UPCAT MATH 1

    Cards (46)

    • What is the Cardinality of a Set (n)?
      The number of elements of a particular set.
    • The set containing all the elements in A or in B or in both A and B. Union of Sets A and B (A u B)
    • The set containing common elements in both A and B. Intersection of Sets A and B (A n B)
    • What is the formula for the of the Cardinality of a Union/Intersection?
      n(A) + n(B) = n(A u B) + n(A n B)
    • The set containing elements in A but not in B. Difference of Sets A and B (A - B)
    • The set containing all elements in the universal set but not in A. Complement of a Set (A’)
    • What solution will you use for this problem?
      How many subsets are in set X if X = {p, q, r} ?
      2n2^n
    • What is the difference between Natural/ Counting Numbers (N) to Whole Numbers (W)?

      Natural is 1,2,3, … and Counting is 0,1,2,3, …
    • What are Integers (Z)?

      negative and positive numbers
    • Rational (Q) vs. Irrational Numbers (Q’)?

      Rational: fractions, decimals, percentages
      Irrational: radicals, Pie
    • What are Real Numbers (R)?

      all the rational and irrational numbers
    • What property of Real Numbers is this? x + y R / x . y ∈ R

      Closure Property or Addition (CA) and Multiplication (CM)
    • What property of Real Numbers is this: x + y = y + x / xy = yx ?
      Commutative Property of Addition (CPA) and Multiplication (CPM)
    • What property of Real Numbers is this: x + (y + z) = (x + y) + z / x . (y . z) = (x . y) . z ?
      Associative Property of Addition (APA) and Multiplication (APM)
    • What property of Real Numbers is this: x . (y + z) = x + y + x . z ?
      Distributive Property of Multiplication over Addition (DPMA)
    • What property of Real Numbers is this: x + 0 = x / x . 1 = x ?
      Identity Element of Addition (AP0) and Multiplication (MP1)
    • What property of Real Numbers is this: x + (-x) = 0 / x . (1/x) = 1 ?
      Additive Inverse (AI) and Multiplicative Inverse (Ml1)
    • How do you know if a number is divisible by 3?
      Sum of all digits
    • How do you know if a number is divisible by 4?
      last two digits is divisible by 4 OR last two digits are both zeroes
    • How do you know if a number is divisible by 6?
      The number is an even number and divisible by 3
    • How do you know if a number is divisible by 7?
      the difference of twice the last digit [-2(a)] is divisible by 7
    • How do you know if a number is divisible by 8?
      The last three digits is divisible by 8 or all zeroes
    • How do you know if a number is divisible by 9?
      The sum of all digits is divisible by 9
    • How do you know if a number is divisible by 11?
      The difference of the sums of the alternating digits equals to zero or divisible by 11
    • How do you arrange these fractions in ascending order: 35,23,34,12\frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{1}{2}
    • turn 0.75 into a fraction
      75100=\frac{75}{100} =34 \frac{3}{4}
    • turn 1.20 into a fraction
      120100=\frac{120}{100} =65 \frac{6}{5}
    • turn 1.25 into percentage
      125%
    • turn 34% to decimal
      0.34
    • What formula should we use in this problem and what is the answer: What is 12% of 800?
      P = R x B and the answer is 96
    • What formula should we use in this problem and what is the answer: 144 is what percent of 900?

      RR = PB\frac{P}{B} and the answer is 16%
    • What formula should we use in this problem and what is the answer: 216 is 30% of what number?
      B=B =PR \frac{P}{R} and the answer is 720
    • How do you factor 9x29x^2-4949, versus, how you factor 4x2+4x^2 +20x+ 20x +25 25 ?

      (3x+7)(3x7)(3x+7)(3x-7)and (2x+5)2(2x+5)^2
    • give 2 ways to solve this problem: Which is NOT a factor of 9w227w2w+9w^2-27w^2-w+33?

      Factoring or substituting the choices
    • Find the LCM of 330, 462, 770
      2310
    • Evaluate: (15322)(82(3))2(\frac{15}{3}-2^2) - (-8-2(-3))^2
      -3
    • How will you add these rational expressions: x+3x+1+\frac{x+3}{x+1} +3x+1 \frac{3}{x+1} ?

      Add normally = x+6x+1\frac{x+6}{x+1}
    • How will you add these rational expressions x+2x3+\frac{x+2}{x-3}+x1x+4\frac{x-1}{x+4} ?

      Multiple the denominators to the other fraction’s numerator and denominator = 2x2+2x+11x2+x12\frac{2x^2+2x+11}{x^2+x-12}
    • How do you factor x31x^3-1
      (x1)(x2+x+1)(x-1)(x^2+x+1)a3±b3=a^3\pm b^3 =(a±b)(a2ab+b2) (a\pm b)(a^2\mp ab +b^2)
    • Give the steps to simplify this problem: xx24+\frac{x}{x^2-4}+24x2\frac{2}{4-x^2}
      1. Factor the denominator
      2. Combine both fractions
      3. Cancel like terms
      = 12+x\frac{1}{2+x}
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