Comming Soon
 
 

State Testing Information and Practice Material
updated 10/8/2003
 

All students graduating from a public high school in New Jersey must pass the New Jersey State Test, the High School Proficiency Assessment (HSPA). It is first taken in the Spring of the studnet's Junior year in high school. The test has four clusters.
 

1) Number Sense: Concepts & Applications
2) Spatial Sense & Geometry
3) Data Analysis, Probability, Statistics, & Discrete Math
4) Patterns, Functions, & Algebra
 

Juniors will take this test in reading, mathematics, and writing on March 2, 3, and 4, 2004.  The make up days are March 9, 10, and 11, 2004.  In order to prepare students for this test, we have integrated the HSPA proficiencies into all our courses.  We have also prepared HSPA review worksheets, which students do throughout the year.  Students in Integrated Math have an HSPA workbook which they use on a regular basis.

Here are the proficiencies for each section and sample test problems:
  Cluster I: Number Sense: Concepts and Applications
The student should have an understanding of:

1. Real Numbers (Rational and Irrational Numbers)
2. Powers, roots, and exponents
3. Absolute Value
4. Scientific Notation
5. Properties of equivalence relations
6. Properties of arithmetic operations
7. Primes, factors and multiples
8. Equivalent and non-equivalent fractions
9. Ratio and Proportion
10. Percent
 
 

1) A fraction is equivalent to 3/8.  The sum of the numerator and denominator is 33.  What is the fraction?

2) A printer charges 4.2 cents per copy for a standard size original.  There is an additional charge of one-half cent for each copy on colored paper.  How much would you pay for 100 copies of an original on white paper and 100 copies on blue paper?

3) Every Monday, at Capri Pizza, lucky customers can get free slices of pizza and free soda.  Every 10th customer gets a free plain slice of pizza and every 12th customer gets a free cup of soda.  On the first Monday of March, Capri pizza had 211 customers.
a) How many free pizza slices were given away?  How many cups of soda were given away?
b) When Jackie came to Capri Pizza, the owner told her that she was the first person to get both free items (the free slice of pizza and the free soda).  What number customer must Jackie have been?  How many other customers (from the 211 customers) would also get both free items?
c) Suppose the owner also decides to give away free bags of potato chips to every 7th customer.  Would any of the 211 customers be lucky enough to get all three free items?  Explain.
 
 
 

Ans.  1) 9/24    2) $8.90    3) a. 21 get free pizza, 17 get free soda   b. 60th customer, 2 others   c. no, to get all three, you would have to be the

420th customer (least common multiple 2*2*3*5*7)

 
 
Cluster II: Spatial Sense and Geometry
The student should have an understanding of:

1. Geometric Terms
2. Standard Notations
3. Properties of geometric figures
4. Fundamental relationships between geometric figures
5. Inductive and deductive reasoning
6. Spatial relationships
7. Similarity and congruence
8. Symmetry
9. Transformations
10. The rectangular coordinate system
11. Matrices
12. Tessellations
13. Vectors
14. Measureable attributes (perimeter, area, volume, circumference, surface area, angle measure)
15. Dimensions, shapes, and properties of figures and objects
16. Right angle relationships (The Pythagorean Theorem, Basic trigonometric ratios)
 
 
 

1) A triangle has vertices at A(-3,1), B(3,1), and C(0,-5).  How many lines of symmetry does this triangle have?

2) The inside of a can of three tennis balls is about 23 cm. high and has a diameter of about 7.5 cm.  Each ball has an outer circumference of about 23 cm.  How much space is left in the can?

3) A tree on level ground casts a shadow 32 feet long.  The angle of elevation from the tip of the shadow to the top of the tree is 60o .  Find the height of the tree.
 
 
 

Ans.  1) 1   2)  400 cu. cm.   3) 55.4 ft
 
 
 

Cluster III: Data Analysis, Probability, Statistics, and Discrete Math
The student should have an understanding of:

1. Probability (Experimental and theoretical, Range of values, Notation)
2. Events/Outcomes (Simple and compound, Equally Likely, Dependant and independent)
3. Simulations
4. Law of Large Numbers
5. Scatter Plot
6. Line of Best Fit
7. Outlier
8. Correlation
9. Curve Fitting
10. Normal Curve Distribution
11. Direct and inverse variation
12. Probability distributions
13. Population
14. Sample - biased and unbiased
15. Measures of Central Tendency
16. Data Displays
17. Counting and sorting techniques
18. Combinations and permutations
19. Trees
20. Networks
21. Basic principles of riteration and recursion
22. Fractals
 
 

1) Two dice are rolled.  What is the probability that the sum is either 3 or 8?
 
  2)  Score  Frequency
 80  2
  82  4
  86  3
  90  5
 

Which of the following is true about the data?
a) The mean is greater than the median.
b) The median is greater than the mean.
c) The mean equals the median.
d) There is no mode.

3) A restaurant offers five entree choices on its dinner menu: turkey, hamburger, chicken, pork chops, and fish.  With each entree, the customer may choose one type of potato: french fried, mashed, or baked, and one of two desserts: ice cream or pudding.
a) Make a tree diagram to show the possible dinner choices.
b) How many different meals are available assuming the customer selects and entree, potato, and dessert?
c) Suppose the diner has the option of not taking a potato or a dessert.  How does that change the number of different meals that are available?  Show all work.
 
 

Ans.  1) 7/36   2)  B.   3) b. 30   c. 60 (doubles number of choices)
 
 
 

Cluster IV: Patterns, Functions, and Algebra
The student should have an understanding of:

1. Patterns
2. Sequences and Series
3. Limits
4. Tables, rules, variables, open sentences and graphs to describe patterns and other relationships
5. Relations and functions (linear and non-linear)
6. Independent and dependent variables
7. Domain and range
8. Rectangular coordinate system
9. Slope
10. Basic transformations (translations, reflections, and dilations)
11. Variables, expressions, number sentences and open sentences
12. Linear equations and inequalities
13. Algebraic order of operations
 
 

1) What digit is in the 20th decimal place in the decimal representation of 35/101?

2) Solve for x:   4(x + 2) -2(x - 3) = 20

3) A display of frisbees has been hung on a wall in the shape of a triangle.
There is 1 frisbee in the top row, 2 frisbees in the second row, 3 in the third row and so on; each row contains one more frisbee than the row above.  There are 12 rows.  How many frisbees are in the entire display?

4) Bob has $310 saved, but needs to withdraw $20 per week to help meet his expenses.  Jack has $100 saved and adds $10 a week.
a) Write an expression that represents the amount of money Jack will have in x weeks.
b) Write an expression that represents the amount of money Bob will have in x weeks.
c) How many weeks will it take until Jack and Bob have the same amount of money?
 
 
 

Ans.  1) 5   2)  x=3   3) 78   4)  a. 100+10x   b. 310-20x   c. 7 weeks