# HSPA Prep Mathematics The HSPA is an exam administered statewide in March to high school juniors. It is designed to test our students’ proficiencies.

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HSPA Prep 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.

Show the reference sheet and explain that they will have to use every part of it

HSPA Clusters Number and Numerical Applications Geometry and Measurement Data Analysis, Probability, and Discrete Mathematics Patterns and Algebra

The following sample questions are from http/www.njpep.org (The answer key is at the end of this presentation.) http/www.njpep.org 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

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.

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. 3x-20 Z X+40 X Y

2. This picture in the response helps to clarify the answer. The length of line yz is 70 3x-20 3(30)-20 90-20=70 x+40 30+40=70 Both sides have the same length because their angles are equal. Z XY 3x-20=x+40 2x=60 x=30 (3x-20) is equal to (x+40) because its opposite sides are congruent This responses scored a “3” because it shows a knowledge of congruent angles and basic geometry.

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? a. b.b. c. d.

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

The following sample open-ended question is from the HSPA website. 4. Belinda wants to determine the number of dots in the 30 th 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 30 th step?  Write an algebraic expression for the number of dots in the nth step.

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, 2 2 = 4 dots. In step 2, 3 2 = 9 dots. Step 30 would be 31 2. The number of dots in step 30 is 31 x 31= 961 N= (x+1) 2 (x = step #) The 9 th step would be 10 2, which gives you 100.

Successful Strategies for the HSPA 1. Make sure you answer what they are asking. They are testing to make sure you can read directions Don’t assume you know what they are asking!!! 2. Go SLOW, read the whole problem. They try to trick you!! Sneak in the word “not”!! Watch out for other words, always, exactly, at least, must, etc. 3. DON’T LEAVE ANYTHING BLANK!!! Always guess on Multiple-Choice Try eliminating answers that don’t make sense. Try substituting in the answer, and see if it works. Remember your first guess is usually right. ESPECIALLY THE OPEN-ENDED Need to write something down even if you don’t know how to answer 4. Draw pictures! And picture yourself in each situation! On multiple choice and open-ended

5. On Open-Ended the explanation is worth more than the answer. Don’t jump around when showing your work. They need to follow your work and know your thought process. Use the written words in the questions in your explanation. Use a closing sentence. 6. BECAREFUL OF INCHES and FEET THEY GIVE DIMENSIONS IN FEET BUT WANT ANSWER IN INCHES 7. All answers they give will be exact! If you get 3.56, and they have 3.5 or 3.555 (repeating) then IT”S WRONG!!! Do the problem again!!! 8. Bring a calculator that you are familiar with. 9. Remember your timing 1 st 20 minutes on multiple choice, then 10 minutes on each open- ended 9. GO TO BED EARLY!!! GET A GOOD BREAKFAST!!!! 10. RELAX….YOU’LL DO FINE.

HSPA SUBJECT REMINDERS 1. Compounded annually?? Quarterly?? Semi-annually?? 2. MEAN, MEDIAN, AND MODE??? 3. DO YOU KNOW A DECK OF CARDS?? HOW MANY SUITS, ETC?? LOT OF PROPABILITY QUESTIONS 4. SLOPE?? SLOPE INTERCEPT?? RATE OF CHANGE?? 5. RATIONAL NUMBER VS. IRRATIONALY NUMBER WHOLE, INTEGERS, REAL VS. IMAGINARY 6. GIVEN VOLUME OR AREA OF A FIGURE, FIND THE HEIGHT OR LENGTH IN OTHER WORDS GIVEN AN ANSWER, WORK BACKWARDS 7. DISTANCE BETWEEN 2 POINTS 8. A LOT OF PATTERN PROBLEMS SEQUENCES AND SERIES FIND THE 100 TH TERM??? 9. MATRICES 10. PROBABILITY OF DICE AND SPINNERS ARE ALWAYS USED 11. YOU WILL HAVE TO MAKE YOUR OWN EQUATIONS 12. IS THIS TABLE A FUNCTION?? OR NOT A FUNCTION?? 13. Trig flag pole problem, soh-cah-toa 14. LOOK ON LIST FROM LAST YEAR’S QUESTIONS!!!

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