SAT Math Practice Questions
SAT Math Revision on Intro to Algebra
Instructions: Click on each question to see the options and after solving you can click to see the explanations
1. Identify the variable, term, and coefficient in the expression \(3x + 5\).
A. Variable: 5
B. Term: 5x
C. Coefficient: 3
D. None of these
In the expression \(3x + 5\):
- \(3\) is the coefficient of the term \(3x\).
- \(x\) is the variable.
- \(3x\) and \(5\) are the terms of the expression.
2. Which of the following is a coefficient in the expression \(7y - 2z + 6\)?
A. 7
B. -6
C. z
D. 0
In the expression \(7y - 2z + 6\),
- \(7\) is the coefficient of \(y\), and \(-2\) is the coefficient of \(z\).
- These coefficients represent the factors multiplying the variables \(y\) and \(z\), respectively.
3. Which term represents the constant in the expression \(5x + 3\)?
A. \(5x\)
B. 3
C. \(x\)
D. 5
The constant in an expression is the term without a variable. Here, \(3\) is the constant because it does not contain \(x\).
4. Identify the coefficient of \(a\) in the expression \(4a + 2b - 5\).
A. 4
B. 2
C. -5
D. \(a\)
The coefficient is the number that multiplies the variable. Here, \(4\) is the coefficient of \(a\).
5. Simplify the expression \(3x + 2x\).
A. \(5x\)
B. \(6x\)
C. \(3x\)
D. \(x\)
Combine like terms: \(3x + 2x = 5x\).
6. Which of the following terms is a like term to \(7y\)?
A. \(7x\)
B. \(7\)
C. \(2y\)
D. \(y^2\)
Like terms have the same variable and exponent. Here, \(2y\) is a like term to \(7y\).
7. What is the numerical value of \(4x\) when \(x = 3\)?
A. 12
B. 15
C. 10
D. 7
Substitute \(x = 3\) into \(4x\): \(4 \times 3 = 12\).
8. Simplify the expression \(2a + 3b + 4a\).
A. \(6a + 3b\)
B. \(5a + b\)
C. \(5b + 4a\)
D. \(a + b\)
Combine like terms: \(2a + 4a = 6a\), so \(2a + 3b + 4a = 6a + 3b\).
9. What is the highest common factor of \(4x\) and \(6x^2\)?
A. \(2x\)
B. \(x\)
C. \(6x\)
D. \(4x\)
The highest common factor is the largest factor that divides both terms. Here, \(2x\) divides both \(4x\) and \(6x^2\).
10. Expand \(3(x + 2)\).
A. \(3x + 6\)
B. \(3x + 2\)
C. \(x + 6\)
D. \(6x + 3\)
Distribute \(3\) to both terms in the parenthesis: \(3(x + 2) = 3x + 6\).
11. Factorize \(5x + 10\).
A. \(5(x + 2)\)
B. \(x + 2\)
C. \(5x + 2\)
D. \(10x + 5\)
Factor out \(5\): \(5x + 10 = 5(x + 2)\).
12. Which of the following terms is a like term to \(3x^2\)?
A. \(3x\)
B. \(3\)
C. \(5x^2\)
D. \(x\)
Like terms have the same variable and exponent. Here, \(5x^2\) is a like term to \(3x^2\).
13. What is the numerical value of \(5a\) when \(a = 4\)?
A. 20
B. 9
C. 12
D. 25
Substitute \(a = 4\) into \(5a\): \(5 \times 4 = 20\).
14. Simplify the expression \(6b + 4b\).
A. \(10b\)
B. \(2b\)
C. \(24b\)
D. \(6b\)
Combine like terms: \(6b + 4b = 10b\).
15. Identify the highest common factor of \(9x\) and \(12\).
A. 3
B. 9
C. \(x\)
D. 1
The highest common factor of \(9x\) and \(12\) is \(3\) because it divides both terms evenly.
16. Expand \(2(y + 4)\).
A. \(2y + 8\)
B. \(y + 8\)
C. \(2y + 4\)
D. \(8y\)
Distribute \(2\) to both terms: \(2(y + 4) = 2y + 8\).
