IBEW Aptitude Test Math Problems: Complete Practice Compilation

This is a consolidated, no-answer-key practice list assembled from the supplied aptitude-test notes, ChatGPT practice sets, and screenshot examples. Duplicate HTML and PDF exports have been combined so each distinct problem appears once.

Work the problems without looking at the choices first when possible. Show your algebra, especially when rearranging a formula or factoring a quadratic.

Selected NJATC/ETA practice order: 13, 15, 25, 16, 17, 18, 19, 20, 21. Questions 16–21 use varied constant offsets to practice the same variable relationships.

Part 1 — Linear equations and basic algebra

1. Solve for $x$.

$4x+7=31$

2. Solve for $x$.

$3(x-5)=21$

3. Simplify.

$5x+3-2x+8$

4. If $y=3x^2-2x+4$, find $y$ when $x=2$.

5. Solve for $x$.

$\frac{x}{4}+6=11$

6. Solve for $x$.

$2x+5=5x-16$

7. Solve for $x$.

$4(x-3)=2x+10$

A. $x=7$
B. $x=9$
C. $x=11$
D. $x=13$

8. Solve for $x$.

$\frac{x}{3}+5=11$

A. $12$
B. $15$
C. $18$
D. $21$

9. Solve for $x$.

$\frac{3x}{5}=18$

10. Solve for $x$.

$5(x+2)-3=2x+16$

11. A wire is 84 feet long and is divided into two pieces. One piece is 12 feet longer than the other. How long is the shorter piece?

12. The value of $y$ is four less than twice the value of $x$. Which formula represents the statement?

A. $y=4x-2$
B. $y=2x+4$
C. $y=4-2x$
D. $y=2x-4$

Part 2 — Formula substitution and variable relationships

13. Consider $A=3B-2C$. If $B=8$ and $C=5$, what is $A$?

A. $10$
B. $14$
C. $19$
D. $34$

14. If $y=\frac{x}{2}-6$, what is $y$ when $x=18$?

A. $2$
B. $3$
C. $6$
D. $12$

15. Consider $a=\frac{3}{4}b-9$. Which statement is true?

A. When $b<12$, $a$ is positive.
B. When $b<12$, $a$ is negative.
C. When $b>9$, $a$ is always positive.
D. When $b>6$, $a$ is always positive.

16. If $12=\frac{7a}{b-4}-c$, where $b>4$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. There is not enough information

