High School Math Exam

1. What is the degree of 7x + 1?

1

7

2

0

The degree of a polynomial is determined by the highest power of the variable. In this case, the variable is x and the highest power is 1. Therefore, the degree of 7x + 1 is 1.

Explanation

The degree of a polynomial is determined by the highest power of the variable. In this case, the variable is x and the highest power is 1. Therefore, the degree of 7x + 1 is 1.

2. What is (x^4)/(x^0)?

X^3

X^5

X^0

X^4

The given expression can be simplified using the rule that any number raised to the power of zero is equal to 1. Therefore, (x^4)/(x^0) can be rewritten as x^4/1, which is equal to x^4.

Explanation

The given expression can be simplified using the rule that any number raised to the power of zero is equal to 1. Therefore, (x^4)/(x^0) can be rewritten as x^4/1, which is equal to x^4.

3. What is the cosine of 45 degrees (to 4 decimal places)?

1

-0.7071

0.7071

0

The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In a right triangle with a 45-degree angle, the adjacent side and the hypotenuse have the same length, which means the cosine of 45 degrees is equal to 1 divided by the square root of 2, which is approximately 0.7071 when rounded to four decimal places.

Explanation

The cosine of an angle is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In a right triangle with a 45-degree angle, the adjacent side and the hypotenuse have the same length, which means the cosine of 45 degrees is equal to 1 divided by the square root of 2, which is approximately 0.7071 when rounded to four decimal places.

4. What is the solution to the system x + y = 5 and 3x - y = 3?

(-2, -3)

(-2, 3)

(2, -3)

(2, 3)

The correct answer is (2, 3) because when we substitute x = 2 and y = 3 into the equations, we get 2 + 3 = 5 and 3(2) - 3 = 3, which are both true. Therefore, (2, 3) is the solution to the system of equations.

Explanation

The correct answer is (2, 3) because when we substitute x = 2 and y = 3 into the equations, we get 2 + 3 = 5 and 3(2) - 3 = 3, which are both true. Therefore, (2, 3) is the solution to the system of equations.

5. IF f(x) = 3x^2 + 2x - 1, what is f(-2)?

7

1

-1

-7

To find f(-2), we substitute -2 into the given equation for x. Plugging in -2 for x, we get f(-2) = 3(-2)^2 + 2(-2) - 1. Simplifying this expression, we get f(-2) = 3(4) - 4 - 1 = 12 - 4 - 1 = 7. Therefore, the value of f(-2) is 7.

Explanation

To find f(-2), we substitute -2 into the given equation for x. Plugging in -2 for x, we get f(-2) = 3(-2)^2 + 2(-2) - 1. Simplifying this expression, we get f(-2) = 3(4) - 4 - 1 = 12 - 4 - 1 = 7. Therefore, the value of f(-2) is 7.

6. What is the least common multiple of 12 and 16?

32

16

24

48

The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. To find the LCM of 12 and 16, we can list the multiples of each number and find the smallest one they have in common. The multiples of 12 are 12, 24, 36, 48, 60, ... and the multiples of 16 are 16, 32, 48, 64, 80, ... The smallest multiple they have in common is 48, so that is the least common multiple of 12 and 16.

Explanation

The least common multiple (LCM) is the smallest multiple that two or more numbers have in common. To find the LCM of 12 and 16, we can list the multiples of each number and find the smallest one they have in common. The multiples of 12 are 12, 24, 36, 48, 60, ... and the multiples of 16 are 16, 32, 48, 64, 80, ... The smallest multiple they have in common is 48, so that is the least common multiple of 12 and 16.

7. What value of x makes "3 to the x power = 81" a true statement?

3

27

4

9

The value of x that makes "3 to the x power = 81" a true statement is 4. This is because 3 raised to the power of 4 is equal to 81.

Explanation

The value of x that makes "3 to the x power = 81" a true statement is 4. This is because 3 raised to the power of 4 is equal to 81.

8. If the original price of a house is $185,000 and it falls to $160,000, what is the percent decrease?

13.51%

19.81%

8.51

25.01%

To find the percent decrease, we need to calculate the difference between the original price and the new price, which is $185,000 - $160,000 = $25,000. Then, we divide this difference by the original price and multiply by 100 to get the percent decrease. So, ($25,000/$185,000) * 100 = 13.51%. Therefore, the percent decrease is 13.51%.

Explanation

To find the percent decrease, we need to calculate the difference between the original price and the new price, which is $185,000 - $160,000 = $25,000. Then, we divide this difference by the original price and multiply by 100 to get the percent decrease. So, ($25,000/$185,000) * 100 = 13.51%. Therefore, the percent decrease is 13.51%.

9. What is (6x^3y^15)/(3xy)?

2x^2y^14

2xy^15

2x^3y

2xy

To simplify the given expression, we can divide the coefficients and subtract the exponents of the variables. Dividing 6 by 3 gives us 2. For the variable x, we subtract the exponent 3 from 1, giving us x^2. For the variable y, we subtract the exponent 15 from 1, giving us y^14. Therefore, the simplified expression is 2x^2y^14.