17. Factorize \(8a + 12\).
A. \(4(2a + 3)\)
B. \(2(a + 6)\)
C. \(2a + 3\)
D. \(8(a + 12)\)
Factor out \(4\): \(8a + 12 = 4(2a + 3)\).
18. Simplify the expression \(4p + 3p - 2p\).
A. \(5p\)
B. \(9p\)
C. \(7p\)
D. \(1p\)
Combine like terms: \(4p + 3p - 2p = 5p\).
19. What is the highest common factor of \(15x\) and \(25\)?
A. 5
B. \(x\)
C. \(15x\)
D. \(10\)
The highest common factor of \(15x\) and \(25\) is \(5\), the largest number that divides both terms.
20. Expand \(3(2x + 5)\).
A. \(6x + 15\)
B. \(5x + 10\)
C. \(3x + 5\)
D. \(2x + 3\)
Distribute \(3\) to both terms: \(3(2x + 5) = 6x + 15\).
21. What is the coefficient of \(x\) in the expression \(4x + 7\)?
A. 7
B. 4
C. \(x\)
D. 1
The coefficient of \(x\) in \(4x + 7\) is \(4\).
22. Simplify the expression \(9a - 3a\).
A. \(6a - 3a\)
B. \(12a\)
C. \(6a\)
D. \(9a\)
Combine like terms: \(9a - 3a = 6a\).
23. Which of the following is the expanded form of \(7(3b + 2)\)?
A. \(7b + 2\)
B. \(21b + 7\)
C. \(3b + 14\)
D. \(21b + 14\)
Distribute \(7\) to both terms: \(7(3b + 2) = 21b + 14\).
24. What is the highest common factor of \(12y\) and \(8\)?
A. \(2\)
B. \(4\)
C. \(8\)
D. \(12\)
The highest common factor of \(12y\) and \(8\) is \(4\).
25. Simplify the expression \(4c + 5c + 6c\).
A. \(15\)
B. \(9c\)
C. \(15c\)
D. \(11c\)
Combine like terms: \(4c + 5c + 6c = 15c\).
26. Factorize \(6x + 9\).
A. \(2(x + 3)\)
B. \(3(2x + 3)\)
C. \(6(x + 9)\)
D. \(6x\)
Factor out \(3\): \(6x + 9 = 3(2x + 3)\).
27. What is the numerical value of \(10 - 2x\) when \(x = 3\)?
A. 4
B. 16
C. \(10\)
D. \(2\)
Substitute \(x = 3\) into \(10 - 2x\): \(10 - 2(3) = 10 - 6 = 4\).
28. Expand \(5(x + 3)\).
A. \(5x + 3\)
B. \(x + 15\)
C. \(5x + 15\)
D. \(15x + 5\)
Distribute \(5\) to both terms: \(5(x + 3) = 5x + 15\).
29. Identify the like term of \(8p\) in the following options.
A. \(p\)
B. \(8\)
C. \(q\)
D. \(3p\)
\(8p\) and \(3p\) are like terms because they both contain the variable \(p\).
30. Simplify \(x + x + x\).
A. \(3\)
B. \(2x\)
C. \(4x\)
D. \(3x\)
Add the like terms: \(x + x + x = 3x\).
31. What is the coefficient of \(m\) in the expression \(12m + 5\)?
A. 12
B. 5
C. \(m\)
D. 1
The coefficient of \(m\) in \(12m + 5\) is \(12\).
32. Simplify the expression \(7n - 3n\).
A. \(10n\)
B. \(4n\)
C. \(7n\)
D. \(3n\)
Combine like terms: \(7n - 3n = 4n\).
33. Which of the following is the expanded form of \(6(2y + 3)\)?
A. \(6y + 3\)
B. \(2y + 18\)
C. \(12y + 18\)
D. \(18y\)
Distribute \(6\) to both terms: \(6(2y + 3) = 12y + 18\).
