HSPA Mathematics
•The HSPA is an exam
administered statewide in March
to high school juniors.
•It is designed to test our
students’ proficiencies in
Mathematics and Language Arts.
•A passing score of 200 in each
section is necessary for
graduation.
Successful Strategies for the HSPA
Answering Math Multiple Choice Questions
1. Each question is worth one point.
2. You are not penalized for guessing. Do not leave an
answer blank.
3. Try to eliminate incorrect choices to help select the
best answer.
4. Use the math reference sheet for formulas and added
information.
Answering Math Open-ended Questions
1. Read the questions carefully.
2. Make sure to show all your work.
3. Try to give a written explanation. Labeled
diagrams can be included.
4. As with the reading open-ended, if you can’t
answer completely, make an attempt.
5. These questions are worth 0-3 points.
Therefore a partial answer can earn you some
points.
•The Mathematic Test of the HSPA assessment is
divided into three 40 minute sections.
•Each of these segments reflects knowledge and
skills specified in the Core Curriculum Content
Standards.
•All three parts consist of 10 multiple-choice and
2 open ended questions.
•Four different mathematics clusters are addressed
in each section.
HSPA Clusters
Number and Numerical Applications
 Geometry and Measurement
 Data Analysis, Probability, and Discrete
Mathematics
 Patterns and Algebra

Number and Numerical Applications
Number Sense
 Numerical Operations
 Estimation

The following sample questions are from
http/www.njpep.org
(The answer key is at the end of this presentation.)
1. Alan bought a dozen donuts. He gave half to his
mother, kept a third of the remaining donuts for
himself, and gave the rest to his friends. How
many donuts did Alan keep?
a. 2
b. 4
c. 3
d. 6
Geometry and Measurement
Geometric Properties
 Transforming Shapes
 Coordinate Geometry
 Units of Measurement
 Measuring Geometric Objects

The following sample open-ended question is from
the HSPA website.
2. In triangle XYZ, angles x and y are congruent. What is the
length of YZ. Explain and show all your work.
Z
3x-20
X
X+40
Y
Data Analysis, Probability, and Discrete
Mathematics
Data Analysis (Statistics)
 Probability
 Discrete Mathematics- Systematic
Listing and Counting
 Discrete Mathematics- Vertex- Edge
Graphs and Algorithms

The following sample question is
from the HSPA website.
3. A drawer contains 4 red pens, 5 blue pens, and 2 black pens. If
you reach into the drawer without looking and pull out a pen for
you and a pen for your work partner, what is the probability that
the first pen will be blue and the second pen will be black?
1
3
2
a.
21
c.
11
b.
40
1
d.
11
Patterns and Algebra
Patterns and Relationships
 Functions
 Modeling
 Procedures

The following sample open-ended question is from
the HSPA website.
4. Belinda wants to determine the number of dots in the
30th step of the following pattern, but she does not want
to actually draw all 30 steps.
Step 1:
**
**
Step 2:
***
***
***
Step 3:
****
****
****
****
Explain how Belinda could find
the number of dots in Step 30
without actually drawing them.
What would be the number of
dots in the 30th step?
Write an algebraic expression
for the number of dots in the nth
step.
The answer key to questions 1-4
is on the following four slides.
1. a
1/2 of a dozen =6
 1/3 of 6 = 2
 He kept 2 for himself
 It does not ask what he gave to his
friends.

2. This picture in the response helps to clarify the answer.
The length of line yz is 70
Z
3x-20
3(30)-20
90-20=70
x+40
30+40=70
Both sides have
the same length
because their
angles are equal.
X
Y
(3x-20) is equal to (x+40)
3x-20=x+40
because its opposite sides are
2x=60
congruent
x=30
This responses scored a “3” because it shows a knowledge
of congruent angles and basic geometry.
3. d
•There are a total of eleven pens.
•Since five of the eleven are blue, we use the ratio 5/11.
•By taking out one of the blue pens, we are left with 10
pens in the drawer.
•Since two of the remaining ten pens are black, we use the
ratio 2/10.
•We now have two independent events, therefore we
multiply the two ratios to get our answer.
5/11 x 2/10 = 1/11
4.
This response received a “3” because it is answered correctly,
although the seventh part of the answer is not asked for in the
question.
• The number of dots in step 1, 2 ,and 3 are perfect
Squares.
• In step 1, 22 = 4 dots.
• In step 2, 32 = 9 dots.
• Step 30 would be 312 .
• The number of dots in step 30 is 31 x 31= 961
• N= (x+1)2
(x = step #)
• The 9th step would be 102, which gives
you 100.