I can't claim to be an expert on the High School Admissions Exam, however I worked side by side with both my kids for many weeks, in 2021 and again in 2023, and they were both very successful. The first was enrolled at Selective Prep, (which has since closed its doors), and self-studied the Barron's Strategies and Practice for the HSPT, and the second attended Test Prep Chicago.
In my personal experience, the group classes they took were not enough. When we started preparing in the Fall before the exams, both kids seemed completely lost and claimed to have never been taught much of the material. For three weeks, I spent about an hour a day reviewing/teaching concepts to them as well. On the final weekend before the exam, I provided my own study guide for the Math portion of the exam. I am sharing that now for anyone interested.
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Mama's 10 Test Taking Tips
- Don't let yourself get stuck. Move on and go back to questions you skipped.
- Don't leave any questions unanswered.
- Immediately eliminate as many of the wrong answers as possible.
- Plug answer options in, if necessary.
- Simplify, distribute, reduce to decrease math calculations and time.
- Don't do anymore extra writing on scrap paper than necessary.
- Be neat in your scrap paper. It will pay off.
- Read questions carefully and look for necessary measurement conversions.
- Answer options could provide hints into how to solve the problem.
- Follow all steps in question.
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Time and time again I see parents on Facebook asking what is on the exam. No one knows exactly, but through the three different resources we have used, we have covered the following content:
- Number Properties
- Order of Operations (PEMDAS - Please Excuse My Dear Aunt Sally)
- Distributive Property a(b+c) = ab+ac
- Negative Number and Absolute Value
- Positive# (*or /) Negative# = Negative#
- Positive# (* or /) Positive# = Positive#
- Negative# (* or /) Negative# = Positive#
- Positive# - Negative# = Add the opposite
- Even and Odd Numbers
- Even#-Odd#=Odd#
- Odd#+Odd#=Even#
- Even#*Odd#=Even#
- Odd#*Odd#=Odd#
- Prime Numbers and Divisibility Rules
- To be divisible by 3: add all digits, sum must be divisible by 3
- To be divisible by 4: last 2 digits must be divisible by 4
- To be divisible by 6: the number must be divisible by 2 and 3
- To be divisible by 9: add all digits, sum must be divisible by 9
- Sequence Patterns - always try addition, then subtraction. If can't figure it out, try working backwards. Write down the differences between the given numbers and see if the pattern lies there.
- Place Value, Rounding, Decimals, and Scientific Notation
- Expanded Notation
- Rounding
- Decimals
- Scientific Notation
- if moving right to left = negative
- if moving left to right = positive
- with division and multiplication - where lots of zeros, calculate on smaller # and then add the zeros not used.
- Fractions and Mixed Numbers
- Adding and Subtracting Fractions
- Multiplying Fractions
- Dividing Fractions
- Improper Fractions and Mixed Numbers
- Always reduce as far as you can
- Percents
- Converting Fraction to Percent
- Converting Decimals to Percent
- Converting Percent to Decimal
- Converting a Percent to Fraction
- Common Percents and their Fractional and Decimal Equivalents
- 50%=1/2=0.5
- 25%=1/4=0.25
- 75%=3/4=0.75
- 33 1/3%=1/3=0.333333
- 66 2/3%=2/3=0.666666
- 10%=1/10=0.10
- 20%=2/10=1/5/0.20
- 30%=3/10=0.30
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- Percents in Word Problems
- Figuring out 10% of a number is pretty easy, (if it ends with zero, just knock one zero off) then you can double it for 20% or half it for 5%.
- Solving for the Part of the Whole in Percent Problems
- When asked % of a number of x% (i.e. 30% of 50% of 30) - work backwards.
- When original number increases by x% and then decreases by another %, be sure to apply the initial result before calculating the next % change.
- i.e. $180 dress discounted by 30% and then 10% tax.
- $180*30%=$54 (think 50% of $180 is $90 and 10% of $180 is $18 so 20% is $36 SO $90-$36=$54)
- $180-$54 discount=$126
- $126*10% tax=$12.6
- $126+12.6=$138.6 final price
- Ratios and Proportions
- Ratios
- Add up numbers i.e. 3:4:5 = 12 which makes first probability 3/12
- Apply the ratio to example total (cross multiply fractions)
- i.e. you are given a total of 60 with the above ratio
- 3/12 = x/60
- 12x = 180
- x = 15
- If a ratio is 2:3, you know that the total number must be a multiple of 5 (2+3)
- Proportions
- Cross Multiplication
- Ratios
- Probability and Combinations
- Probability
- Combinations
- Multiply probabilities for multiple selections (assume first selection is removed)
- Averages
- Simple Averages
- If numbers are equally spaced, i.e. 320, 322, 324, 326, 328, the average is 324.
- Weighted Average
- Questions that Begin with Averages
- Simple Averages
- Units of Measurement (American and Metric System)
- Length
- Weight
- Liquid Volume
- Common conversions to know:
- 12 inches = 1 foot
- 5,280 feet = 1 mile
- 1,000 millimeters = 100 centimeters = 1 meter
- 1,000 meters = 1 kilometer
- 16oz = 1 pound
- 1 ton = 2,000 lbs
- 1 kilogram = 1,000 grams
- 8 fluid oz = 1 cup
- 2 cups = 1 pint
- 2 pints = 1 quart
- 4 quarts = 1 gallon
- 1 liter = 1,000 millimeters
- Square yard = 3x3 ft
- Exponents and Square Roots
- Exponent multiplication
- Add the powers (base must be the same)
- Exponent Division
- Subtract the powers (base must be the same)
- Raising One Power to Another
- Multiply the powers (base must be the same)
- Negative to an even power is positive
- Negative to an odd power is negative
- Exponent multiplication
- Square Roots (addition/subtraction/multiplication/division)
- Basic Algebra
- Work backwards when necessary.
- Equations
- Inequalities
- Equations
- Number lines
- Lines and Angles
- Supplementary
- Complementary
- Obtuse
- Acute
- Triangle Rules/Formulas
- 3 angles = 180
- Longest side is opposite the biggest angle, the shortest side is opposite smallest angle.
- The sum of any two sides of a triangle must be greater than the 3rd.
- A = 1/2 b*h
- Isosceles
- Equilateral
- Right Triangle and the Pythagorean Theorem
- a2+b2=c2
- 3,4,5 rule
- In all geometry questions - ask yourself would the pythagorean theorem help me find the answer!
- The larger the angle, the larger the side opposite of the angle.
- Rectangles and Squares Rules/Formulas
- Circles Rules/Formulas
- Volume and Surface Area Formulas
- Coordinate Geometry
- Charts and Graphs
- Pay attention to the details!
- Advanced Algebra
- Factoring Equations
- Charts into Equations
- Algebra Word Problems
- Advanced Coordinate Geometry/Calculating Slope!
- Advanced Geometry and Statistics
- Mean/Median/Mode/Range
- Whisker plots
