Free GED Math Algebraic Thinking Advanced Practice Test — Questions and Answers

Question 1: Solve for x: 4x - 3 = 2x + 11

5
6
7 (Correct answer)
8

Correct answer: 7

4x - 3 = 2x + 11 → 2x = 14 → x = 7.

Question 2: A function is defined as f(x) = 3x - 5. What is f(4)?

5
7 (Correct answer)
9
12

Correct answer: 7

f(4) = 3(4) - 5 = 12 - 5 = 7.

Question 3: Solve the inequality: 2x + 5 > 13

x > 3
x > 4 (Correct answer)
x > 5
x > 8

Correct answer: x > 4

2x + 5 > 13 → 2x > 8 → x > 4.

Question 4: Factor: x² + 5x + 6

(x + 2)(x + 3) (Correct answer)
(x + 1)(x + 6)
(x - 2)(x - 3)
(x + 6)(x - 1)

Correct answer: (x + 2)(x + 3)

Find two numbers that multiply to 6 and add to 5: they are 2 and 3. So x² + 5x + 6 = (x + 2)(x + 3).

Question 5: If y varies directly with x and y = 15 when x = 3, what is y when x = 7?

25
30
35 (Correct answer)
45

Correct answer: 35

Direct variation: y = kx. k = 15/3 = 5. When x = 7: y = 5 × 7 = 35.

Question 6: Solve the system: 2x + y = 10 and 3x - y = 5.

x = 2, y = 6
x = 3, y = 4 (Correct answer)
x = 3, y = 3
x = 4, y = 2

Correct answer: x = 3, y = 4

Add equations: 5x = 15 → x = 3. Substitute: 2(3) + y = 10 → y = 4.

Question 7: What is the slope of the line passing through (-2, 1) and (4, 7)?

1 (Correct answer)
2
3
4

Correct answer: 1

Slope = (7 - 1)/(4 - (-2)) = 6/6 = 1.

Question 8: A linear equation has the form y = mx + b. If m = -2 and b = 6, what is y when x = 4?

-2 (Correct answer)
0
2
4

Correct answer: -2

y = -2(4) + 6 = -8 + 6 = -2.

Question 9: Which value of x satisfies: 3(x - 2) = 2(x + 1)?

6
7
8 (Correct answer)
9

Correct answer: 8

3x - 6 = 2x + 2 → x = 8.

Question 10: The formula for distance is d = rt. If r = 55 mph and t = 3 hours, what is d?

150 miles
160 miles
165 miles (Correct answer)
180 miles

Correct answer: 165 miles

d = 55 × 3 = 165 miles.

Question 11: What is the value of the expression 2a² - 3b when a = 3 and b = 4?

6 (Correct answer)
10
12
14

Correct answer: 6

2(3)² - 3(4) = 2(9) - 12 = 18 - 12 = 6.

Question 12: If f(x) = x² + 2, what is f(-3)?

7
9
11 (Correct answer)
13

Correct answer: 11

f(-3) = (-3)² + 2 = 9 + 2 = 11.

Question 13: Solve: 5x/2 = 20

4
6
8 (Correct answer)
10

Correct answer: 8

Multiply both sides by 2: 5x = 40. Divide by 5: x = 8.

Question 14: An arithmetic sequence starts at 4 and increases by 7 each term. What is the 6th term?

35
39 (Correct answer)
42
46

Correct answer: 39

nth term = a + (n-1)d = 4 + (6-1)(7) = 4 + 35 = 39.

Question 15: Which expression represents 'three more than twice a number n'?

3n + 2
2n + 3 (Correct answer)
2(n + 3)
3(n + 2)

Correct answer: 2n + 3

'Twice a number n' is 2n. 'Three more than' adds 3: 2n + 3.

Question 16: If the perimeter of a square is 36 cm, what is the area?

64 cm²
81 cm² (Correct answer)
100 cm²
144 cm²

Correct answer: 81 cm²

Side = 36 ÷ 4 = 9 cm. Area = 9² = 81 cm².

Question 17: Solve for y: 2y/3 + 4 = 10

6
7
8
9 (Correct answer)

Correct answer: 9

2y/3 = 6 → 2y = 18 → y = 9.

Question 18: A table shows that for every hour worked, a plumber earns $65. Which algebraic rule describes the relationship (e = earnings, h = hours)?

h = 65e
e = h + 65
e = 65h (Correct answer)
e = 65 - h

Correct answer: e = 65h

Earnings = $65 × hours worked → e = 65h.

Question 19: Which of the following correctly simplifies 4(2x - 3) - 2(x + 1)?

6x - 14 (Correct answer)
6x - 10
8x - 14
10x - 14

Correct answer: 6x - 14

4(2x - 3) = 8x - 12. -2(x + 1) = -2x - 2. Total = 8x - 12 - 2x - 2 = 6x - 14.

