Practice Test GeeksGED Practice Test
← All GED Flashcard Decks

Free GED Math Algebraic Thinking Advanced Practice Test Flashcards

36 cards from real GED practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

Read the first 20 Free GED Math Algebraic Thinking Advanced Practice Test flashcards as text

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

    Answer: 7

    4x - 3 = 2x + 11 → 2x = 14 → x = 7.

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

    Answer: 7

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

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

    Answer: x > 4

    2x + 5 > 13 → 2x > 8 → x > 4.

  4. Factor: x² + 5x + 6

    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).

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

    Answer: 35

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

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

    Answer: x = 3, y = 4

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

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

    Answer: 1

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

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

    Answer: -2

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

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

    Answer: 8

    3x - 6 = 2x + 2 → x = 8.

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

    Answer: 165 miles

    d = 55 × 3 = 165 miles.

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

    Answer: 6

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

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

    Answer: 11

    f(-3) = (-3)² + 2 = 9 + 2 = 11.

  13. Solve: 5x/2 = 20

    Answer: 8

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

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

    Answer: 39

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

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

    Answer: 2n + 3

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

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

    Answer: 81 cm²

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

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

    Answer: 9

    2y/3 = 6 → 2y = 18 → y = 9.

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

    Answer: e = 65h

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

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

    Answer: 6x - 14

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

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

    Answer: 8

    Add equations: 2x = 16 → x = 8.