Test Your Mathematical Skills: A Quiz For 12th Grade

1. Simplify: (4 – 5) – (13 – 18 + 2).

-1

–2

1

2

The given expression involves subtracting two sets of numbers within parentheses. First, we simplify the numbers within the first set of parentheses: 4 - 5 = -1. Next, we simplify the numbers within the second set of parentheses: 13 - 18 + 2 = -3. Finally, we subtract the result of the second set of parentheses from the result of the first set: -1 - (-3) = -1 + 3 = 2. Therefore, the correct answer is 2.

Explanation

The given expression involves subtracting two sets of numbers within parentheses. First, we simplify the numbers within the first set of parentheses: 4 - 5 = -1. Next, we simplify the numbers within the second set of parentheses: 13 - 18 + 2 = -3. Finally, we subtract the result of the second set of parentheses from the result of the first set: -1 - (-3) = -1 + 3 = 2. Therefore, the correct answer is 2.

2. What is the radius of a circle that has a circumference of 3.14 meters?

0.2 meter

0.3 meter

0.4 meter

0.5 meter

The radius of a circle can be found by dividing the circumference by 2π. In this case, the given circumference is 3.14 meters. Dividing this by 2π (approximately 6.28) gives a radius of approximately 0.5 meters.

Explanation

The radius of a circle can be found by dividing the circumference by 2π. In this case, the given circumference is 3.14 meters. Dividing this by 2π (approximately 6.28) gives a radius of approximately 0.5 meters.

3. Simplify:(4x² - 2x) - (-5x² - 8x)

9x(3x + 2)

8x(3x + 2)

4x(3x + 2)

3x(3x + 2)

The given expression is (4x^2 - 2x) - (-5x^2 - 8x). Simplifying this expression, we can remove the parentheses and combine like terms. The negative sign in front of the second set of parentheses means that we need to distribute the negative sign to each term inside the parentheses. Doing this, we get 4x^2 - 2x + 5x^2 + 8x. Combining like terms, we have 9x^2 + 6x. Therefore, the correct answer is 3x(3x + 2), which is equivalent to 9x^2 + 6x.

Explanation

The given expression is (4x^2 - 2x) - (-5x^2 - 8x). Simplifying this expression, we can remove the parentheses and combine like terms. The negative sign in front of the second set of parentheses means that we need to distribute the negative sign to each term inside the parentheses. Doing this, we get 4x^2 - 2x + 5x^2 + 8x. Combining like terms, we have 9x^2 + 6x. Therefore, the correct answer is 3x(3x + 2), which is equivalent to 9x^2 + 6x.

4. A wire is wound around a rod. The wire goes exactly 5 times around the rod. The circumference of the rod is 12 cm and the height is 25 cm. What's the length of the wire?

70

60

65

80

The length of the wire can be calculated by multiplying the number of times the wire goes around the rod by the circumference of the rod. In this case, the wire goes 5 times around the rod, and the circumference of the rod is 12 cm. Therefore, the length of the wire is 5 times 12 cm, which equals 60 cm.

Explanation

The length of the wire can be calculated by multiplying the number of times the wire goes around the rod by the circumference of the rod. In this case, the wire goes 5 times around the rod, and the circumference of the rod is 12 cm. Therefore, the length of the wire is 5 times 12 cm, which equals 60 cm.

5. In the sequence 8 5 4 9 7 6 3 2 arranged by Garry, where should the digit 1 be inserted?

At the end

At the beginning

Between 9 and 7

Between 6 and 3

The given order of digits is in ascending order. To maintain this order and place the digit 1 in the correct position, it should be placed between the digits 9 and 7. This would result in the following order: 8 5 4 9 1 7 6 3 2.

Explanation

The given order of digits is in ascending order. To maintain this order and place the digit 1 in the correct position, it should be placed between the digits 9 and 7. This would result in the following order: 8 5 4 9 1 7 6 3 2.

6. Mary can complete an activity in 40 days. John can complete an activity in 50 days. Estimate for how many days they work on 2 activities if they change them at the best moment?

46

45

43

44.44

Mary can complete 1 activity in 40 days, which means she can complete 1/40 of the activity in one day. Similarly, John can complete 1/50 of the activity in one day. When they work together, they can complete 1/40 + 1/50 = 9/200 of the activity in one day. To complete 2 activities, they need to work for 2 / (9/200) = 400/9 days, which is approximately 44.44 days.

