ParaPro Algebra and Patterns — Questions and Answers

Question 1: Solve for x: 3x + 7 = 22

x = 5 (Correct answer)
x = 4
x = 6
x = 7

Correct answer: x = 5

Subtract 7 to get 3x = 15, then divide by 3 to get x = 5.

Question 2: What is the next number in the pattern 2, 6, 18, 54, ...?

108
162 (Correct answer)
72
216

Correct answer: 162

Each term is multiplied by 3, so 54 × 3 = 162.

Question 3: Evaluate 4a − 2b when a = 3 and b = 5.

22
−2
2 (Correct answer)
7

Correct answer: 2

4(3) − 2(5) = 12 − 10 = 2.

Question 4: Which expression represents "7 less than twice a number n"?

7 − 2n
2(n − 7)
n − 14
2n − 7 (Correct answer)

Correct answer: 2n − 7

Twice a number is 2n, and 7 less than that means subtracting 7 from 2n.

Question 5: Solve for x: x/4 − 3 = 5

x = 8
x = 32 (Correct answer)
x = 20
x = 2

Correct answer: x = 32

Add 3 to get x/4 = 8, then multiply by 4 to get x = 32.

Question 6: Simplify: 5x + 3 − 2x + 8

7x + 11
3x + 5
3x + 11 (Correct answer)
14x

Correct answer: 3x + 11

Combine x-terms (5x − 2x = 3x) and constants (3 + 8 = 11).

Question 7: Which inequality is the solution to 2x − 5 > 9?

x > 7 (Correct answer)
x < 7
x > 2
x > 14

Correct answer: x > 7

Add 5 to get 2x > 14, then divide by 2 to get x > 7.

Question 8: In the arithmetic sequence 7, 11, 15, 19, ..., what is the 10th term?

47
43 (Correct answer)
39
40

Correct answer: 43

The 10th term is 7 + 9(4) = 43.

Question 9: A table shows x-values 1, 2, 3, 4 paired with y-values 5, 8, 11, 14. Which rule fits the table?

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

Correct answer: y = 3x + 2

y increases by 3 each time, and 3(1) + 2 = 5 matches the first pair.

Question 10: What is the slope of the line through the points (2, 3) and (6, 11)?

1/2
4
2 (Correct answer)
8

Correct answer: 2

Slope = (11 − 3) / (6 − 2) = 8/4 = 2.

Question 11: What is the next number in the pattern 1, 4, 9, 16, 25, ...?

30
36 (Correct answer)
35
49

Correct answer: 36

These are perfect squares, so the next is 6² = 36.

Question 12: A gym charges a $25 sign-up fee plus $15 per month. Which expression gives the total cost for m months?

15 + 25m
40m
25 + 15m (Correct answer)
15m − 25

Correct answer: 25 + 15m

The one-time fee is constant (25) and the monthly charge multiplies by m (15m).

Question 13: If f(x) = x² − 3x, what is f(4)?

4 (Correct answer)
28
−4
1

Correct answer: 4

f(4) = 16 − 12 = 4.

Question 14: Solve for x: 5(x − 2) = 3x + 4

x = 3
x = 2
x = 14
x = 7 (Correct answer)

Correct answer: x = 7

5x − 10 = 3x + 4 gives 2x = 14, so x = 7.

Question 15: Which ordered pair (x, y) solves the system x + y = 10 and x − y = 4?

(6, 4)
(3, 7)
(8, 2)
(7, 3) (Correct answer)

Correct answer: (7, 3)

Adding the equations gives 2x = 14, so x = 7 and y = 3.

Question 16: Solve the proportion 3/8 = x/40.

x = 12
x = 15 (Correct answer)
x = 20
x = 120

Correct answer: x = 15

Since 40 = 8 × 5, x = 3 × 5 = 15.

Question 17: The sum of three consecutive integers is 48. What is the smallest integer?

15 (Correct answer)
16
14
17

Correct answer: 15

n + (n + 1) + (n + 2) = 48 gives 3n = 45, so n = 15.

Question 18: What value of x makes 2x + 3 = 3x − 4 true?

x = 1
x = −7
x = 7 (Correct answer)
x = −1

Correct answer: x = 7

Subtract 2x and add 4 to both sides to get x = 7.

Question 19: A pattern repeats: triangle, square, circle, triangle, square, circle, ... What is the 20th shape?

Triangle
Square (Correct answer)
Circle
Rectangle

Correct answer: Square

20 ÷ 3 leaves a remainder of 2, so the 20th shape is the 2nd in the cycle, a square.

Question 20: Which expression is equivalent to −3(2x − 5)?

−6x − 15
6x − 15
−6x + 15 (Correct answer)
−6x + 5

Correct answer: −6x + 15

−3 × 2x = −6x and −3 × −5 = +15.

Question 21: Maria earns $12 per hour and needs at least $180. Which inequality shows the hours h she must work?

12h ≥ 180 (Correct answer)
12h ≤ 180
h + 12 ≥ 180
180h ≥ 12

Correct answer: 12h ≥ 180

Earnings are 12h, and "at least" means greater than or equal to 180.

ParaPro Algebra and Patterns

Solve for x: 3x + 7 = 22

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