HESI A2 Math Practice Test – 50 Essential
Questions with Step-by-Step Answers &
Explanations (2025 Edition)
1. 1. QUESTION
Solve for x:
5(4x+3)–4(2x+1)=47
o x=3
o x = 20
o x = 12
o x = 36
Correct
Answer: x=3
Step 1: Apply the distributive law
The first step is to expand the terms 5(4x+3) and 4(2x+1) by distribution
so 5(4x+3)–4(2x+1)=47 becomes
20x+15–8x–4=47
Step 2: Combine like terms
We can then collect like terms in:
20x–8x+15–4=47
12x+11=47
Step 3: Subtract 11 on both sides
We then have to subtract 11 on both sides to isolate the term with x.
12x+11–11=47–11
12x=36
Step 4: Divide by 12 on both sides
We then divide both sides of the equation by 12 to isolate x.
12x12=3612
, 1x=3
We can drop the 1 on the left-hand side to x=3
x=3 is the solution of the equation.
2. 2. QUESTION
Solve for x:
4x2–61=135
o x=7
o x=14
o x=14 or −14
o x=−7 or 7
Incorrect
Answer: x=7 or −7
Step 1: Add 61 on both sides
The first step in solving this problem is to add 61 from both sides of the equation.
4x2–61+61=135+61
You should then carry out the addition of the numbers on both sides of the
equation.
4x2=196
Step 2: Divide by 4 on both sides
We then divide both sides of the equation by 4.
4x24=1964
x2=49
Step 3: Take the square root on both sides
The final step is to take the square root on both sides to solve for x.
x2=49
x2−−√=49−−√
x=7 or –7
If you are asking WHY the -7 gets included as well, it’s because any negative
number squared, is positive.
7×7=49
But so does:
−7×−7=49
, Since both options work, we have to include both.
3. 3. QUESTION
Jordy buys 5 lottery tickets for $17.50.
How much would Jordy pay if he wanted to buy 7 lottery tickets?
o $28
o $24.50
o $25
o $32.50
Correct
Answer: $24.50
This is a proportion problem and the given information allows us to formulate the
equation below:
5tickets$17.50=7ticketsx
where x is the cost of 7 lottery tickets. We can solve this equation by first cross-
multiplying.
5tickets×x=7tickets×17.50$
Carrying out the product on the right-hand side, we get;
5tickets×x=122.5tickets∙$
We can solve for x by dividing both sides of the equation by 5 tickets.
5tickets×x5tickets=122.5tickets∙$5tickets
Carrying out the division, we get a 1 on the left-hand side and a 24.5 on the right-
hand side.
1x=24.5$
We can drop the 1 next to x, to get x=24.5$. It would cost Jordy $24.50 to buy 7
lottery tickets.
4. 4. QUESTION
In 18 hours, 42 trains pass near Emma’s house.
How many trains pass near her house in 12 hours?
, o 28 trains
o 56 trains
o 14 trains
o 2 trains
Correct
Answer: 28 trains
This is a proportion problem and the given information allows us to formulate the
equation below:
42trains18hours=x12hours
where x is the number of trains that pass near Emma’s house in 12 hours. We
can solve this equation by first cross-multiplying.
18hours×x=42trains×12hours
Carrying out the product on the right-hand side, we get:
18hours×x=504trains∙hours
We can solve for x by dividing both sides of the equation by 18 hours.
18hours×x18hours=504trains∙hours18hours
Carrying out the division, we get a 1 on the left-hand side and a 28 on the right-
hand side.
1x=28trains
We can drop the 1 next to x, to get x=28 trains. In 12 hours, 28 trains pass near
Emma’s house.
5. 5. QUESTION
5:12=x:36
What is the value of x?
o x=3
o x=15
o x=12
o x=7.2
Correct
Answer: x=15
Questions with Step-by-Step Answers &
Explanations (2025 Edition)
1. 1. QUESTION
Solve for x:
5(4x+3)–4(2x+1)=47
o x=3
o x = 20
o x = 12
o x = 36
Correct
Answer: x=3
Step 1: Apply the distributive law
The first step is to expand the terms 5(4x+3) and 4(2x+1) by distribution
so 5(4x+3)–4(2x+1)=47 becomes
20x+15–8x–4=47
Step 2: Combine like terms
We can then collect like terms in:
20x–8x+15–4=47
12x+11=47
Step 3: Subtract 11 on both sides
We then have to subtract 11 on both sides to isolate the term with x.
12x+11–11=47–11
12x=36
Step 4: Divide by 12 on both sides
We then divide both sides of the equation by 12 to isolate x.
12x12=3612
, 1x=3
We can drop the 1 on the left-hand side to x=3
x=3 is the solution of the equation.
2. 2. QUESTION
Solve for x:
4x2–61=135
o x=7
o x=14
o x=14 or −14
o x=−7 or 7
Incorrect
Answer: x=7 or −7
Step 1: Add 61 on both sides
The first step in solving this problem is to add 61 from both sides of the equation.
4x2–61+61=135+61
You should then carry out the addition of the numbers on both sides of the
equation.
4x2=196
Step 2: Divide by 4 on both sides
We then divide both sides of the equation by 4.
4x24=1964
x2=49
Step 3: Take the square root on both sides
The final step is to take the square root on both sides to solve for x.
x2=49
x2−−√=49−−√
x=7 or –7
If you are asking WHY the -7 gets included as well, it’s because any negative
number squared, is positive.
7×7=49
But so does:
−7×−7=49
, Since both options work, we have to include both.
3. 3. QUESTION
Jordy buys 5 lottery tickets for $17.50.
How much would Jordy pay if he wanted to buy 7 lottery tickets?
o $28
o $24.50
o $25
o $32.50
Correct
Answer: $24.50
This is a proportion problem and the given information allows us to formulate the
equation below:
5tickets$17.50=7ticketsx
where x is the cost of 7 lottery tickets. We can solve this equation by first cross-
multiplying.
5tickets×x=7tickets×17.50$
Carrying out the product on the right-hand side, we get;
5tickets×x=122.5tickets∙$
We can solve for x by dividing both sides of the equation by 5 tickets.
5tickets×x5tickets=122.5tickets∙$5tickets
Carrying out the division, we get a 1 on the left-hand side and a 24.5 on the right-
hand side.
1x=24.5$
We can drop the 1 next to x, to get x=24.5$. It would cost Jordy $24.50 to buy 7
lottery tickets.
4. 4. QUESTION
In 18 hours, 42 trains pass near Emma’s house.
How many trains pass near her house in 12 hours?
, o 28 trains
o 56 trains
o 14 trains
o 2 trains
Correct
Answer: 28 trains
This is a proportion problem and the given information allows us to formulate the
equation below:
42trains18hours=x12hours
where x is the number of trains that pass near Emma’s house in 12 hours. We
can solve this equation by first cross-multiplying.
18hours×x=42trains×12hours
Carrying out the product on the right-hand side, we get:
18hours×x=504trains∙hours
We can solve for x by dividing both sides of the equation by 18 hours.
18hours×x18hours=504trains∙hours18hours
Carrying out the division, we get a 1 on the left-hand side and a 28 on the right-
hand side.
1x=28trains
We can drop the 1 next to x, to get x=28 trains. In 12 hours, 28 trains pass near
Emma’s house.
5. 5. QUESTION
5:12=x:36
What is the value of x?
o x=3
o x=15
o x=12
o x=7.2
Correct
Answer: x=15