17. If $-5=\frac{6a}{b-2}-c$, where $b>2$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

18. If $9=\frac{4a}{b-5}+c$, where $b>5$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

19. If $-8=\frac{8a}{3-b}-c$, where $b>3$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

20. If $\frac32=\frac{5a}{b+1}-c$, where $b>-1$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

21. If $20=\frac{9a}{2-b}+c$, where $b>2$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

22. If $0=\frac{a+4}{b-1}-c$, where $b>1$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

23. If $0=\frac{12a}{b-6}-3c$, where $b>6$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

24. If $0=\frac{10a}{b+2}+2c$, where $b>-2$ and $b$ is held constant, what happens to $c$ as $a$ increases?

A. $c$ increases
B. $c$ decreases
C. $c$ remains constant
D. Cannot be determined

25. If $b=4(a+2)$, what happens to $b$ as $a$ increases?

A. Increases
B. Decreases
C. Stays the same
D. Cannot determine

26. If $y=-2(x-5)$, what happens to $y$ as $x$ increases?

A. Increases
B. Decreases
C. Stays the same
D. Cannot determine

27. If $c=7-3d$, what happens to $c$ as $d$ decreases?

A. Increases
B. Decreases
C. Stays the same
D. Cannot determine

28. If $m=\frac{n}{4}+6$, what happens to $m$ as $n$ increases?

A. Increases
B. Decreases
C. Stays the same
D. Cannot determine

29. If $p=10-5q$, what must happen to $q$ as $p$ increases?

A. $q$ increases
B. $q$ decreases
C. $q$ stays the same
D. Cannot determine

30. If $b=\frac{15}{a+2}$, where $a>-2$, what happens to $b$ as $a$ increases?

A. $b$ increases
B. $b$ decreases
C. $b$ stays constant
D. Cannot determine

31. If $c=\frac{4a}{7}$, what happens to $c$ as $a$ decreases?

A. $c$ increases
B. $c$ decreases
C. $c$ stays constant
D. Cannot determine

32. If $y=\frac{8}{5-x}$, where $x<5$, what happens to $y$ as $x$ increases?

A. $y$ increases
B. $y$ decreases
C. $y$ stays constant
D. Cannot determine

33. If $m=-\frac{12}{n+4}$, where $n>-4$, what happens to $m$ as $n$ increases?

A. $m$ increases
B. $m$ decreases
C. $m$ stays constant
D. Cannot determine

34. If $p=\frac{3q+6}{10}$, what happens to $p$ as $q$ increases?

A. $p$ increases
B. $p$ decreases
C. $p$ stays constant
D. Cannot determine

Part 3 — Functions, tables, and systems

35. If $f(x)=2x+7$, what is $f(6)$?

36. If $f(x)=3x^2-2x+1$, what is $f(2)$?

A. $5$
B. $7$
C. $9$
D. $11$

37. Consider $y=-2x+9$. What is $y$ when $x=-3$?

A. $3$
B. $6$
C. $12$
D. $15$

38. A function contains the points $(-1,7)$, $(0,4)$, $(1,1)$, and $(2,-2)$. Which rule fits?

A. $y=-3x+4$
B. $y=3x+4$
C. $y=-4x+3$
D. $y=-3x-4$

39. Which equation fits the table?

$x$	$y$
$-2$	$11$
$-1$	$7$
$0$	$3$
$1$	$-1$

A. $y=4x+3$
B. $y=-4x+3$
C. $y=-3x+4$
D. $y=4x-3$

40. Which equation fits the table?

$x$	$y$
$0$	$-2$
$1$	$1$
$2$	$4$
$3$	$7$

A. $y=3x-2$
B. $y=-3x-2$
C. $y=2x+3$
D. $y=3x+2$

41. Which equation fits the table?

$x$	$y$
$-1$	$-1$
$0$	$2$
$1$	$5$
$2$	$8$

A. $y=-3x+2$
B. $y=3x-2$
C. $y=3x+2$
D. $y=2x+3$

42. Which equation fits the table?

$x$	$y$
$-2$	$-3$
$0$	$1$
$2$	$5$
$4$	$9$

A. $y=2x+1$
B. $y=-2x+1$
C. $y=x+2$
D. $y=2x-1$

43. A line passes through $(-2,9)$ and $(1,0)$. Which equation describes the line?

A. $y=3x+3$
B. $y=-3x+3$
C. $y=-3x-3$
D. $y=3x-3$

44. Which equation fits the table?

$x$	$y$
$-1$	$11$
$0$	$6$
$1$	$1$
$2$	$-4$

A. $y=5x+6$
B. $y=-5x+6$
C. $y=-6x+5$
D. $y=5x-6$

45. A line passes through $(0,-4)$ and $(2,2)$. Which equation describes the line?

A. $y=-3x-4$
B. $y=3x+4$
C. $y=3x-4$
D. $y=-3x+4$

46. Consider the equations $y=2x+1$ and $y=-x+10$. At what value of $x$ do the two equations produce the same value of $y$?