Explanation

To simplify the given expression, we can divide the coefficients and subtract the exponents of the variables. Dividing 6 by 3 gives us 2. For the variable x, we subtract the exponent 3 from 1, giving us x^2. For the variable y, we subtract the exponent 15 from 1, giving us y^14. Therefore, the simplified expression is 2x^2y^14.

10. How do you write an algebraic equation for "the opposite of a number added to 3 is 16"?

-(n + 3) = 16

-(n) + 3 = 16

-n + 3 = -16

N + 3 = 16

The given statement "the opposite of a number added to 3 is 16" can be translated into an algebraic equation as "-(n) + 3 = 16". This equation represents the opposite of a number (represented by -n) added to 3, which should equal 16.

Explanation

The given statement "the opposite of a number added to 3 is 16" can be translated into an algebraic equation as "-(n) + 3 = 16". This equation represents the opposite of a number (represented by -n) added to 3, which should equal 16.

11. What direction does the parabola y = -3x^2 - 1 open?

Up

Right

Left

Down

The parabola y = -3x^2 - 1 opens downwards because the coefficient of the x^2 term is negative (-3). In general, when the coefficient of the x^2 term is negative, the parabola opens downwards.

Explanation

The parabola y = -3x^2 - 1 opens downwards because the coefficient of the x^2 term is negative (-3). In general, when the coefficient of the x^2 term is negative, the parabola opens downwards.

12. What values of x makes "5x^2 + 2x - 7 = 0" a true statement?

1 & -7/5

-1-1.4

1 & 7/5

-11.4

The given equation is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 5, b = 2, and c = -7. To find the values of x that make the equation true, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values, we get x = (-2 ± √(2^2 - 4(5)(-7))) / (2(5)). Simplifying further, x = (-2 ± √(4 + 140)) / 10, x = (-2 ± √144) / 10, x = (-2 ± 12) / 10. Therefore, the values of x that make the equation true are 1 and -7/5.

Explanation

The given equation is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 5, b = 2, and c = -7. To find the values of x that make the equation true, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values, we get x = (-2 ± √(2^2 - 4(5)(-7))) / (2(5)). Simplifying further, x = (-2 ± √(4 + 140)) / 10, x = (-2 ± √144) / 10, x = (-2 ± 12) / 10. Therefore, the values of x that make the equation true are 1 and -7/5.

13. What values of x will make 2x^2 - 9x + 10 = 0 a true statement?

-5/2 And 2

5/2 And -2

-5/2 And -2

5/2 And 2

To find the values of x that make the equation 2x^2 - 9x + 10 = 0 true, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 2, b = -9, and c = 10. Plugging these values into the quadratic formula, we get x = (9 ± √((-9)^2 - 4(2)(10))) / (2(2)). Simplifying further, we have x = (9 ± √(81 - 80)) / 4, which becomes x = (9 ± √1) / 4. Since √1 = 1, we have x = (9 ± 1) / 4. This gives us two possible solutions: x = (9 + 1) / 4 = 10/4 = 5/2, and x = (9 - 1) / 4 = 8/4 = 2. Therefore, the correct answer is 5/2 and 2.

Explanation

To find the values of x that make the equation 2x^2 - 9x + 10 = 0 true, we can use the quadratic formula. The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by x = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = 2, b = -9, and c = 10. Plugging these values into the quadratic formula, we get x = (9 ± √((-9)^2 - 4(2)(10))) / (2(2)). Simplifying further, we have x = (9 ± √(81 - 80)) / 4, which becomes x = (9 ± √1) / 4. Since √1 = 1, we have x = (9 ± 1) / 4. This gives us two possible solutions: x = (9 + 1) / 4 = 10/4 = 5/2, and x = (9 - 1) / 4 = 8/4 = 2. Therefore, the correct answer is 5/2 and 2.

14. How many ways can a group of 12 choose a committee of 9?

21

108

220

200

The question is asking for the number of ways to choose a committee of 9 from a group of 12. This is a combination problem, where order doesn't matter. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values, we get 12C9 = 12! / (9!(12-9)!) = 12! / (9!3!) = (12*11*10) / (3*2*1) = 220. Therefore, the correct answer is 220.

Explanation

The question is asking for the number of ways to choose a committee of 9 from a group of 12. This is a combination problem, where order doesn't matter. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen. Plugging in the values, we get 12C9 = 12! / (9!(12-9)!) = 12! / (9!3!) = (12*11*10) / (3*2*1) = 220. Therefore, the correct answer is 220.

15. In right triangle trig, if sin A = 3/5, what is cos A?

3/5

2/5

1/5

4/5

The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. Therefore, if sin A = 3/5, it means that the side opposite angle A has a length of 3, and the hypotenuse has a length of 5. To find the cosine of angle A, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, we have 5^2 = 3^2 + x^2, where x represents the length of the adjacent side. Solving for x, we get x = 4. Therefore, cos A = 4/5.

Explanation

The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. Therefore, if sin A = 3/5, it means that the side opposite angle A has a length of 3, and the hypotenuse has a length of 5. To find the cosine of angle A, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, we have 5^2 = 3^2 + x^2, where x represents the length of the adjacent side. Solving for x, we get x = 4. Therefore, cos A = 4/5.