SHS REV ENTRANCE EXAM!!

• Prime numbers


  Numbers that can only be multiplied by 1 and itself
• Prime numbers


  • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, etc.
• Composite numbers


  Opposite of prime numbers (have 3 factors or more)
• Composite numbers


  • 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, etc.
• Number types


  • Integers
  • Whole numbers
  • Counting numbers
• Counting consecutive integers


  Subtract smallest from the largest and add 1
• Absolute value


  Distance between 0 and x on the number line
• Absolute value


  • |4|= 4 , |-4| = 4
• Absolute value property


  If x is any number or zero, then the absolute value of x and –x are both equal to x
• Absolute value property


  • |x|=x, |-x|=x
• Prime factorization


  Breaking numbers into factors until all the numbers are prime
• Relative primes


  Integers that have no common factor other than one
• Least Common Multiple (LCM)


  To find the lcm, divide until all numbers are 1
• Greatest Common Factor (GCF)


  Multiply all the prime factors they have in common
• Comparing fractions


  Cross multiply the fractions. Bigger result = bigger number
• Converting fractions to decimals

  Divide top by bottom number
• Converting decimals to fractions

  Set the decimal over 1 and multiply the numerator and denominator by 100
• Dividing decimals


  Move the decimal point in the divisor and dividend until the divisor becomes a whole number
• Converting percents to fractions

  Drop % and multiply by 1/100
• Converting percents to decimals

  Drop % and move the decimal point two places to the left
• Percent formula


  Part = percent * whole - to find part, percent, or whole use same formula
• Percent formula


  • Ex.1 What is 15% of 60? Part = 0.15*60 = 9

  Ex.2 6 is 4% of what number? (divide 6 by 0.04) 6 = 0.04 * whole = 150

  Ex.3 36 is what percent of 64? (divide 36 by 64 and then move the decimal by 2) 36 = percent*64 = 56.25%
• Percent increase and decrease

  Add the percent to 100%, convert to decimal, and multiply
• Combined percent increase and decrease

  To determine the combined effect of multiple percents increase and/or decrease, start with 100 and see what happens
• Converting percents to decimals

  • 62.5% = 0.625
• Percent Formula


  1. Part = percent * whole

  2. To find part, percent, or whole use same formula
• Percent Formula


  • What is 15% of 60? Part = 0.15*60 = 9
  • 6 is 4% of what number? (divide 6 by 0.04) 6 = 0.04 * whole = 150
  • 36 is what percent of 64? (divide 36 by 64 and then move the decimal by 2) 36 = percent*64 = 56.25%
• Percent Increase and Decrease

  • Increase 40 by 35% Add 35% to 100% = 135% convert to decimal -> 1.35 = 1.35 * 40 = 54
• Combined Percent Increase and Decrease

  1. Start with 100 and see what happens

  2. 1st yr: 100+(10% of 100)=110

  3. 2nd yr: 110+(30% of 100)=143

  4. That's a combined 43% increase
• Rate


  Write units
• Rate


  • If water level is increasing at the rate of 2cm for every 5 hours, how many cm will the water level increase in 7 hours? 2cm 2 cm 5hours = x cm 7hours --> 5x = 2*7 --> x = 2.8cm
• Average rate


  • Average A per B = total A total B
  • Average Speed = totaldistance total time
• Substitute: X = −3±√(3) ² – 4(1)(2) 2(1) X = −3±√9−8 2 X = −3±√1 2 X1 = −3+1 2 = −2 2 = X1 = -1 X2 = −3−1 2 = −4 2 = X2 = -2
• Problem solving


  1. Given: 3a – 2 = 2b, b = 3c + 5

  2. Solve: 3a – 2 = 2(3c + 5)

  3. 3a – 2 = 6c + 10

  4. 3a = 6c + 10 + 2

  5. 3a = 6c + 12

  6. A = 2c + 4
• Roman numerals


  • I – 1
  • V – 5
  • X – 10
  • L – 50
  • C – 100
  • D – 500
  • M – 1,000
  • V – 5,000
  • X – 10,000
  • L – 50,000
  • C – 100,000
  • D – 500,000
  • M – 1,000,000
• Fractional Exponents


  • 36 ½ = 2√36
  • 100-½ = 2√100-1 = 2√ 1 100= 1 10
  • (−64 ) 1 3= 3√-64 = -4
  • (16 3 4)(8 4 3) = (4√163)(3√84) (23)(24) = (8)(16) = 128
• Different types of conics

  • Parabola: - has only 1 variable squared

  Circle: - must always have a positive sign, same coefficient, same denominator

  Ellipse: - must have different denominators, but always has a positive sign

  Hyperbola: -one positive sign, one negative sign, must have different denominators
• Parabola


  • (x-h)2 = ±4p(y-k) ; vertical

  (y-k)2 = ±4p(x-h) ; horizontal
• Circle


  • (x-h)2 + (y-k)2 = r2
• Ellipse


  • (x−h)2 a2 + ( y−k)2 b2 = 1