A. $2$
B. $3$
C. $4$
D. $5$

47. For $4y+8x=12z$, which condition guarantees that $y$ is positive?

A. $z>4$ and $x<2$
B. $z<1$ and $x>2$
C. $z>0$ and $x>3$
D. $z<0$ and $x>1$

48. For $6y+12x=18z$, which condition guarantees that $y$ is positive?

A. $z>2$ and $x<2$
B. $z<1$ and $x>2$
C. $z<0$ and $x>0$
D. $z>0$ and $x>5$

49. For $3y+9x=6z$, which condition guarantees that $y$ is negative?

A. $z>3$ and $x<1$
B. $z<1$ and $x>1$
C. $z>2$ and $x<0$
D. $z>0$ and $x<0$

50. For $5y-10x=15z$, which condition guarantees that $y$ is positive?

A. $z>1$ and $x>0$
B. $z<0$ and $x<0$
C. $z<-2$ and $x<1$
D. $z<1$ and $x<-3$

51. For $2y+6x=-4z$, which condition guarantees that $y$ is positive?

A. $z>0$ and $x>0$
B. $z<0$ and $x<0$
C. $z>2$ and $x<1$
D. $z<1$ and $x>2$

52. For $4y-8x=12z$, which condition guarantees that $y$ is negative?

A. $z>2$ and $x>1$
B. $z<-2$ and $x<1$
C. $z>0$ and $x<0$
D. $z>1$ and $x>0$

53. For $10y+5x=20z$, which condition guarantees that $y$ is positive?

A. $z>2$ and $x<4$
B. $z<0$ and $x>2$
C. $z<1$ and $x>5$
D. $z>0$ and $x>10$

Part 4 — Factoring, products, and exponents

54. Solve $x^2-9x+20=0$.

A. $x=2,10$
B. $x=4,5$
C. $x=-4,-5$
D. $x=1,20$

55. Solve $x^2-9=0$.

56. Solve $x^2-11x+24=0$.

A. $x=-3,-8$
B. $x=3,8$
C. $x=-3,8$
D. $x=4,6$

57. Solve $x^2+9x+20=0$.

A. $x=4,5$
B. $x=-4,-5$
C. $x=-4,5$
D. $x=2,10$

58. Solve $x^2-x-12=0$.

A. $x=4,-3$
B. $x=-4,3$
C. $x=6,-2$
D. $x=-4,-3$

59. Solve $x^2+2x-15=0$.

A. $x=-3,5$
B. $x=3,-5$
C. $x=-3,-5$
D. $x=3,5$

60. Solve $x^2-16=0$.

A. $x=4$ only
B. $x=-4$ only
C. $x=4,-4$
D. $x=8,-2$

61. Solve $2x^2-10x=0$.

A. $x=0,5$
B. $x=0,-5$
C. $x=2,5$
D. $x=-2,5$

62. Solve $x^2+7x+12=0$.

A. $x=3,4$
B. $x=-3,-4$
C. $x=-3,4$
D. $x=2,6$

63. Solve $x^2-5x-24=0$.

A. $x=-8,3$
B. $x=8,-3$
C. $x=-8,-3$
D. $x=6,-4$

64. Simplify.

$3x^2-7x+7$

65. Simplify.

$x^2+7x+12$

A. $(x+2)(x+6)$
B. $(x+3)(x+4)$
C. $(x-3)(x-4)$
D. $(x+1)(x+12)$

66. Simplify.

$4(2x-3)-3(x+2)$

A. $5x-18$
B. $5x-6$
C. $11x-18$
D. $8x-9$

67. Which expression is equivalent to $y=4(x-3)(x+2)$?

A. $y=4x^2-4x-24$
B. $y=4x^2-20x-24$
C. $y=4x^2+4x-24$
D. $y=x^2-x-6$

68. Multiply.

$(3x^2y-2y)(2x+5y)$

69. Expand an expression with a monomial and two binomials.

$2x(3x-y)(x+4y)$

70. Expand an expression with a monomial and two binomials.

$-3xy(2x+y)(x-5y)$

71. Simplify.

$\frac{12x^2y^2}{4xy}$

A. $3xy$
B. $3x^2y$
C. $8xy$
D. $3y$

72. Simplify.

$\frac{(3a^{-2}b^3)^2}{9a^{-1}b}$

A. $\frac{b^5}{a^3}$
B. $\frac{b^6}{a^3}$
C. $a^3b^5$
D. $\frac{a^3}{b^5}$

73. Simplify.

$\frac{x^7}{x^3}$

A. $x^2$
B. $x^3$
C. $x^4$
D. $x^{10}$

Part 5 — Number series

74. What is the next number?

$3,7,15,31,63,?$

75. What is the next number?

$2,6,18,54,?$

76. What is the next number?

$5,8,14,23,35,?$

A. $47$
B. $48$
C. $50$
D. $52$

77. What comes next?

$3,6,18,72,360,?$

A. $720$
B. $1{,}080$
C. $1{,}800$
D. $2{,}160$

Part 6 — Electrical and applied formula prompts

78. Approximate conductor sag

Given

$s\approx\frac{wL^2}{8T}$

Reverse-engineer the formula to solve for $L$.

79. Approximate horizontal conductor tension

Given

$T\approx\frac{wL^2}{8s}$

Reverse-engineer the formula to solve for the requested variable.

80. AC impedance

Given

$Z=\sqrt{R^2+X^2}$

Write the formula for $X$.

81. Three-phase line current

Given

$I=\frac{P}{\sqrt{3}V\,PF}$

Identify the formula and rearrange it when a different variable is requested.

82. Line-to-neutral voltage on a grounded-wye system

Given

$V_{\phi}=\frac{V_L}{\sqrt{3}}$

Identify the formula and rearrange it when a different variable is requested.

83. Three-phase real power

Given

$P_{3\phi}=\sqrt{3}V_LI_LPF$

Identify the formula and rearrange it when a different variable is requested.