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Q1 Indices and Surds Numerical Arithmetic with Fractions and Decimals View

$$\frac { 0,2 - 0,025 } { 0,5 }$$
What is the result of this operation?
A) $\frac { 3 } { 5 }$
B) $\frac { 4 } { 5 }$
C) $\frac { 7 } { 20 }$
D) $\frac { 8 } { 25 }$
E) $\frac { 12 } { 25 }$

Q2 Indices and Surds Numerical Arithmetic with Fractions and Decimals View

$$\frac { 5 \left( 2 - \frac { 3 } { 5 } \right) } { 2 \left( 3 - \frac { 5 } { 2 } \right) }$$
What is the result of this operation?
A) $\frac { 5 } { 2 }$
B) $\frac { 7 } { 2 }$
C) 3
D) 5
E) 7

Q3 Indices and Surds Simplifying Surd Expressions View

$$\frac { 6 } { \sqrt { 3 } } - \frac { 2 } { \sqrt { 3 } + 1 }$$
What is the result of this operation?
A) $\sqrt { 3 }$
B) $2 \sqrt { 3 }$
C) $\sqrt { 3 } - 1$
D) $\sqrt { 3 } + 1$
E) $2 \sqrt { 3 } - 1$

Q4 Indices and Surds Algebraic Expansion and Simplification View

$$( a + 1 ) ^ { 2 } - ( a - 1 ) ^ { 2 }$$
Which of the following is this expression equal to?
A) a
B) $2 a$
C) $3 a$
D) 4 a
E) $5 a$

Q5 Indices and Surds Evaluating Expressions Using Index Laws View

$10 ^ { -1 } + 10 ^ { -2 } + 10 ^ { -3 }$
What is the result of this operation?
A) 0,011
B) 0,101
C) 0,111
D) 0,123
E) 0,321

Q6 Indices and Surds Solving Exponential or Index Equations View

$( 16 ) ^ { 3 n } = 8 ^ { 5 }$
Given this, what is n?
A) $\frac { 3 } { 2 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 3 } { 5 }$
D) $\frac { 5 } { 4 }$
E) $\frac { 5 } { 6 }$

Q7 Indices and Surds Evaluating Expressions Using Index Laws View

$15 ^ { 13 } + 6 \cdot 15 ^ { 13 } + 8 \cdot 15 ^ { 13 }$
What is the result of this operation?
A) $15 ^ { 15 }$
B) $15 ^ { 14 }$
C) $14 \cdot 15 ^ { 13 }$
D) $10 \cdot 16 ^ { 13 }$
E) $16 ^ { 13 }$

Q8 Simultaneous equations View

$$\frac { 1 } { 2 } - 3 a = \frac { 1 } { 8 } + 3 b$$
Given this, what is the sum $\mathbf { a } + \mathbf { b }$?
A) $\frac { 3 } { 4 }$
B) $\frac { 5 } { 6 }$
C) $\frac { 1 } { 8 }$
D) $\frac { 5 } { 8 }$
E) $\frac { 4 } { 9 }$

Q9 Inequalities Integer Solutions of an Inequality View

$$\frac { - 5 } { 4 } < x < \frac { 7 } { 3 }$$
What is the sum of the integers $x$ that satisfy this inequality?
A) - 2
B) - 1
C) 0
D) 1
E) 2

Q10 Simultaneous equations View

$$\begin{aligned} & x ^ { 3 } - 2 y = 7 \\ & x ^ { 4 } - 2 x y = 21 \end{aligned}$$
Given this, what is $\mathbf { x }$?
A) 3
B) 5
C) 7
D) 9
E) 11

Q11 Number Theory Linear Diophantine Equations View

For natural numbers $x$ and $y$
$$\begin{array} { r | r | r } x & \frac { 10 } { m } \\ { } ^ { - } & = ^ { y } \frac { 15 } { 3 } \end{array}$$
Given this, what is the remainder when the product $x \cdot y$ is divided by 5?
A) 0
B) 1
C) 2
D) 3
E) 4

Q12 Simultaneous equations View

Let $\mathrm { a } , \mathrm { b } , \mathrm { x }$ and y be positive numbers such that
$$\begin{aligned} & \frac { x } { a } \cdot \frac { b } { y } = 2 \\ & \frac { a ^ { 2 } } { x ^ { 2 } } + \frac { b ^ { 2 } } { y ^ { 2 } } = 20 \end{aligned}$$
Given this, which of the following is the value of x in terms of a?
A) $\frac { a } { 2 }$
B) $\frac { 3 a } { 4 }$
C) $\frac { 3 a } { 5 }$
D) $\frac { 4 a } { 5 }$
E) $\frac { 5 a } { 6 }$