Explanation

Mary can complete 1 activity in 40 days, which means she can complete 1/40 of the activity in one day. Similarly, John can complete 1/50 of the activity in one day. When they work together, they can complete 1/40 + 1/50 = 9/200 of the activity in one day. To complete 2 activities, they need to work for 2 / (9/200) = 400/9 days, which is approximately 44.44 days.

7. If Jack walks up on an escalator at a rate of one step per second, 12 steps take him to the top. If Jack goes up at two steps per second, he reaches the top in 20 steps. How many steps are there on the escalator?

40

120

80

60

Let's assume the number of steps on the escalator is 'x'. When Jack walks up at a rate of one step per second, he takes 12 steps to reach the top. This means that the escalator is moving at a rate of (x-12) steps per second. Similarly, when Jack goes up at two steps per second, he takes 20 steps to reach the top. This means that the escalator is moving at a rate of (x-20) steps per second. We can set up two equations using this information: x - 12 = (x-20)/2 and x - 20 = (x-12)/1. Solving these equations, we find that x = 60. Therefore, there are 60 steps on the escalator.

Explanation

Let's assume the number of steps on the escalator is 'x'. When Jack walks up at a rate of one step per second, he takes 12 steps to reach the top. This means that the escalator is moving at a rate of (x-12) steps per second. Similarly, when Jack goes up at two steps per second, he takes 20 steps to reach the top. This means that the escalator is moving at a rate of (x-20) steps per second. We can set up two equations using this information: x - 12 = (x-20)/2 and x - 20 = (x-12)/1. Solving these equations, we find that x = 60. Therefore, there are 60 steps on the escalator.

8. How man "yes" or "no" questions are needed to guess any 5-digit code?

21

19

17

23

To guess any 5-digit code using "yes" or "no" questions, we need to consider that each question can only provide one bit of information. Since there are 10 possible digits (0-9) for each position in the code, we need to find the minimum number of questions required to narrow down the possibilities to just one code. In this case, the correct answer is 17, which means that it is possible to guess any 5-digit code by asking 17 "yes" or "no" questions.

Explanation

To guess any 5-digit code using "yes" or "no" questions, we need to consider that each question can only provide one bit of information. Since there are 10 possible digits (0-9) for each position in the code, we need to find the minimum number of questions required to narrow down the possibilities to just one code. In this case, the correct answer is 17, which means that it is possible to guess any 5-digit code by asking 17 "yes" or "no" questions.

9. 9+99+999+...+999999999999999999999= ? The addition shown above has 21 terms and the last element consists of 21 9's. Find the three last digits of the sum?

999

089

989

789

The sum of the given addition can be simplified by noticing that each term is formed by concatenating a certain number of 9's. In this case, the last term consists of 21 9's. When we add these numbers, the sum of the digits in each column will be 9, except for the rightmost column which will be 1. Therefore, the three last digits of the sum will be 089.

Explanation

The sum of the given addition can be simplified by noticing that each term is formed by concatenating a certain number of 9's. In this case, the last term consists of 21 9's. When we add these numbers, the sum of the digits in each column will be 9, except for the rightmost column which will be 1. Therefore, the three last digits of the sum will be 089.

10. A cube is painted on theside and then divided into one-unit cubes. The total number of painted faces equals the total number of unpainted faces. What was thesidelengthof the cube before it was painted?

4 units

3 unites

2 units

5 units

If we consider a cube with a side length of 2 units, it has 6 faces. When we paint one side of the cube, only 5 faces remain unpainted. However, if we divide the cube into one-unit cubes, each face of the original cube will be divided into 4 smaller faces. Therefore, the total number of painted faces will be 5 * 4 = 20, which is greater than the total number of unpainted faces (5). This means that the side length of the cube cannot be 2 units.

Explanation

If we consider a cube with a side length of 2 units, it has 6 faces. When we paint one side of the cube, only 5 faces remain unpainted. However, if we divide the cube into one-unit cubes, each face of the original cube will be divided into 4 smaller faces. Therefore, the total number of painted faces will be 5 * 4 = 20, which is greater than the total number of unpainted faces (5). This means that the side length of the cube cannot be 2 units.