Question 20: If x + y = 12 and x - y = 4, what is x?

4
6
7
8 (Correct answer)

Correct answer: 8

Add equations: 2x = 16 → x = 8.

Question 21: The inequality -3x ≤ 9 solves to:

x ≤ -3
x ≥ -3 (Correct answer)
x ≤ 3
x ≥ 3

Correct answer: x ≥ -3

Divide both sides by -3, reversing the inequality: x ≥ -3.

Question 22: A geometric sequence starts at 2 and is multiplied by 3 each term. What is the 5th term?

54
81
162 (Correct answer)
486

Correct answer: 162

Terms: 2, 6, 18, 54, 162. The 5th term is 162.

Question 23: What is the x-intercept of y = 2x - 8?

2
4 (Correct answer)
6
8

Correct answer: 4

Set y = 0: 0 = 2x - 8 → 2x = 8 → x = 4.

Question 24: Simplify: (3x + 4) + (2x - 7)

5x - 3 (Correct answer)
5x + 3
x - 3
5x - 11

Correct answer: 5x - 3

Combine like terms: 3x + 2x = 5x and 4 - 7 = -3. Result: 5x - 3.

Question 25: A car's value depreciates by $1,500 per year. If it was worth $18,000 initially, which equation describes its value V after t years?

V = 1,500t + 18,000
V = 18,000 - 1,500t (Correct answer)
V = 18,000 + 1,500t
V = 1,500 - 18,000t

Correct answer: V = 18,000 - 1,500t

The car loses $1,500 each year: V = 18,000 - 1,500t.

Question 26: What is the solution to the system: x = 2y and x + y = 9?

x = 4, y = 2
x = 6, y = 3 (Correct answer)
x = 8, y = 4
x = 9, y = 0

Correct answer: x = 6, y = 3

Substitute x = 2y: 2y + y = 9 → 3y = 9 → y = 3. Then x = 2(3) = 6.

Question 27: What is the value of 3² + 4²?

7
14
25 (Correct answer)
49

Correct answer: 25

3² = 9 and 4² = 16. 9 + 16 = 25.

Question 28: Which expression is equivalent to -2(3x - 4)?

-6x - 8
-6x + 8 (Correct answer)
6x - 8
6x + 8

Correct answer: -6x + 8

-2 × 3x = -6x and -2 × (-4) = +8. So -2(3x - 4) = -6x + 8.

Question 29: The equation C = 0.10m + 25 models a phone plan where C is cost and m is minutes. What is the cost for 150 minutes?

$35
$40 (Correct answer)
$50
$60

Correct answer: $40

C = 0.10(150) + 25 = 15 + 25 = $40.

Question 30: Solve for x: |x - 3| = 7

x = 4 or x = 10
x = -4 or x = 10 (Correct answer)
x = 4 or x = -10
x = -10 or x = -4

Correct answer: x = -4 or x = 10

|x - 3| = 7 gives x - 3 = 7 (x = 10) or x - 3 = -7 (x = -4). Solutions: x = 10 or x = -4.

Question 31: A plumber charges $80 for the first hour and $55 for each additional hour. For a job that costs $245, how many total hours did the plumber work?

2
3
4 (Correct answer)
5

Correct answer: 4

80 + 55(n-1) = 245 → 55(n-1) = 165 → n-1 = 3 → n = 4 hours.

Question 32: Which algebraic expression represents 'the product of a number and 6, decreased by 10'?

6 + n - 10
6(n - 10)
6n - 10 (Correct answer)
6n + 10

Correct answer: 6n - 10

'Product of a number and 6' is 6n. 'Decreased by 10' subtracts 10: 6n - 10.

Question 33: What is the y-intercept of the line y = -4x + 9?

-4
4
9 (Correct answer)
-9

Correct answer: 9

In y = mx + b, the y-intercept is b = 9.

Question 34: A table of values shows: x = 1, y = 5; x = 2, y = 8; x = 3, y = 11. What is the linear equation?

y = 2x + 3
y = 3x + 2 (Correct answer)
y = 4x + 1
y = 5x

Correct answer: y = 3x + 2

The pattern increases by 3 each time (slope = 3). At x = 1: 5 = 3(1) + b → b = 2. Equation: y = 3x + 2.

Question 35: If 5 times a number decreased by 3 equals 22, what is the number?

4
5 (Correct answer)
6
7

Correct answer: 5

5n - 3 = 22 → 5n = 25 → n = 5.

Question 36: Which of the following is equivalent to 2x² + 4x?

2(x² + 4)
2x(x + 2) (Correct answer)
4x(x + 1)
2(x + 2)²

Correct answer: 2x(x + 2)

Factor out the GCF: 2x² + 4x = 2x(x + 2).

Free GED Math Algebraic Thinking Advanced Practice Test

Solve for x: 4x - 3 = 2x + 11