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Quizzes > High School Quizzes > Electives

Master Your HSPT Math Practice Test

Sharpen skills with engaging SHSAT math challenges

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting a timed HSPT and SHSAT Math Blitz trivia for middle school students.

Easy
What is the sum of 45 and 32?
87
67
77
72
Adding 45 and 32 gives 77. This is a straightforward addition problem, and the other options do not match the correct sum.
Simplify the fraction 12/16.
2/3
4/3
6/8
3/4
Dividing both numerator and denominator by 4 simplifies 12/16 to 3/4. The other fractions are not reduced to their simplest form.
What is 25% of 80?
15
25
20
30
25% of 80 is calculated as 0.25 multiplied by 80, which equals 20. The other options are the result of miscalculations.
What is the area of a rectangle with a length of 8 and a width of 3?
11
32
24
22
The area of a rectangle is found by multiplying its length by its width (8 x 3 = 24). The other options do not correctly represent the product of the dimensions.
What is 7 multiplied by 6?
48
42
40
36
Multiplying 7 by 6 gives 42. This basic multiplication problem confirms that the other answers are incorrect.
Medium
Solve for x: 2x + 5 = 17.
8
7
6
5
Subtracting 5 from both sides gives 2x = 12, so dividing by 2 shows that x = 6. The other options do not satisfy the equation.
What is the value of 3^3 - 2^3?
15
19
21
17
Calculating the exponents gives 3^3 = 27 and 2^3 = 8, and subtracting produces 27 - 8 = 19. The alternative answers arise from common arithmetic mistakes.
A store offers a 15% discount on a $200 item. What is the sale price?
$170
$160
$150
$180
A 15% discount on $200 amounts to $30, so subtracting this discount from the original price yields $170. The other options are the result of incorrect percentage calculations.
If the ratio of cats to dogs is 3:4 and there are 21 cats, how many dogs are there?
35
32
28
24
Since the ratio indicates that for every 3 cats there are 4 dogs, multiplying by 7 (because 21/3 = 7) gives 4 x 7 = 28 dogs. The other options result from incorrect scaling of the ratio.
What is the probability of drawing an ace from a standard 52-card deck?
1/12
1/13
1/14
1/10
There are 4 aces in a 52-card deck, so the probability is 4/52, which simplifies to 1/13. Other options represent common simplification errors.
Which expression is equivalent to 2(3x + 4) - x?
5x + 8
7x + 8
6x + 8
5x - 8
Expanding the expression gives 6x + 8, and subtracting x results in 5x + 8. The other options include errors in either expansion or combining like terms.
What is the value of 4! (4 factorial)?
12
24
48
16
4! is calculated as 4 x 3 x 2 x 1, which equals 24. The other options are a result of miscomputing the factorial.
Solve for y in the equation 3y - 15 = 0.
15
0
5
3
Adding 15 to both sides gives 3y = 15, so dividing by 3 shows that y = 5. The alternative solutions come from common algebraic errors.
A car's value depreciates by 10% each year. What is its value after one year if its initial price is $15,000?
$13,000
$13,500
$12,500
$14,000
A 10% depreciation on $15,000 results in a $1,500 decrease, making the new value $13,500. The other options are due to miscalculating the percentage decrease.
Which of the following is the equation of a line parallel to y = 2x + 3?
y = -2x + 3
y = 3x + 2
y = 2x + 3
y = 2x - 5
Parallel lines have the same slope, which is 2 in y = 2x + 3, so any line with a slope of 2 is parallel. The line y = 2x - 5 is parallel with a different y-intercept, while the other options do not share the same slope.
Hard
Find the sum of the solutions for x² - 5x + 6 = 0.
6
8
7
5
Factoring the quadratic gives (x - 2)(x - 3) = 0, leading to solutions x = 2 and x = 3 with a sum of 5. This also aligns with Vieta's formulas.
In a group of 6 students, how many different teams of 3 can be formed?
12
20
18
15
Using the combination formula, C(6, 3) yields 20 possible teams. The other options result from common errors in computing combinations.
If f(x) = 2x² - 3x + 1, what is the value of f(3)?
7
9
8
10
Substituting x = 3 into the function yields 2(9) - 3(3) + 1 = 18 - 9 + 1 = 10. The other choices are due to errors in substitution or arithmetic.
A right triangle has legs of lengths 6 and 8. What is the length of the hypotenuse?
10
14
12
8
By applying the Pythagorean theorem, the hypotenuse is found by √(6² + 8²) = √(36 + 64) = √100 = 10. The other options do not satisfy the theorem.
If the area of a circle is 49π, what is the radius of the circle?
7
21
14
49
The area of a circle is given by πr²; equating πr² to 49π leads to r² = 49 and thus r = 7. The other responses come from improper manipulation of the area formula.
0
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Study Outcomes

  1. Analyze complex math problems using efficient problem-solving techniques.
  2. Apply core mathematical concepts to solve problems under timed conditions.
  3. Evaluate and improve computational accuracy through practice exercises.
  4. Implement effective test-taking strategies to enhance exam performance.

HSPT & SHSAT Math Practice Tests Cheat Sheet

  1. Master Key Math Formulas - Tackle area and perimeter calculations for triangles, circles, and rectangles, conquer the Pythagorean theorem, and breeze through basic algebraic equations. These formulas are your trusty sidekicks for solving a wild range of problems. ivytutorsnetwork.com
  2. Translate Word Problems - Practice turning real‑world scenarios into clear-cut mathematical equations, so you can unravel tricky questions step by step. Once you get the hang of keyword clues, even the trickiest story problems will feel like a breeze. effortlessmath.com
  3. Crunch Probability & Statistics - Get cozy with mean, median, mode, range, and basic probability rules. These stats superpowers frequently pop up on exams, and mastering them helps you spot patterns like a pro. ivytutorsnetwork.com
  4. Rock Ratios, Proportions & Percentages - From scaling recipes to calculating discounts, these topics are everywhere! Nail down the tricks for swapping ratios, setting up proportions, and converting percentages. ivytutorsnetwork.com
  5. Boost Number Sense - Strengthen your skills with fractions, decimals, and integers until you can juggle them without batting an eye. A solid number sense foundation makes complex calculations feel effortless. ivytutorsnetwork.com
  6. Explore Geometry - Dive into the world of triangles, circles, and polygons, and get hands‑on with volume and surface area. Visualizing shapes and their properties turns geometry from a puzzle into a playground. ivytutorsnetwork.com
  7. Power Up Algebra - Simplify expressions, solve equations and inequalities, and demystify functions. Algebra is the backbone of higher‑level math, so give these skills top priority. ivytutorsnetwork.com
  8. Time Management Training - Simulate test day by taking timed practice tests to sharpen your pacing and avoid last‑minute panic. Knowing when to move on and when to dig deeper is half the battle. varsitytutors.com
  9. Sample Question Drills - Review and tackle common question types to build go‑to strategies for each problem. The more patterns you recognize, the faster you'll solve them under pressure. effortlessmath.com
  10. Stay Positive & Confident - Keep a growth mindset, celebrate small wins, and remember that practice makes progress. A confident attitude can turn challenges into achievable goals and boost your performance on test day.
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