Q13 Inequalities Ordering and Sign Analysis from Inequality Constraints View

For real numbers $x , y$ and $z$
$$\begin{aligned} & y > 0 \\ & x - y > z \end{aligned}$$
Given this, which of the following is always true?
A) $x > z$
B) $x > y$
C) $z > y$
D) $x > 0$
E) $z > 0$

Q14 Indices and Surds Identifying Rational vs Irrational Numbers View

Which of the following is a rational number?
A) $\sqrt { 2 } + 1$
B) $2 \sqrt { 2 } - 1$
C) $\frac { 1 } { \sqrt { 2 } }$
D) $\frac { \sqrt { 2 } } { \sqrt { 2 } + 1 }$
E) $\frac { 2 \sqrt { 2 } - 2 } { 3 \sqrt { 2 } - 3 }$

Q15 Composite & Inverse Functions Evaluate Composition from Algebraic Definitions View

$$\begin{aligned} & f ( x ) = x ^ { 2 } \\ & g ( x ) = 2 x - 1 \end{aligned}$$
For these functions, what is $\mathbf { g } ( \mathbf { f } ( \mathbf { 2 } ) )$?
A) 0
B) 3
C) 5
D) 7
E) 9

Q16 Proof Proof of Equivalence or Logical Relationship Between Conditions View

Let $\mathbf { p } , \mathbf { q }$ and $\mathbf { r }$ be propositions with their negations denoted by $\mathbf { p } ^ { \prime } , \mathbf { q } ^ { \prime } , \mathbf { r } ^ { \prime }$ respectively. Which of the following is equivalent to the proposition
$$p \vee q \Rightarrow q \wedge r$$
?
A) $\mathrm { p } ^ { \prime } \wedge \mathrm { q } ^ { \prime } \Rightarrow \mathrm { q } ^ { \prime } \vee \mathrm { r } ^ { \prime }$
B) $\mathrm { p } ^ { \prime } \wedge \mathrm { q } ^ { \prime } \Rightarrow \mathrm { q } ^ { \prime } \wedge \mathrm { r } ^ { \prime }$
C) $p ^ { \prime } \vee q ^ { \prime } \Rightarrow q ^ { \prime } \wedge r ^ { \prime }$
D) $q ^ { \prime } \wedge r ^ { \prime } \Rightarrow p ^ { \prime } \vee q ^ { \prime }$
E) $q ^ { \prime } \vee r ^ { \prime } \Rightarrow p ^ { \prime } \wedge q ^ { \prime }$

Q17 Probability Definitions Combinatorial Counting (Non-Probability) View

$$\begin{aligned} & A = \{ a , b , e \} \\ & B = \{ a , b , c , d \} \end{aligned}$$
Given this, how many sets $K$ satisfy the condition $( A \cap B ) \subseteq K \subseteq ( A \cup B )$?
A) 3
B) 4
C) 5
D) 8
E) 9

Q18 Number Theory GCD, LCM, and Coprimality View

On the set of positive integers, the operations $\oplus$ and $\otimes$ are defined using the greatest common divisor and least common multiple as follows:
$$\begin{aligned} & a \oplus b = \operatorname { GCD } ( a , b ) \\ & a \otimes b = \operatorname { LCM } ( a , b ) \end{aligned}$$
Accordingly, what is the result of the operation $18 \oplus ( 12 \otimes 4 )$?
A) 2
B) 3
C) 6
D) 8
E) 9

Q19 Simultaneous equations View

The sum of a three-digit number $ABC$ and a two-digit number $AB$ is 392.
Accordingly, what is the sum $\mathrm { A } + \mathrm { B } + \mathrm { C }$?
A) 7
B) 9
C) 11
D) 15
E) 19

Q20 Number Theory Prime Number Properties and Identification View

A two-digit number $AB$ is called a symmetric prime if both $AB$ and $BA$ are prime numbers.
For a symmetric prime number $AB$, which of the following cannot be the product A.B?
A) 7
B) 9
C) 15
D) 21
E) 63

