Top 10 CHSPE Math Practice Questions
TL;DR: Got the California High School Proficiency Exam coming up? These ten CHSPE Math practice questions are picked to cover the topics you are most likely to see on test day, organized as a focused 20-minute review. A calculator is allowed, so you can practice with the same tools you will have during the real exam. A clean quick warm-up to spot which topics still deserve a little more time before you sit for the real thing.
Key takeaways:
- 10 questions hitting the highest-weighted CHSPE Math topics.
- Calculator allowed, matching the real test policy.
- Quick 20-minute drill for focused review sessions.
- Covers number sense, algebra, geometry, and statistics.
- Pairs well with the full-length practice test for complete prep.
Start your CHSPE Math test prep journey right now with these sample CHSPE Math questions.
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C. 44
D. 35
8- A swimming pool holds 2,000 cubic feet of water. The swimming pool is 25 feet long and 10 feet wide. How deep is the swimming pool?_______
9- The area of a circle is \(64 π\). Which of the following is the circumference of the circle?
A. 8\(\pi\)
B. 12\(\pi\)
C. 16\(\pi\)
D. 64\(\pi\)
10- What is the value of \(3^6 \) ?______
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Answers:
1- D
Plug in the value of \(x\) and \(y\).
\(x=3\) and \(y=-2\)
\((5(x-2y)+(2-x))^2=(5(3-2(-2))+(2-3))^2=(5(3+4)+(-1))^2 = (34)^2=36\)
2- D
The equation of a line in slope intercept form is: \(y=mx+b\)
Solve for y.
\(4x-2y=12 {\Rightarrow} -2y=12-4x {\Rightarrow} y=(12-4x){\div}(-2) {\Rightarrow} y=2x-6\)
The slope of this line is 2.
The product of the slopes of two perpendicular lines is \(-1\).
Therefore, the slope of a line that is perpendicular to this line is:
\(m_{1} {\times} m_{2} = -1 {\Rightarrow} 2 {\times} m_{2} = -1 {\Rightarrow} m_{2} = \frac{-1}{2}\)
3- D
Use FOIL method.
\((2x+2y)(2x-y) = 4x^2-2xy+4xy-2y^2=4x^2+2xy-2y^2\)
4- D
To solve absolute values equations, write two equations.
\(x-10\) could be positive 3, or negative 3. Therefore,
\(x-10=3 \Rightarrow x=13\)
\(x-10=-3 \Rightarrow x=7\)
Find the product of solutions: \(7 \times 13 = 91\)
5- C
Use PEMDAS (order of operation):
\([6 {\times} (- 24) + 8] – (- 4) + [4 × 5] {\div} 2 \)
\( [- 144 + 8] – (- 4) + [20] {\div} 2 =
[- 144 + 8] – (- 4) + 10 \)
\([- 136] – (- 4) + 10 = [- 136] + 4 + 10 = – 122\)
6- D
Solving Systems of Equations by Elimination
Multiply the first equation by \((-2)\), then add it to the second equation.
\({-2(2x+5y= 11) \ 4x-2y=-14} {\Rightarrow} {-4x-10y= -22 \ 4x-2y=-14} {\Rightarrow} {-12y= -36} {\Rightarrow} {y= 3}\)
Plug in the value of y into one of the equations and solve for \(x\).
\(2x+5(3)= 11 {\Rightarrow} 2x+15= 11 {\Rightarrow} 2x= -4 {\Rightarrow} x= -2\)
7- B
Write the numbers in order:
2, 19, 27, 28, 35, 44, 67
Median is the number in the middle. So, the median is 28
8- 8
Use formula of rectangle prism volume.
\(V = (length) (width) (height) {\Rightarrow} 2000 = (25) (10) (height) {\Rightarrow} height = 2000 {\div} 250 = 8\)
9- C
The area of the circle is \(16 π\). Use the formula of areas of circles.
\(Area = πr^2 ⇒ 64 π> πr^2⇒ 64 > r^2⇒ r < 8\)
The radius of the circle is 8. Let’s put 8 for the radius. Now, use the circumference formula:
\(Circumference =2πr=2π (8)=16π\)
10- 729
\((3^6 ) = 3 × 3 × 3 × 3 × 3 × 3 = 729\)
Looking for the best resource to help you succeed on the CHSPE Math test?
The Best Books to Ace the CHSPE Math Test
Recommended EffortlessMath Books
If you need a structured workbook beyond these 10 questions, the CHSPE Math for Beginners walks through every CHSPE topic with worked examples. For multiple complete timed practice tests, the CHSPE Math Test Prep Bundle rounds out the prep.
Frequently Asked Questions
Are these the hardest CHSPE Math questions?
No — they’re the most representative. The 10 questions reflect the topic mix and difficulty distribution of the actual CHSPE Math: linear equations, percent calculations, area and volume, the Pythagorean theorem, slope, and basic statistics. Hitting these well usually means you’re tracking toward the 350 passing score.
How long should this take?
Most test-takers finish in about 20 minutes. If you take longer, that’s fine — note which questions slowed you down, since those are the topics to focus on next. The real CHSPE Math gives you roughly 1 minute 45 seconds per question, but this short set isn’t worth timing strictly.
Is a calculator allowed?
Yes. The CHSPE allows your own approved scientific or graphing calculator. Use one on these practice questions — it matches the real test policy and lets you focus on the reasoning rather than arithmetic.
What topics do the 10 questions cover?
The four CHSPE content areas in roughly the right proportions: Number Sense (arithmetic, fractions, percents), Patterns and Algebra (linear equations, slope), Geometry and Measurement (area, volume, the Pythagorean theorem), and Statistics (mean, median, reading data displays).
I got 7 right. Is that good?
7 out of 10 is 70% — that’s above the typical CHSPE passing threshold (about 60-65% correct). If you want a comfortable margin on the real test, aim for 8-9 out of 10 on this set. Focus your remaining prep on the 3 missed topics to build confidence.
Should I do these before or after a full-length practice test?
Either works. Many test-takers find it useful to start with the top-10 set as a warmup to see which topics need work, take a full-length practice test in the middle of their prep, then return to the top-10 set the week of the real CHSPE for a confidence-building review.
Are these the actual CHSPE test questions?
No. CHSPE test items are secure and never released publicly. These are practice questions written to match the style, format, and topic mix of the real CHSPE Math. The skills tested are identical.
How should I show my work?
On scratch paper, in clear steps. Even for multiple-choice questions, written work helps catch arithmetic mistakes and lets you find where your thinking went wrong if you missed something. The real CHSPE provides scratch paper at the testing site.
What if a question seems too hard?
Mark it, skip to the next one, then come back if there’s time. This is the same strategy that works on the real CHSPE. Don’t burn 8 minutes on one question when you could grab points elsewhere. Educated guessing on a question you can narrow down to 2-3 choices is usually better than leaving blank.
Where can I find more practice?
EffortlessMath has a free full-length CHSPE Math practice test, free sample practice questions, CHSPE practice test questions, the CHSPE Math for Beginners workbook covering every topic, and the CHSPE Math Test Prep Bundle with multiple timed practice tests.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
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