Mathematics Challenge for Grade 8

Simplify the expression: 3x + 5x - 2.

• 8x + 2

• 5x - 2

• 3x + 2

• 8x - 2

Answer explanation

Combine like terms: 3x + 5x = 8x. The constant -2 remains unchanged. Thus, the simplified expression is 8x - 2, which matches the correct answer.

If the area of a triangle is 24 cm² and the base is 8 cm, what is the height?

• 4 cm

• 8 cm

• 10 cm

• 6 cm

Answer explanation

To find the height of the triangle, use the formula: Area = 1/2 * base * height. Rearranging gives height = (2 * Area) / base. Substituting the values: height = (2 * 24) / 8 = 6 cm. Thus, the height is 6 cm.

What is the value of x in the equation: 2(x - 3) = 10?

• 8

• 5

• 10

• 3

Answer explanation

To solve 2(x - 3) = 10, first divide both sides by 2: x - 3 = 5. Then, add 3 to both sides: x = 8. Thus, the value of x is 8.

Calculate the circumference of a circle with a radius of 7 cm.

• 50.24 cm

• 28.00 cm

• 43.98 cm

• 21.99 cm

Answer explanation

The circumference of a circle is calculated using the formula C = 2πr. For a radius of 7 cm, C = 2 × π × 7 ≈ 43.98 cm. Thus, the correct answer is 43.98 cm.

If a bag contains 3 red, 5 blue, and 2 green marbles, what is the probability of picking a blue marble?

• 0.1

• 0.25

• 0.75

• 0.5

Answer explanation

The total number of marbles is 3 red + 5 blue + 2 green = 10. The probability of picking a blue marble is the number of blue marbles (5) divided by the total (10), which is 5/10 = 0.5.

Find the least common multiple (LCM) of 12 and 15.

• 30

• 60

• 75

• 45

Answer explanation

To find the LCM of 12 and 15, we can list the multiples: 12 (12, 24, 36, 48, 60...) and 15 (15, 30, 45, 60...). The smallest common multiple is 60, making it the LCM.

A rectangle has a length of 10 cm and a width of 4 cm. What is its perimeter?

• 28 cm

• 30 cm

• 24 cm

• 20 cm

Answer explanation

To find the perimeter of a rectangle, use the formula P = 2(length + width). Here, P = 2(10 cm + 4 cm) = 2(14 cm) = 28 cm. Thus, the correct answer is 28 cm.

If the ratio of boys to girls in a class is 3:4 and there are 28 students, how many boys are there?

• 16

• 14

• 12

• 10

Answer explanation

The ratio of boys to girls is 3:4, meaning for every 7 students, 3 are boys. With 28 students, we have 28/7 = 4 groups. Thus, boys = 4 groups * 3 boys/group = 12 boys.

What is the sum of the first five prime numbers?

• 28

• 24

• 32

• 30

Answer explanation

The first five prime numbers are 2, 3, 5, 7, and 11. Their sum is 2 + 3 + 5 + 7 + 11 = 28. Therefore, the correct answer is 28.

If 5x = 20, what is the value of x?

• 4

• 5

• 10

• 2

Answer explanation

To find x, divide both sides of the equation 5x = 20 by 5. This gives x = 20 / 5, which simplifies to x = 4. Therefore, the correct answer is 4.