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Papers (30)
2025
yks-ayt 36 yks-tyt 7
2024
yks-ayt 34 yks-tyt 7
2023
yks-ayt 24 yks-tyt 38
2021
yks-ayt 36 yks-tyt 13
2020
yks-ayt 35 yks-tyt 36
2019
yks-ayt 39 yks-tyt 9
2018
yks-ayt 39 yks-tyt 8
2017
lys1-math 56 ygs 18
2016
lys1-math 49 ygs 13
2015
lys1-math 50 ygs 13
2014
lys1-math 50 ygs 17
2013
lys1-math 50 ygs 25
2012
lys1-math 46 ygs 17
2011
lys1-math 49 ygs 19
2010
lys1-math 50 ygs 28
2016 ygs

13 maths questions

Q2 Indices and Surds Evaluating Expressions Using Index Laws View
$$\frac { 6 ^ { -8 } \cdot 9 ^ { 4 } } { 4 ^ { -6 } }$$
What is the result of this operation?
A) 8
B) 9
C) 12
D) 16
E) 18
Q3 Indices and Surds Simplifying Surd Expressions View
$$\frac { \sqrt { 12 } } { \sqrt { 27 } + \frac { 1 } { \sqrt { 3 } } }$$
What is the result of this operation?
A) $\frac { 2 } { 3 }$
B) $\frac { 3 } { 5 }$
C) $\frac { 1 } { 2 }$
D) $\sqrt { 3 }$
E) $\sqrt { 6 }$
Q6 Indices and Surds Ordering and Comparing Surd or Numerical Values View
$$\begin{aligned} & a = \sqrt { 2 } + \sqrt { 45 } \\ & b = \sqrt { 5 } + \sqrt { 18 } \\ & c = \sqrt { 8 } + \sqrt { 20 } \end{aligned}$$
Given this, which of the following orderings is correct?
A) a $<$ b $<$ c
B) b $<$ a $<$ c
C) c $<$ b $<$ a
D) b $<$ c $<$ a
E) c $<$ a $<$ b
Q7 Inequalities Integer Solutions of an Inequality View
For real numbers $x$ and $y$,
$$\begin{aligned} & 3 < x < 12 \\ & \frac { x } { y } = \frac { 3 } { 2 } \end{aligned}$$
Given this, what is the sum of the integer values that $y$ can take?
A) 18
B) 21
C) 25
D) 28
E) 32
Q8 Polynomial Division & Manipulation View
$$\frac { x ^ { 4 } + x ^ { 2 } y - x ^ { 2 } y ^ { 2 } - y ^ { 3 } } { x ^ { 3 } + x y - x ^ { 2 } y - y ^ { 2 } }$$
Which of the following is the simplified form of this expression?
A) $x$
B) $y$
C) $x y$
D) $x - y$
E) $x + y$
Q10 Exponential Equations & Modelling Solve Exponential Equation for Unknown Variable View
$$3 ^ { x } \cdot 12 ^ { 2 - x } = 18$$
Given this, what is $x$?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 4 } { 3 }$
E) $\frac { 5 } { 4 }$
Q11 Indices and Surds Solving Equations Involving Surds View
$$\frac { 1 } { \sqrt { 2 x } } + \frac { 4 } { \sqrt { 8 x } } = 6$$
Given this, what is $x$?
A) $\frac { 1 } { 2 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 1 } { 8 }$
E) $\frac { 1 } { 12 }$
Q13 Inequalities Absolute Value Inequality View
On the real number line, numbers whose distance to point 2 is less than half the distance to point $-4$ form the solution set of which of the following inequalities?
A) $| x - 2 | < | x + 4 |$
B) $| x + 2 | < | x - 4 |$
C) $| 2 x - 4 | < | x + 4 |$
D) $| 2 x - 4 | < | x - 4 |$
E) $| 2 x + 4 | < | x + 4 |$
Q15 Composite & Inverse Functions Evaluate Composition from Algebraic Definitions View
Functions $f$ and $g$ with domain of integers are defined as
$$\begin{aligned} & f ( n ) = n + \frac { 1 } { 3 } \\ & g ( n ) = n + \frac { 1 } { 6 } \end{aligned}$$
Given this, I. $f \circ f \circ f$ II. $f \circ g \circ f$ III. $g \circ f \circ g$ For which of these functions does the image set consist only of integers?
A) Only I
B) Only II
C) I and II
D) II and III
E) I, II and III
Q20 Arithmetic Sequences and Series Counting or Combinatorial Problems on APs View
A school principal sends an electronic mail on Monday to some students of the school containing the note, ``Every student who receives this message should send it to two students the next day.'' The students who receive the message follow what is written in that note.
By the end of Friday of the same week, this message reaches all students in the school and each student receives this message only once.
Given that the number of students in the school is 930, how many students was this message initially sent to?
A) 6
B) 10
C) 15
D) 21
E) 30
Q33 Probability Definitions Finite Equally-Likely Probability Computation View
In a cube, 6 of its 8 vertices are randomly painted white and the other 2 are painted black.
What is the probability that there is an edge with both endpoints painted black in this cube?
A) $\frac { 1 } { 7 }$
B) $\frac { 2 } { 7 }$
C) $\frac { 3 } { 7 }$
D) $\frac { 4 } { 7 }$
E) $\frac { 5 } { 7 }$
Q39 Volumes of Revolution Volume by Displacement or Composite Solid View
The position of two iron balls in the shape of spheres with radius 3 units placed inside a right circular cylinder with radius 6 units is shown in Figure 1.
The cylinder is filled with water until both balls are completely submerged in water and the view in Figure 2 is obtained.
Accordingly, what is the volume of water in the cylinder in Figure 2 in cubic units?
A) $96 \pi$
B) $108 \pi$
C) $120 \pi$
D) $132 \pi$
E) $144 \pi$
Q40 Straight Lines & Coordinate Geometry Line Equation and Parametric Representation View
In the rectangular coordinate plane, the line $y = \frac { x } { 7 }$ intersects the lines $x = 2$ and $x = 9$ at points $P$ and $R$ respectively.
Accordingly, what is the length $| \mathrm { PR } |$ in units?
A) $5 \sqrt { 2 }$
B) $6 \sqrt { 2 }$
C) $4 \sqrt { 10 }$
D) 8
E) 9