Mathematics Challenge

Henrika, Henry, and Henrietta are working on a group project. They need to simplify the expression: 3x + 2y - 5z + 4x - y + 2z

• 7x + y - 2z

• 3x + 3y - 5z

• 5x + y - 3z

• 7x + y - 3z

Answer explanation

To simplify the expression, combine like terms: 3x + 4x = 7x, 2y - y = y, -5z + 2z = -3z. Therefore, the simplified expression is 7x + y - 3z.

Henry went to the store with $5 in his pocket. He bought a toy for $2 and some candies. If he has $11 left after buying the candies, how much did the candies cost?

• $3

• $6

• $2

• $4

Answer explanation

Henry had $5, spent $2 on a toy, and had $11 left. So, he spent $5 - $2 - $11 = $3 on candies. Therefore, the candies cost $3.

Henry wants to plant some flowers in his garden. He needs to find the roots of the quadratic equation: x^2 - 4x + 4 = 0 to determine the spacing between the flowers. What are the roots of the equation?

• x = -2

• x = 2

• x = 1

• x = 3

Answer explanation

To find the roots of the quadratic equation x^2 - 4x + 4 = 0, we factor the equation to (x-2)(x-2) = 0. Therefore, the roots are x = 2.

Henrika, Henrietta, and Henry are sharing a cake. If each person gets more than 3 slices, how many slices can each person have?

• More than 3 slices

• Exactly 3 slices

• Less than 3 slices

• At most 3 slices

Answer explanation

Each person can have less than 3 slices since the question states that each person gets more than 3 slices, implying they cannot have exactly 3 or more than 3 slices.

Graph the function: y = 2x + 3

• The graph of the function y = 2x + 3 is a straight line passing through the points (0, 3) and (1, 5).

• The graph of the function y = 2x + 3 is a hyperbola

• The graph of the function y = 2x + 3 is a circle

• The graph of the function y = 2x + 3 is a parabola

Answer explanation

The graph of the function y = 2x + 3 is a straight line passing through the points (0, 3) and (1, 5).

Henry, Henrietta, and Henrika are playing a game with a fair six-sided die. What is the probability of rolling a prime number?

• 1/2

• 1/3

• 1/4

• 1/5

Answer explanation

The probability of rolling a prime number on a fair six-sided die is 1/2 because there are three prime numbers (2, 3, 5) out of a total of six possible outcomes.

Henrika and Henrietta are planning a party. They need to solve the simultaneous equations: 2x + 3y = 8 and x - y = 1 to determine the number of guests and tables needed.

• x = -1, y = 2

• x = 0, y = 1

• x = 2, y = 1

• x = 3, y = 2

Answer explanation

To solve the simultaneous equations, we can first solve for x in the second equation to get x = y + 1. Then substitute x in the first equation to get 2(y + 1) + 3y = 8. Solving this gives y = 1. Substituting y back gives x = 2. Therefore, x = 2, y = 1.

At a bakery, the ratio of chocolate cupcakes to vanilla cupcakes is 4:6. If there are 10 cupcakes in total, how many are chocolate cupcakes?

• 2

• 3

• 5

• 6

Answer explanation

To find the number of chocolate cupcakes, first calculate the total parts in the ratio (4+6=10). Then, divide the total cupcakes by the total parts (10/10=1). Finally, multiply the parts for chocolate cupcakes (4*1=4) to get the number of chocolate cupcakes, which is 4.

Calculate the average age of the following group of friends: Henrika, Henry, Henrietta, who are 25, 27, and 30 years old respectively.

• 27

• 28

• 29

• 30

Answer explanation

To calculate the average age, add the ages together (25+27+30=82) and divide by the number of friends (3). 82/3 = 27.3, which rounds to 29.

Graph the equation: y = -2x + 4

• The graph is a circle

• The graph of the equation y = -2x + 4 is a straight line passing through the points (0, 4) and (1, 2).

• The graph is a hyperbola

• The graph is a parabola

Answer explanation

The graph of the equation y = -2x + 4 is a straight line passing through the points (0, 4) and (1, 2).