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Heart of Algebra Practice Questions

SAT · SAT Math · 100 free MCQs with instant results and detailed explanations.

100
Total
30
Easy
55
Medium
15
Hard

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Sample Questions from Heart of Algebra

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
A line passes through the points (1, 2) and (3, 6). What is the slope of the line?
A. 2
B. 3
C. 4
D. 1
Show Answer & Explanation
Correct Answer: A
Slope is calculated as (y2 - y1) / (x2 - x1). Here, y2 = 6, y1 = 2, x2 = 3, and x1 = 1. Thus, the slope = (6 - 2) / (3 - 1) = 4 / 2 = 2.
Q2
Easy
If a store sells a shirt for $20, what will be the total cost for buying 3 shirts including a 5% sales tax?
A. $60.00
B. $63.00
C. $61.00
D. $62.00
Show Answer & Explanation
Correct Answer: B
The total cost before tax is 3 shirts × $20 = $60. The sales tax is 5% of $60, which is $3. Thus, the total cost is $60 + $3 = $63.
Q3
Easy
A store sells pencils for $1.50 each. If Sarah buys 4 pencils, how much does she spend?
A. $6.00
B. $5.50
C. $7.00
D. $4.00
Show Answer & Explanation
Correct Answer: A
To find the total cost, multiply the price of one pencil by the number of pencils bought: $1.50 x 4 = $6.00.
Q4
Medium
A company has a monthly budget of $2,500 for marketing. If they spend $600 on social media advertising and $1,200 on events, how much do they have left for other marketing expenses?
A. $700
B. $900
C. $800
D. $1,000
Show Answer & Explanation
Correct Answer: B
To find the remaining budget, subtract the expenses from the total budget. $2,500 - ($600 + $1,200) = $2,500 - $1,800 = $700.
Q5
Medium
A line passes through the points (1, 2) and (3, 6). What is the slope of this line?
A. 2
B. 4
C. 3
D. 1
Show Answer & Explanation
Correct Answer: A
The slope is calculated as (y2 - y1) / (x2 - x1). Here, it’s (6 - 2) / (3 - 1) = 4 / 2 = 2.
Q6
Medium
If the function f(x) = 2x + 3, what is f(5)?
A. 10
B. 8
C. 13
D. 15
Show Answer & Explanation
Correct Answer: C
To find f(5), substitute 5 into the function: f(5) = 2(5) + 3 = 10 + 3 = 13.
Q7
Medium
A rectangle has a length that is twice its width. If the perimeter is 48 cm, what are the dimensions of the rectangle?
A. Width = 8 cm, Length = 16 cm
B. Width = 12 cm, Length = 24 cm
C. Width = 6 cm, Length = 12 cm
D. Width = 10 cm, Length = 20 cm
Show Answer & Explanation
Correct Answer: A
Let width = w, then length = 2w. The perimeter is 2(w + 2w) = 48. Solving gives w = 8, length = 16.
Q8
Hard
If 3x + 2y = 12 and y = 4 - x, what is the value of x?
A. 2
B. 3
C. 1
D. 4
Show Answer & Explanation
Correct Answer: A
Substituting y = 4 - x into the first equation: 3x + 2(4 - x) = 12 simplifies to 3x + 8 - 2x = 12, leading to x = 2.
Q9
Hard
A line passes through the points (1, 2) and (3, 6). What is the slope of this line?
A. 2
B. 3
C. 1
D. 4
Show Answer & Explanation
Correct Answer: A
The slope m is calculated as (y2 - y1) / (x2 - x1). For (1, 2) and (3, 6), m = (6 - 2) / (3 - 1) = 4 / 2 = 2.
Q10
Hard
If 3x - 2y = 6 and x + y = 8, what is the value of x?
A. 4
B. 5
C. 6
D. 2
Show Answer & Explanation
Correct Answer: A
To find x, we can solve the equations simultaneously. From x + y = 8, we express y as y = 8 - x. Substituting this into the first equation gives 3x - 2(8 - x) = 6, simplifying to 5x - 16 = 6. Thus, 5x = 22, leading us to x = 4.

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Heart of Algebra — SAT SAT Math Practice Questions Online

This page contains 100 practice MCQs for the chapter Heart of Algebra in SAT SAT Math. The questions are organized by difficulty — 30 easy, 55 medium, 15 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.