California High School Proficiency Examination (CHSPE) Mathematics: Number Sense and Operations Syllabus

Mathematics: Number Sense and Operations syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics: Number Sense and Operations in California High School Proficiency Examination (CHSPE), not a summary of it.

1. 1

   Whole Numbers and Integers

   4 topics

   • Place Value and Number Representation
     • Reading and writing large numbers
     • Expanded and standard form
   • Four Operations with Whole Numbers
     • Multi-digit multiplication and division
     • Order of operations
   • Integer Operations
     • Adding and subtracting signed numbers
     • Multiplying and dividing negatives
   • Factors, Multiples, and Primes
     • GCF and LCM
     • Prime factorization
2. 2

   Fractions, Decimals, and Percents

   4 topics

   • Operations with Fractions
     • Adding and subtracting unlike fractions
     • Multiplying and dividing fractions and mixed numbers
   • Operations with Decimals
     • Aligning and computing decimal sums
     • Rounding and estimating decimals
   • Percent Concepts
     • Finding the percent of a number
     • Percent increase and decrease
   • Converting Among Forms
     • Fraction to decimal to percent
     • Comparing and ordering rational numbers
3. 3

   Ratios, Proportions, and Rates

   4 topics

   • Writing and Simplifying Ratios
     • Part-to-part and part-to-whole ratios
     • Equivalent ratios
   • Solving Proportions
     • Cross-multiplication
     • Scale and similar-figure problems
   • Unit Rates and Pricing
     • Best-buy comparisons
     • Speed, distance, and time rates
   • Applications of Proportional Reasoning
     • Recipes and mixtures
     • Maps and models
4. 4

   Powers, Roots, and Estimation

   4 topics

   • Exponents
     • Evaluating powers
     • Rules for multiplying and dividing powers
   • Square Roots
     • Perfect squares and their roots
     • Estimating non-perfect roots
   • Scientific Notation
     • Writing very large and small numbers
     • Computing in scientific notation
   • Estimation and Reasonableness
     • Rounding to estimate answers
     • Checking results for reasonableness

Mathematics: Number Sense and Operations flashcards for California High School Proficiency Examination (CHSPE)

23 of 50 cards from the Mathematics: Number Sense and Operations deck — real questions with worked answers.

1. What is the place value of the digit 7 in the number 4,720?

   Hundreds (7 represents 700).

2. Write the number 'three hundred five thousand, sixty' in standard form.

   305,060

3. In a multi-digit number, how does the value of a digit change as it moves one place to the left?

   It becomes 10 times greater than it would be one place to the right.

4. Write 2,408 in expanded form.

   2,000 + 400 + 0 + 8 (i.e., 2,000 + 400 + 8).

5. What are the four basic operations on whole numbers and their result names?

   Addition (sum), subtraction (difference), multiplication (product), and division (quotient).

6. In long division, what is the relationship among dividend, divisor, quotient, and remainder?

   Dividend = (divisor x quotient) + remainder.

7. State the order of operations (PEMDAS).

   Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right).

8. What is the result of adding two negative integers, such as (-6) + (-4)?

   A negative number: -10. Add the absolute values and keep the negative sign.

9. What is the sign rule for multiplying or dividing two integers with different signs?

   The result is negative (e.g., (-3) x 4 = -12).

10. What is the sign rule for multiplying or dividing two integers with the same sign?

    The result is positive (e.g., (-3) x (-4) = 12).

11. How do you subtract a negative integer, as in 5 - (-3)?

    Adding the opposite: 5 - (-3) = 5 + 3 = 8.

12. What is the absolute value of a number, and what is |-9|?

    The distance of a number from zero on the number line; |-9| = 9.

13. What is a factor of a number?

    A whole number that divides the number evenly with no remainder.

14. What is a multiple of a number?

    The product of that number and any whole number (e.g., multiples of 4: 4, 8, 12, 16, ...).

15. Define a prime number and give the smallest one.

    A whole number greater than 1 with exactly two factors, 1 and itself; the smallest prime is 2.

16. Define a composite number.

    A whole number greater than 1 that has more than two factors (i.e., it is not prime).

17. What is the prime factorization of 36?

    2 x 2 x 3 x 3, or 2^2 x 3^2.

18. What is the greatest common factor (GCF) of 12 and 18?

    6.

19. What is the least common multiple (LCM) of 4 and 6?

    12.

20. How do you add or subtract fractions with unlike denominators?

    Find a common denominator, rewrite each fraction with it, then add or subtract the numerators and keep the denominator.

21. How do you multiply two fractions?

    Multiply the numerators together and the denominators together, then simplify (e.g., 2/3 x 4/5 = 8/15).

22. How do you divide by a fraction, as in (3/4) ÷ (2/5)?

    Multiply by the reciprocal of the divisor: 3/4 x 5/2 = 15/8.

23. How do you convert the mixed number 3 1/4 to an improper fraction?

    Multiply whole number by denominator and add numerator: (3x4+1)/4 = 13/4.

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