 are 1, 2, 3, 4, 6, and 12. The divisors of 18 are 1, 2, 3, 6, 9, and 18. The common divisors are 1, 2, 3, and 6, with the largest among them being 6.
Question 9: What is the solution to the equation 5x = 20?
- x = 4 (Correct answer)
- x = 5
- x = 3
- x = 2
Correct answer: x = 4
To solve the equation 5x = 20 for x, one must isolate x by performing the inverse operation of multiplication. Divide both sides of the equation by 5. This operation yields x = 20 ÷ 5, which simplifies to x = 4.
WVGSA Mathematics
What is the value of x in the equation 2x + 4 = 12?