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UPCAT MATH 1
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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} ?
2
n
2^n
2
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:
3
5
,
2
3
,
3
4
,
1
2
\frac{3}{5}, \frac{2}{3}, \frac{3}{4}, \frac{1}{2}
5
3
,
3
2
,
4
3
,
2
1
turn 0.75 into a fraction
75
100
=
\frac{75}{100} =
100
75
=
3
4
\frac{3}{4}
4
3
turn 1.20 into a fraction
120
100
=
\frac{120}{100} =
100
120
=
6
5
\frac{6}{5}
5
6
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?
R
R
R
=
P
B
\frac{P}{B}
B
P
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 =
B
=
P
R
\frac{P}{R}
R
P
and the answer is
720
How do you factor
9
x
2
9x^2
9
x
2
-
49
49
49
, versus, how you factor
4
x
2
+
4x^2 +
4
x
2
+
20
x
+
20x +
20
x
+
25
25
25
?
(
3
x
+
7
)
(
3
x
−
7
)
(3x+7)(3x-7)
(
3
x
+
7
)
(
3
x
−
7
)
and
(
2
x
+
5
)
2
(2x+5)^2
(
2
x
+
5
)
2
give 2 ways to solve this problem: Which is NOT a factor of
9
w
2
−
27
w
2
−
w
+
9w^2-27w^2-w+
9
w
2
−
27
w
2
−
w
+
3
3
3
?
Factoring
or
substituting
the
choices
Find the LCM of 330, 462, 770
2310
Evaluate:
(
15
3
−
2
2
)
−
(
−
8
−
2
(
−
3
)
)
2
(\frac{15}{3}-2^2) - (-8-2(-3))^2
(
3
15
−
2
2
)
−
(
−
8
−
2
(
−
3
)
)
2
-3
How will you add these rational expressions:
x
+
3
x
+
1
+
\frac{x+3}{x+1} +
x
+
1
x
+
3
+
3
x
+
1
\frac{3}{x+1}
x
+
1
3
?
Add
normally
=
x
+
6
x
+
1
\frac{x+6}{x+1}
x
+
1
x
+
6
How will you add these rational expressions
x
+
2
x
−
3
+
\frac{x+2}{x-3}+
x
−
3
x
+
2
+
x
−
1
x
+
4
\frac{x-1}{x+4}
x
+
4
x
−
1
?
Multiple
the
denominators
to the
other
fraction’s
numerator
and
denominator
=
2
x
2
+
2
x
+
11
x
2
+
x
−
12
\frac{2x^2+2x+11}{x^2+x-12}
x
2
+
x
−
12
2
x
2
+
2
x
+
11
How do you factor
x
3
−
1
x^3-1
x
3
−
1
(
x
−
1
)
(
x
2
+
x
+
1
)
(x-1)(x^2+x+1)
(
x
−
1
)
(
x
2
+
x
+
1
)
a
3
±
b
3
=
a^3\pm b^3 =
a
3
±
b
3
=
(
a
±
b
)
(
a
2
∓
a
b
+
b
2
)
(a\pm b)(a^2\mp ab +b^2)
(
a
±
b
)
(
a
2
∓
ab
+
b
2
)
Give the steps to simplify this problem:
x
x
2
−
4
+
\frac{x}{x^2-4}+
x
2
−
4
x
+
2
4
−
x
2
\frac{2}{4-x^2}
4
−
x
2
2
Factor
the
denominator
Combine
both
fractions
Cancel
like
terms
=
1
2
+
x
\frac{1}{2+x}
2
+
x
1
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