1. Which of the following is the additive inverse of -15?
a) -15
b) 15
c) -1/15
d) 1/15
The additive inverse of a number x is the number that, when added to x, gives a sum of zero. The
additive inverse of -15 is the number that, when added to -15, gives a sum of zero. Therefore, the
additive inverse of -15 is (b) 15.
2. What is the sum of the first 25 odd positive integers?
a) 300
b) 400
c) 625
d) 6250
The first 25 odd positive integers can be represented as 1, 3, 5, 7, 9, ..., 49. The sum of these
numbers can be calculated using the formula for the sum of an arithmetic series: Sum = (n/2) * (first
term + last term), where n is the number of terms.
In this case, n = 25, the first term is 1, and the last term is 49. So, the sum of the first 25 odd positive
integers is (a) 300.
3. Find the product of (-7) and (-5).
a) 35
b) -35
c) -25
d) 25
The product of two negative numbers is positive. Therefore, the product of (-7) and (-5) is positive,
which is (a) 35.
4. The product of three consecutive odd integers is 11,475. What is the smallest of
these integers?
a) 45
b) 47
c) 49
d) 51
Let the three consecutive odd integers be x, x+2, and x+4. The product of these three integers is x *
(x+2) * (x+4). According to the problem, x * (x+2) * (x+4) = 11,475.
Solving this equation, we get x = 45. Therefore, the smallest of these integers is (a) 45.
5. Which of the following numbers is both rational and an integer?
a) √2
b) 0.25
c) 2.5
d) -7
Among the given options:
a) √2 is an irrational number because the square root of 2 cannot be expressed as a fraction of two
integers. Therefore, it is not rational.
b) 0.25 is a rational number because it can be expressed as 1/4, which is a fraction of two integers.
However, it is not an integer as it has a decimal part.
c) 2.5 is a rational number because it can be expressed as 5/2, which is a fraction of two integers.
However, it is not an integer as it has a decimal part.
d) -7 is an integer because it is a whole number without any fractional or decimal part. It is also a
rational number because it can be expressed as -7/1, which is a fraction of two integers.
Therefore, the number that is both rational and an integer is (d) -7.
6. Find the value of √(3 + √7) + √(3 - √7).
a) 2√3
b) √7
c) 2
d) 3
7. If x is an irrational number and y is a rational number, what type of number is x
+ y?
a) Rational
b) Irrational
c) Integer
d) Real
When you add an irrational number (x) to a rational number (y), the result can be classified as (b)
Irrational. In general, the sum of an irrational number and a rational number will always be irrational.
This is because the sum of a rational and an irrational number cannot be expressed as a fraction of
two integers, making it impossible to write it in the form a/b where a and b are integers.
So, the answer is (b) Irrational.
8. A car travels 320 miles in 4 hours. What is its average speed in miles per hour?
a) 80 mph
b) 100 mph
c) 60 mph
d) 85 mph
To find the average speed of the car, we use the formula:
Average speed = Total distance / Total time
In this case, the car travels 320 miles in 4 hours. So, we can calculate the average speed as follows:
Average speed = 320 miles / 4 hours
Average speed = 80 miles per hour
Therefore, the average speed of the car is (a) 80 mph.
9. The ratio of the sides of two similar triangles is 3:5. If the perimeter of the smaller
triangle is 30 units, find the perimeter of the larger triangle.
a) 54 units
b) 50 units
c) 48 units
d) 40 units
Let's assume the sides of the smaller triangle are 3x and the sides of the larger triangle are 5x, as the
ratio of their sides is 3:5. Given that the perimeter of the smaller triangle is 30 units, we can set up
the equation:
Perimeter of smaller triangle = 2 * (side1 + side2 + side3) = 30
Substitute the values of the sides in terms of x:
2 * (3x + 3x + 3x) = 30
Simplify:
2 * 9x = 30
Divide by 2:
9x = 15
Now, solve for x:
x = 15 / 9
x = 5/3
Now that we have the value of x, we can find the sides of the larger triangle:
Side1 = 5 * (5/3) = 25/3
Side2 = 5 * (5/3) = 25/3
Side3 = 5 * (5/3) = 25/3
Now, find the perimeter of the larger triangle:
Perimeter of larger triangle = 2 * (side1 + side2 + side3) = 2 * (25/3 + 25/3 + 25/3) = 2 * (75/3) = 50
units
Therefore, the perimeter of the larger triangle is (b) 50 units.
