1.
Evaluate 3^{4 }
Correct Answer
D. 81
2.
Write the following expression with exponents.
b × b × b × b × b × b × b × b × b
Correct Answer
B. B^9
Explanation
The given expression represents the multiplication of b repeated 9 times. In exponent notation, when a base is multiplied by itself multiple times, the exponent represents the number of times the base is multiplied. Therefore, the expression can be written as b^9.
3.
Write a power that represents the number of small squares in the large square.
Correct Answer
A. 5^2
Explanation
The expression 5^2 represents the number of small squares in the large square. This is because when we raise 5 to the power of 2, it means we are multiplying 5 by itself 2 times. In this case, it represents multiplying the length and width of the large square, which are both 5, to find the total number of small squares. So, the correct answer is 5^2.
4.
Write a verbal expression for the algebraic expression (2 - y) × 6.
Correct Answer
C. Two minus y times six
Explanation
The verbal expression for the algebraic expression (2 - y) × 6 is "two minus y times six". This is because the expression (2 - y) represents the difference between 2 and y, and when this difference is multiplied by 6, it can be verbalized as "two minus y times six".
5.
What is the next term in the sequence 1, 4, 7, 10, …?
Correct Answer
A. 13
Explanation
The next term in the sequence is 13. The pattern of the sequence is that each term is obtained by adding 3 to the previous term. Starting with 1, we add 3 to get 4, then add 3 again to get 7, and so on. Therefore, the next term after 10 would be 13.
6.
What is the next term in the sequence 1, 2, 3, 5, 8, 13, …?
Correct Answer
B. 21
Explanation
The given sequence follows the pattern of Fibonacci numbers, where each term is the sum of the previous two terms. Starting with 1 and 2, the next term would be 3. Therefore, the correct answer is 21.
7.
Evaluate 3 × 2 - 6 ÷ 2 + 5.
Correct Answer
B. 8
Explanation
To evaluate the expression, we follow the order of operations (PEMDAS/BODMAS). First, we perform the division: 6 ÷ 2 = 3. Then, we perform the multiplication: 3 × 2 = 6. Next, we perform the addition and subtraction from left to right: 6 - 3 + 5 = 8. Therefore, the answer is 8.
8.
What is the next term in the sequence 1, 3, 9, 27, 81, ...?
Correct Answer
B. 243
Explanation
The sequence is formed by multiplying each term by 3. Starting with 1, the next term is obtained by multiplying 81 by 3, which equals 243. Therefore, the next term in the sequence is 243.
9.
Solve 15 + a = 10.
Correct Answer
A. A = -5
Explanation
To solve the equation 15 + a = 10, we need to isolate the variable "a" on one side. To do this, we can subtract 15 from both sides of the equation. This gives us a = 10 - 15, which simplifies to a = -5. Therefore, the correct answer is a = -5.
10.
Solve 115 - b = 200.
Correct Answer
B. -85
Explanation
To solve the equation 115 - b = 200, we need to isolate the variable b. We can do this by subtracting 115 from both sides of the equation. This gives us -b = 85. To solve for b, we need to multiply both sides of the equation by -1 to get b = -85. Therefore, the correct answer is -85.
11.
If a = 3 and b = —2, what is the value of the expression
Correct Answer
D. -18/91
Explanation
The value of the expression can be found by substituting the given values of a and b into the expression. Plugging in a = 3 and b = -2, we get (-210/31) as the result. Therefore, the correct answer is -210/31.
12.
The area of a circle is given by the formula Find A when r = 3.
Correct Answer
C. 9(pi)
Explanation
The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Given that r = 3, we can substitute this value into the formula to find the area. Therefore, A = π(3^2) = 9π.
13.
The formula for finding the perimeter of a square is P = 4s. Find P when s = 5.
Correct Answer
C. 20
Explanation
The formula for finding the perimeter of a square is P = 4s, where s represents the length of one side of the square. In this case, the given value of s is 5. Substituting this value into the formula, we get P = 4(5) = 20. Therefore, the perimeter of the square is 20.
14.
Which number is not rational?
Correct Answer
C. Square root of 3
Explanation
The square root of 3 is not a rational number because it cannot be expressed as a fraction of two integers. Rational numbers can be written as fractions, where the numerator and denominator are both integers. However, the square root of 3 is an irrational number, meaning it is a non-repeating, non-terminating decimal and cannot be written as a fraction.
15.
Non-repeating, non-terminating decimals are always
Correct Answer
A. Irrational
Explanation
Non-repeating, non-terminating decimals are always irrational because they cannot be expressed as a fraction or a ratio of two integers. Irrational numbers cannot be written as a finite or repeating decimal, and they have an infinite number of non-repeating digits after the decimal point. Examples of irrational numbers include √2, π, and e.
