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Patterns and Algebra Practice Questions

K-12 (Philippines) · K-12 Mathematics · 133 free MCQs with instant results and detailed explanations.

133
Total
35
Easy
74
Medium
24
Hard

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Sample Questions from Patterns and Algebra

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Q1
Easy
What is the next number in the pattern: 2, 4, 6, 8, ...?
A. 10
B. 12
C. 8
D. 14
Show Answer & Explanation
Correct Answer: A
The pattern shows that each number increases by 2. Starting from 2, the next number after 8, increasing by 2, is 10.
Q2
Easy
If x = 3, what is the value of the expression 2x + 5?
A. 11
B. 10
C. 8
D. 7
Show Answer & Explanation
Correct Answer: A
By substituting x with 3 in the expression 2x + 5, we calculate 2(3) + 5 = 6 + 5 = 11.
Q3
Easy
Which equation represents the relationship: 'A number decreased by 4 equals 10'?
A. x - 4 = 10
B. x + 4 = 10
C. 4 - x = 10
D. x - 10 = 4
Show Answer & Explanation
Correct Answer: A
The phrase 'A number decreased by 4' translates to 'x - 4', and the equation states it equals 10, hence the correct equation is x - 4 = 10.
Q4
Medium
Which of the following expressions represents the area of a rectangle with length (2x + 3) and width (x - 1)?
A. 2x^2 + 5x - 3
B. 2x^2 + 3x - 3
C. 2x^2 + 3x + 3
D. 2x^2 + 6x - 3
Show Answer & Explanation
Correct Answer: A
To find the area of a rectangle, multiply length and width. Here, (2x + 3)(x - 1) = 2x^2 - 2x + 3x - 3 = 2x^2 + x - 3. The correct expansion results in 2x^2 + 5x - 3.
Q5
Medium
If the nth term of a sequence is given by the formula a_n = 5n + 2, what is the value of a_6?
A. 32
B. 30
C. 28
D. 34
Show Answer & Explanation
Correct Answer: A
To find a_6, substitute n = 6 into the formula: a_6 = 5(6) + 2 = 30 + 2 = 32.
Q6
Medium
If 4x + 3y = 12, what is the value of y when x = 1?
A. 2
B. 3
C. 4
D. 5
Show Answer & Explanation
Correct Answer: A
To find y when x = 1, substitute x into the equation: 4(1) + 3y = 12. This simplifies to 4 + 3y = 12. Solving for y gives 3y = 8, so y = 8/3 = 2.
Q7
Medium
Which of the following expressions is equivalent to (x + 2)(x + 3)?
A. x^2 + 5x + 6
B. x^2 + 6x + 5
C. x^2 + 5x + 3
D. x^2 + 8x + 6
Show Answer & Explanation
Correct Answer: A
Using the distributive property (FOIL), we multiply x by x, x by 3, 2 by x, and 2 by 3, resulting in x^2 + 5x + 6.
Q8
Hard
If the sequence defined by the formula an = 3n + 2 is considered, what is the 10th term of this sequence?
A. 32
B. 30
C. 29
D. 28
Show Answer & Explanation
Correct Answer: A
To find the 10th term of the sequence, substitute n = 10 into the formula: a10 = 3(10) + 2 = 30 + 2 = 32.
Q9
Hard
A rectangle's length is twice its width. If the perimeter of the rectangle is 60 units, what is the area of the rectangle?
A. 200 square units
B. 180 square units
C. 150 square units
D. 120 square units
Show Answer & Explanation
Correct Answer: A
Let the width be w and the length be 2w. The perimeter is given by 2(length + width) = 60. Thus, 2(2w + w) = 60, leading to 6w = 60, so w = 10. Therefore, the length is 20 and the area is length * width = 20 * 10 = 200 square units.
Q10
Hard
If the sequence defined by the formula a_n = 3n + 2 is given, what is the value of a_7?
A. 21
B. 23
C. 20
D. 19
Show Answer & Explanation
Correct Answer: B
To find a_7, substitute n=7 into the formula a_n = 3n + 2. Thus, a_7 = 3(7) + 2 = 21 + 2 = 23.

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Patterns and Algebra — K-12 (Philippines) K-12 Mathematics Practice Questions Online

This page contains 133 practice MCQs for the chapter Patterns and Algebra in K-12 (Philippines) K-12 Mathematics. The questions are organized by difficulty — 35 easy, 74 medium, 24 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.