HESI A2 Math Diagnostic Test 2025/2026 – 50 Practice Questions with Full Verified Answers & Step-by-Step Solutions

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HESI A2 Math Diagnostic Test (50
Questions) full Answers
Question 1 of 50
Solve for
x
:
5(4x+3)–4(2x+1)=47
x = 12
x = 36
x = 20
x=3
End Quiz
Answer Explanation


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




HESI A2 Math Diagnostic Test (50 Questions)
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,HESI A2 Math Diagnostic Test (50 Questions)
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.
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
.
12x
12
=
36
12
1x=3
We can drop the 1 on the left-hand side to
x=3



x=3
is the solution of the equation.
Question 2 of 50
Solve for
x
:
4
x
2
–61=135
x=7
x=14
or
−14
x=−7
or
7
x=14
End Quiz




HESI A2 Math Diagnostic Test (50 Questions)
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,HESI A2 Math Diagnostic Test (50 Questions)
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Answer Explanation


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.
4
x
2

–61+61=135+61
You should then carry out the addition of the numbers on both sides of the
equation.
4
x
2

=196
Step 2: Divide by 4 on both sides
We then divide both sides of the equation by 4.
4
x
2

4
=
196
4
x
2

=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
.
x
2




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=49
x
2

−
−
√
=
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.
Question 3 of 50
Jordy buys 5 lottery tickets for $17.50.
How much would Jordy pay if he wanted to buy 7 lottery
tickets?
$28
$24.50
$25
$32.50
End Quiz
Answer Explanation


Answer: $24.50


This is a proportion problem and the given information allows us to formulate the
equation below:
5tickets





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