Q32 Combinations & Selection Combinatorial Probability View

A bag contains 2 red, 2 white, and 1 yellow marble.
When 4 marbles are randomly drawn from the bag, what is the probability that the remaining marble in the bag is red?
A) $\frac { 1 } { 2 }$
B) $\frac { 2 } { 3 }$
C) $\frac { 3 } { 4 }$
D) $\frac { 2 } { 5 }$
E) $\frac { 3 } { 5 }$

Q33 Sine and Cosine Rules Find a side or angle using the sine rule View

ABC is a triangle
$$\begin{aligned} & \mathrm { m } ( \widehat { \mathrm { ABC } } ) = 50 ^ { \circ } \\ & \mathrm { m } ( \widehat { \mathrm { CAB } } ) = 100 ^ { \circ } \end{aligned}$$
According to the given information, the expression $\frac { | a - b | + | b - c | + | c - a | } { 2 }$ is equal to which of the following?
A) a-c
B) $a - b$
C) $b - c$
D) $b - a$
E) $\mathrm { c } - \mathrm { b }$

Q34 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View

ABCD is a rectangle $| \mathrm { AD } | = 1 \mathrm {~cm}$ $| \mathrm { AE } | = | \mathrm { EB } | = 2 \mathrm {~cm}$ $|FE| = \mathrm { x }$
According to the given information, what is x in cm?
A) $\frac { \sqrt { 3 } } { 2 }$
B) $\frac { \sqrt { 5 } } { 2 }$
C) $\frac { \sqrt { 3 } } { 3 }$
D) $\frac { \sqrt { 5 } } { 3 }$
E) $\frac { \sqrt { 7 } } { 3 }$

Q35 Straight Lines & Coordinate Geometry Area Computation in Coordinate Geometry View

ABCD is a parallelogram AECD is a trapezoid $| \mathrm { BE } | = 3 \mathrm {~cm}$ $| \mathrm { DC } | = 4 \mathrm {~cm}$
If the area of the parallelogram ABCD in the figure is $20 \mathrm {~cm} ^ { 2 }$, what is the area of triangle $CBE$ in $\mathbf { cm } ^ { \mathbf { 2 } }$?
A) 7
B) 7,5
C) 8
D) 8,5
E) 9

Q36 Radians, Arc Length and Sector Area View

ABCD is a rectangle $\wideparen { \mathrm { CE } }$ is a circular arc with center A $| \mathrm { DA } | = 4 \mathrm {~cm}$ $| \mathrm { AC } | = 8 \mathrm {~cm}$
According to the given information, what is the area of the shaded circular sector in $\mathbf { cm } ^ { \mathbf { 2 } }$?
A) $\frac { 16 \pi } { 3 }$
B) $\frac { 20 \pi } { 3 }$
C) $\frac { 25 \pi } { 3 }$
D) $\frac { 28 \pi } { 3 }$
E) $\frac { 32 \pi } { 3 }$

Q37 Radians, Arc Length and Sector Area View

O is the center of the circle
AT is tangent to the circle at point T
$$\begin{aligned} & | A T | = 3 \mathrm {~cm} \\ & \mathrm {~m} ( \widehat { \mathrm { OAT } } ) = 45 ^ { \circ } \end{aligned}$$
According to the given information, what is the length of arc BT in cm?
A) $\frac { \pi } { 2 }$
B) $\frac { 2 \pi } { 3 }$
C) $\frac { 3 \pi } { 4 }$
D) $\frac { 4 \pi } { 5 }$
E) $\frac { 5 \pi } { 6 }$

Q39 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View

In the Cartesian coordinate plane, the perpendicular drawn from point $A ( 1,0 )$ to the line $\mathbf { y } + \mathbf { 2 x } - \mathbf { 1 } = \mathbf { 0 }$ intersects the Y-axis at which point?
A) $\frac { - 1 } { 2 }$
B) $\frac { - 1 } { 3 }$
C) $\frac { - 1 } { 4 }$
D) $\frac { - 1 } { 5 }$
E) $\frac { - 1 } { 6 }$

Q40 Straight Lines & Coordinate Geometry Geometric Figure on Coordinate Plane View

The vertices of a parallelogram with diagonals $[ AC ]$ and $[ BD ]$ are $\mathrm { A } ( 3,1 ) , \mathrm { B } ( 5,3 ) , \mathrm { C } ( 2,5 )$ and $\mathrm { D } ( \mathrm { a } , \mathrm { b } )$. What is the length of diagonal $[ BD ]$ in units?
A) 1
B) 2
C) 3
D) 4
E) 5

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2010 ygs