CHSPE Math FREE Sample Practice Questions
TL;DR: Want a low-pressure way to feel out the CHSPE before committing to a full-length test? This short set of free CHSPE Math sample questions covers the topics on the official California High School Proficiency Exam blueprint. Calculator allowed, just like the real thing. Use them as a warm-up to spot weak areas, then move on to a full-length practice test once you know where to focus.
Key takeaways:
- Short sample set — about 8 questions for a 15-minute warm-up.
- Calculator allowed, matching the real CHSPE policy.
- Topics span Number Sense, Algebra, Geometry, and Statistics.
- Designed as a low-pressure first look at CHSPE-style items.
- Use as a warm-up before a full-length practice test.
3- B
The area of the square is 595.36. Therefore, the side of the square is the square root of the area.
\(\sqrt{595.36}=24.4\)
Four times the size of the square is the perimeter:\(4 \times 24.4 = 97.6\) For additional educational resources, .
4- A
The width of the rectangle is twice its length. Let \(x\) be the length. Then, width \(=2x\)
Perimeter of the rectangle is \(2 (width + length)\) \(= 2(2x+x)=60 {\Rightarrow} 6x=60 {\Rightarrow} x=10\)
The length of the rectangle is 10 meters. For additional educational resources, .
5- D
average \(= \frac{sum \space of \space terms}{number \space of \space terms} {\Rightarrow} (average \space of \space 6 \space numbers) \space 12 = \frac{sum \space of \space terms}{6} ⇒\) sum of 6 numbers is
\(12 {\times} 6 = 72\)
(average of 4 numbers) 10 \(= \frac{sum \space of \space terms}{4}{\Rightarrow}\) sum of 4 numbers is \(10 {\times} 4 = 40\)
sum of 6 numbers \(-\) sum of 4 numbers = sum of 2 numbers
\(72 – 40 = 32\)
average of 2 numbers \(= \frac{32}{2} = 16 \) For additional educational resources, .
6- C
Let \(x\) be the number. Write the equation and solve for \(x\).
\(40\%\) of \(x=4{\Rightarrow} 0.40 x=4 {\Rightarrow} x=4 {\div}0.40=10\) For additional educational resources, .
7- C
First, find the sum of five numbers.
average \(=\frac{ sum \space of \space terms }{ number \space of \space terms } ⇒ 24 = \frac{ sum \space of \space 5 \space numbers }{5}
⇒\) sum of 5 numbers \(= 24 × 5 = 120\)
The sum of 5 numbers is 120. If a sixth number that is 42 is added to these numbers, then the sum of 6 numbers is 162.
\(120 + 42 = 162\)
average \(=\frac{ sum \space of \space terms }{ number \space of \space terms } = \frac{162}{6}=27\) For additional educational resources, .
8- C
The ratio of boy to girls is 4:7.
Therefore, there are 4 boys out of 11 students.
To find the answer, first, divide the total number of students by 11, then multiply the result by 4.
\(44 {\div} 11 = 4 {\Rightarrow} 4 {\times} 4 = 16\)
There are 16 boys and \(28 (44 – 16)\) girls. So, 12 more boys should be enrolled to make the ratio 1:1 For additional educational resources, .
9- 2
Solve for \(y\).
\(4x-2y=6 {\Rightarrow} -2y=6-4x {\Rightarrow} y=2x-3\)
The slope of the line is \(2\). For additional educational resources, .
10- A
Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase \(120 x\).
The team had \($20,000\) and spent \($14000\). Now the team can spend on new shoe \($6000\) at most.
Now, write the inequality:
\(120x+14,000 {\leq}20,000\) For additional educational resources, .
Looking for the best resource to help you succeed on the CHSPE Math test? For additional educational resources, .
The Best Books to Ace the CHSPE Math Test
Recommended EffortlessMath Books
If you need more than these sample 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
How many sample questions are on this page?
About 8 questions — designed for a quick 15-minute warm-up rather than a full practice session. Use these to get familiar with the CHSPE Math style and question format before tackling more comprehensive practice.
Is a calculator allowed?
Yes. The CHSPE allows your own approved scientific or graphing calculator. Use one while you work through these sample questions — that’s exactly how you’ll work on the real test.
What topics do the sample questions cover?
A mix from each of the four CHSPE Math content areas: arithmetic with fractions and percents (Number Sense), basic linear equations (Algebra), area or volume (Geometry), and a basic statistics question (mean or reading a chart). The mix is intentionally representative of the real test.
How should I use these sample questions?
Three good options: (1) as a warm-up before a full-length practice test, (2) as a low-pressure first look at CHSPE-style items if you’re just starting prep, or (3) as a quick weekly check-in during your prep weeks. Don’t expect them to cover every topic — that’s what the full-length test is for.
I got most wrong. What do I do?
Don’t panic — that’s useful diagnostic information. Look at which topics tripped you up. If it’s basic algebra, start there. If it’s geometry formulas, drill those. Spend 2-3 sessions on the weakest area, then come back to these sample questions. Improvement on familiar items builds confidence quickly.
How is this different from the full-length practice test?
The sample set is a quick 15-minute warm-up of about 8 questions. The full-length practice test has roughly 50 questions and takes about 90 minutes. Use the sample to get familiar with style; use the full test closer to your CHSPE date to build stamina.
Are these the actual CHSPE test questions?
No. The real CHSPE items are secure and never released. These are practice questions written to match the style, format, and topic mix of the real test. The skills they test are the same.
What’s the CHSPE passing score?
The scaled passing score is 350 on each subtest. That’s roughly 60-65% of questions correct. You need to pass both the Math and the Language Arts subtests to earn the Certificate of Proficiency.
Who is eligible to take the CHSPE?
California residents 16+ who meet specific eligibility rules: age 16 with one year of 10th grade attendance, age 16 with 10th grade completed, or 17.5+ regardless of enrollment. The CHSPE is California-only — out-of-state test-takers aren’t eligible.
Where can I find more CHSPE practice?
EffortlessMath has a free full-length CHSPE Math practice test, the Top 10 CHSPE Math practice questions, more CHSPE Math practice test questions, the CHSPE Math Formula Cheat Sheet, the CHSPE Math for Beginners workbook, and the CHSPE Math Test Prep Bundle.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
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