10. Express 7/8 as a percentage.
a) 70%
b) 78%
c) 87.5%
d) 62.5%
To express a fraction as a percentage, we multiply the fraction by 100.
To convert 7/8 to a percentage:
Percentage = (7/8) * 100
Percentage = 0.875 * 100
Percentage = 87.5%
Therefore, 7/8 as a percentage is (c) 87.5%.
11. A shirt is initially priced at $40, but it is on sale for 20% off. What is the sale
price?
a) $28
b) $32
c) $36
d) $38
To find the sale price of the shirt, we need to calculate the discount amount and subtract it from the
original price. Discount amount = 20% of $40 = 0.20 * $40 = $8
Sale price = Original price - Discount amount = $40 - $8 = $32
Therefore, the sale price of the shirt is (b) $32.
12. A student scored 84% on one test and 92% on another test. What is the average
percentage score of the two tests?
a) 88%
b) 87%
c) 85%
d) 89%
To find the average percentage score of the two tests, we add the percentages and divide by the
number of tests.
Average percentage = (84% + 92%) / 2 = 176% / 2 = 88%
Therefore, the average percentage score of the two tests is (a) 88%.
13. Simplify: (2^3)^4
a) 2^12
b) 2^7
c) 2^1
d) 2^81
To simplify the expression (2^3)^4, we perform the exponentiation operation first:
(2^3)^4 = 2^(3*4) = 2^12
Therefore, the simplified expression is (a) 2^12.
14. What is the value of (-3)^4?
a) 81
b) -81
c) 9
d) -9
To find the value of (-3)^4, we raise -3 to the power of 4:
(-3)^4 = (-3) * (-3) * (-3) * (-3) = 81 Therefore, the value of (-3)^4 is (a) 81.
15. Simplify: (x^2)^3 * (x^4)^2
a) x^9
b) x^10
c) x^12
d) x^14
To simplify the expression (x^2)^3 * (x^4)^2, we perform the exponentiation operation first:
(x^2)^3 = x^(23) = x^6
(x^4)^2 = x^(42) = x^8
Now, the expression becomes x^6 * x^8 = x^(6+8) = x^14
Therefore, the simplified expression is (d) x^14.
16. Simplify: 5x^2 + 3x - 7x^2 + 2x
a) -2x^2 + 5x
b) -2x^2 - 5x
c) 2x^2 - 5x
d) 2x^2 + 5x
To simplify the expression 5x^2 + 3x - 7x^2 + 2x, we combine like terms:
(5x^2 - 7x^2) + (3x + 2x) = -2x^2 + 5x
Therefore, the simplified expression is (a) -2x^2 + 5x.
17. If a = 3 and b = -2, find the value of 4a^2 - 3b + 2ab.
a) -28
b) 28
c) 30
d) -14
To find the value of 4a^2 - 3b + 2ab, substitute the given values a = 3 and b = -2 into the expression:
4(3^2) - 3(-2) + 2(3)(-2) = 4(9) + 6 - 12 = 36 + 6 - 12 = 30
Therefore, the value of 4a^2 - 3b + 2ab is (c) 30.
18. Factorize: x^3 - 8
a) (x - 2)(x^2 + 2x + 4)
b) (x + 2)(x^2 - 2x + 4)
c) (x - 2)(x^2 - 2x + 4)
d) (x + 2)(x^2 + 2x + 4)
To factorize x^3 - 8, we use the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2)
In this case, a = x and b = 2:
x^3 - 8 = (x - 2)(x^2 + 2x + 4)
Therefore, the factorization of x^3 - 8 is (a) (x - 2)(x^2 + 2x + 4).
19. Divide (2x^3 - 3x^2 + 5x + 1) by (x - 2).
a) 2x^2 + x + 3
b) 2x^2 - x + 3
c) 2x^2 - 7x + 13
d) 2x^2 + 7x + 13
2x^2 + x + 3
____________________
x - 2 | 2x^3 - 3x^2 + 5x + 1
- (2x^3 - 4x^2)
_______________
x^2 + 5x
- (x^2 - 2x^2)
_______________
7x + 1
- (7x - 14)
_______________
15
20. Find the remainder when x^3 + 2x^2 - 5x + 3 is divided by (x - 1).
a) 1
b) 0
c) -1
d) 3