34. What is the highest common factor of \(10x\) and \(15\)?
A. \(2\)
B. \(10\)
C. \(5\)
D. \(15\)
The highest common factor of \(10x\) and \(15\) is \(5\).
35. Simplify the expression \(3a + 4a + 5a\).
A. \(12\)
B. \(7a\)
C. \(12a\)
D. \(9a\)
Combine like terms: \(3a + 4a + 5a = 12a\).
36. Factorize \(9y + 12\).
A. \(3(y + 4)\)
B. \(3(3y + 4)\)
C. \(9(y + 12)\)
D. \(3y\)
Factor out \(3\): \(9y + 12 = 3(3y + 4)\).
37. What is the numerical value of \(8 - 3x\) when \(x = 2\)?
A. 2
B. 6
C. \(8\)
D. \(5\)
Substitute \(x = 2\) into \(8 - 3x\): \(8 - 3(2) = 8 - 6 = 2\).
38. Expand \(4(x + 5)\).
A. \(4x + 5\)
B. \(x + 20\)
C. \(4x + 20\)
D. \(5x + 4\)
Distribute \(4\) to both terms: \(4(x + 5) = 4x + 20\).
39. Identify the like term of \(5x\) in the following options.
A. \(3x\)
B. \(2y\)
C. \(6\)
D. \(5xy\)
Only \(3x\) is a like term because it contains the variable \(x\).
40. Which expression is equivalent to \(4(3a + 2)\)?
A. \(12a + 8\)
B. \(6a + 2\)
C. \(7a + 2\)
D. \(4a + 6\)
Distributing \(4\) gives \(4(3a + 2) = 12a + 8\).
41. What is the value of \(4 + 3(2)\)?
A. \(10\)
B. \(5\)
C. \(8\)
D. \(12\)
Calculate: \(4 + 3(2) = 4 + 6 = 10\).
42. Which of the following expressions is simplified correctly?
A. \(6x + 3x = 9x\)
B. \(6x + 3x = 9x\)
C. \(6x - 3x = 3x\)
D. \(3x + 3 = 6\)
Combining like terms gives \(6x + 3x = 9x\).
43. What is the product of \(3a\) and \(4b\)?
A. \(12ab\)
B. \(7ab\)
C. \(3b\)
D. \(12a\)
Multiplying gives \(3a \times 4b = 12ab\).
44. Factor the expression \(4x + 8\).
A. \(4(x + 2)\)
B. \(2(x + 4)\)
C. \(8(x + 4)\)
D. \(4x + 4\)
Factor out \(4\): \(4x + 8 = 4(x + 2)\).
45. Simplify the expression \(10 - 2(3 + 1)\).
A. \(6\)
B. \(4\)
C. \(2\)
D. \(8\)
Calculate: \(10 - 2(4) = 10 - 8 = 6\).
46. Which of the following is an expression?
A. \(5 = 5\)
B. \(3x + 2\)
C. \(x^2\)
D. \(x - y = 4\)
An expression is a combination of numbers and variables, such as \(3x + 2\).
47. Simplify \(x^2 + 3x + 2 + x^2\).
A. \(3x^2 + 2\)
B. \(2x^2 + 3x + 2\)
C. \(x^2 + 3\)
D. \(4x\)
Combine like terms: \(x^2 + x^2 = 2x^2\) resulting in \(2x^2 + 3x + 2\).
48. What is the sum of \(4y + 3y\)?
A. \(7y\)
B. \(12y\)
C. \(y\)
D. \(4\)
Adding the coefficients gives \(4y + 3y = 7y\).
49. Factor the expression \(6x + 9\).
A. \(3(2x + 3)\)
B. \(2(3x + 3)\)
C. \(6(x + 3)\)
D. \(9(3x)\)
Factoring out \(3\) gives \(6x + 9 = 3(2x + 3)\).
50. What is the value of \(2^3 + 3^2\)?
A. \(17\)
B. \(8\)
C. \(9\)
D. \(10\)
Calculating gives \(2^3 = 8\) and \(3^2 = 9\), so \(8 + 9 = 17\).
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