16.
The number -4 is which of the following?
Correct Answer
C. An integer
Explanation
The number -4 is an integer because it is a whole number that can be positive, negative, or zero. It is not a natural number because natural numbers are positive integers starting from 1. It is also not a positive number because it is negative. It is not an irrational number because it can be expressed as a ratio of two integers (-4/1).
17.
George is 20 years younger than Sam. In 4 years Sam will be 40. How is old is George?
The process of solving this problem involves:
Correct Answer
C. (40 - 4) - 20
Explanation
In order to find George's age, we need to determine how much younger he is than Sam. We are given that in 4 years, Sam will be 40. So, to find Sam's current age, we subtract 4 from 40, which gives us 36. Since George is 20 years younger than Sam, we subtract 20 from Sam's current age of 36. Therefore, George's age is (36 - 20) which is equal to 16.
18.
The 10th grade class has 13 more girls than boys. If there are 95 students in the 10th grade, how many of them are girls?
Correct Answer
C. 54
Explanation
If there are 13 more girls than boys in the 10th grade class, and the total number of students is 95, we can set up the equation x + (x+13) = 95, where x represents the number of boys. Simplifying this equation, we get 2x + 13 = 95. Solving for x, we find that x = 41, which represents the number of boys. Since there are 13 more girls than boys, the number of girls is 41 + 13 = 54. Therefore, the correct answer is 54.
19.
You are trying to determine the gas mileage of a car. The car used 15 gallons of gas and traveled 450 miles. Which reasoning would NOT lead to the correct gas mileage?
Correct Answer
C. The car goes 45 miles on a gallon and a half, and therefore gets 30 miles/gallon.
Explanation
The reasoning that would NOT lead to the correct gas mileage is "The car goes 45 miles on a gallon and a half, and therefore gets 30 miles/gallon." This reasoning is incorrect because it assumes that the car traveled 45 miles on only 1.5 gallons of gas, which is not the case. The car actually used 15 gallons of gas and traveled 450 miles, so the correct gas mileage is 30 miles per gallon.
20.
Use this information to answer the next question.
Hours
1
1.5
2
2.5
3
Total
Charge
$58
$67
$76
$85
$94
The table above shows the total labor charges for an electrician. The electrician charges $40 for the service call, plus an hourly flat rate for the time spent on the job. Which equation best represents the relationship between the number of hours spent on the job, x, and the total charges, c?
Correct Answer
D. C = 40 + 18x
Explanation
The correct equation that represents the relationship between the number of hours spent on the job, x, and the total charges, c, is c = 40 + 18x. This equation takes into account the $40 service call charge and adds $18 for each hour spent on the job.
21.
What is (x^{2} + 3x + 4) – (3x^{2} +x – 1)?
Correct Answer
B. -2x^2 + 2x + 5
Explanation
The given expression is a subtraction of two polynomials. To simplify, we need to distribute the negative sign to each term in the second polynomial and then combine like terms. After distributing and combining like terms, we get -2x^2 + 2x + 5. Therefore, the correct answer is -2x^2 + 2x + 5.
22.
Simplify: -5x(2x^{2} - 3x + 7)
Correct Answer
D. -10x^3+ 15x^2 - 35x
Explanation
The given expression is simplified by distributing the -5x to each term inside the parentheses. This results in -10x^3 + 15x^2 - 35x.
23.
Simplify: (x – 9)(x + 8)
Correct Answer
A. X^2 – x – 72
Explanation
The given expression is a product of two binomials, (x - 9) and (x + 8). To simplify the expression, we can use the distributive property to multiply the terms of the two binomials.
(x - 9)(x + 8) = x(x) + x(8) - 9(x) - 9(8)
= x^2 + 8x - 9x - 72
= x^2 - x - 72
Therefore, the correct answer is x^2 - x - 72.
24.
Simplify: (x + 5)(x^{2} – 5x – 1)
Correct Answer
C. X^3 – 26x – 5
Explanation
The given expression can be simplified by using the distributive property. Multiplying (x + 5) with (x^2 – 5x – 1) yields x^3 – 26x – 5.
25.
Translate: “The product of 9 and the quantity a decreased by 6.”
Correct Answer
B. 9(a – 6)
Explanation
The given expression "9(a - 6)" represents the product of 9 and the quantity obtained by decreasing a by 6. The expression is formed by multiplying 9 with the quantity (a - 6), which clearly matches the given translation.