LFM Pure and Mechanics

turkey-yks 2013 Q3 Solving Equations Involving Surds View

$$\frac { 1 + \sqrt { a } } { 1 - a } - \frac { a } { 1 - \sqrt { a } } = \frac { 5 } { 3 }$$
Given this, what is a?
A) $\frac { 1 } { 2 }$
B) $\frac { 3 } { 2 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 1 } { 9 }$
E) $\frac { 4 } { 9 }$

turkey-yks 2014 Q1 Evaluating Expressions Using Index Laws View

$$\left[ \left( \frac { - 1 } { 2 } \right) ^ { - 2 } \right] ^ { 3 }$$
What is the result of this operation?
A) - 32
B) - 16
C) 12
D) 32
E) 64

turkey-yks 2014 Q3 Evaluating Expressions Using Index Laws View

$6 ^ { - 3 } \left( 8 ^ { 3 } - 6 ^ { 3 } + 4 ^ { 3 } \right)$ What is the result of this operation?
A) $\frac { 1 } { 2 }$
B) $\frac { 4 } { 3 }$
C) $\frac { 5 } { 3 }$
D) $\frac { 9 } { 4 }$
E) $\frac { 5 } { 6 }$

turkey-yks 2014 Q4 Solving Equations Involving Surds View

For a real number $\mathbf { x }$,
$$\sqrt { \frac { \sqrt { x } + 2 } { \sqrt { x } - 2 } } = \sqrt { x } + 2$$
Given that, what is x?
A) 3
B) 4
C) 5
D) 6
E) 7

turkey-yks 2014 Q10 Solving Equations Involving Surds View

Given that $x \neq - 1$ and
$$( x + 1 ) \sqrt { x - 1 } = \sqrt { 2 x + 2 }$$
What is $x$?
A) $\frac { 3 \sqrt { 3 } } { 2 }$
B) $\frac { 2 \sqrt { 3 } } { 3 }$
C) $\frac { 4 \sqrt { 2 } } { 3 }$
D) $\sqrt { 2 }$
E) $\sqrt { 3 }$

turkey-yks 2015 Q1 Evaluating Expressions Using Index Laws View

$$3 ^ { 2 } \cdot \frac { 1 - 3 ^ { - 4 } } { 1 - 3 ^ { - 2 } }$$
What is the result of this operation?
A) 4
B) 5
C) 8
D) 9
E) 10

turkey-yks 2015 Q3 Simplifying Surd Expressions View

$$\frac { \sqrt [ 3 ] { 2 \cdot \sqrt { 54 } } } { \sqrt { 2 } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $\sqrt { 3 }$ C) $\sqrt { 6 }$ D) $\sqrt [ 3 ] { 4 }$ E) $\sqrt [ 3 ] { 9 }$

turkey-yks 2016 Q1 Numerical Arithmetic with Fractions and Decimals View

$$\frac { 6 ^ { 4 } - 4 ^ { 4 } } { 5 \cdot 2 ^ { 4 } }$$
What is the result of this operation?
A) 9
B) 12
C) 13
D) 14
E) 16

turkey-yks 2016 Q2 Numerical Arithmetic with Fractions and Decimals View

$$\frac { 4 } { 9 - \frac { 49 } { 9 } } - \frac { 1 } { 8 }$$
What is the result of this operation?
A) 1
B) 2
C) 3
D) $\frac { 1 } { 2 }$
E) $\frac { 1 } { 4 }$

turkey-yks 2016 Q2 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

turkey-yks 2016 Q3 Simplifying Surd Expressions View

$$\frac { \sqrt { 48 } } { \frac { 1 } { \sqrt { 3 } } + \frac { 1 } { \sqrt { 27 } } }$$
What is the result of this operation?
A) 3
B) 5
C) 8
D) 9
E) 12

turkey-yks 2016 Q3 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) $\sqrt { 6 }$

turkey-yks 2016 Q6 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

turkey-yks 2016 Q8 Ratio and Proportion Problems View

Positive real numbers $a$ and $b$ satisfy the equality
$$a ^ { 2 } - 2 a b - 3 b ^ { 2 } = 0$$
Accordingly, what is the value of the expression $\frac { a + b } { a - b }$?
A) 2
B) 3
C) 4
D) 5
E) 6

turkey-yks 2016 Q11 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) $\frac { 1 } { 12 }$

turkey-yks 2017 Q1 Numerical Arithmetic with Fractions and Decimals View

$\frac { 5 - \frac { 25 } { 9 } } { \frac { 2 } { 3 } } - \frac { 1 } { 3 }$\ What is the result of this operation?\ A) 1\ B) 2\ C) 3\ D) 4\ E) 5

turkey-yks 2017 Q2 Numerical Arithmetic with Fractions and Decimals View

$\frac { 60 ^ { 2 } \cdot 3 } { 15 ^ { 3 } }$\ What is the result of this operation?\ A) 2.4\ B) 2.6\ C) 2.8\ D) 3\ E) 3.2

turkey-yks 2017 Q3 Simplifying Surd Expressions View

$\frac { \sqrt { 48 } + \sqrt { 75 } } { \sqrt { 108 } - \sqrt { 27 } }$\ What is the result of this operation?\ A) 1\ B) 2\ C) 3\ D) 4\ E) 5

turkey-yks 2017 Q3 Simplifying Surd Expressions View

$$\sqrt [ 3 ] { \frac { 32 } { \sqrt { 8 } - \sqrt { 2 } } }$$
What is the result of this operation?
A) $\sqrt { 2 }$ B) $2 \sqrt { 2 }$ C) $\sqrt [ 3 ] { 2 }$ D) 2 E) 4

turkey-yks 2017 Q10 Solving Equations Involving Surds View

$\frac { 1 } { \sqrt { \mathrm{a} } } - \frac { 2 } { \sqrt { 9 \mathrm{a} } } = 1$\ Given this, what is a?\ A) $\frac { 1 } { 3 }$\ B) $\frac { 2 } { 3 }$\ C) $\frac { 1 } { 4 }$\ D) $\frac { 1 } { 9 }$\ E) $\frac { 4 } { 9 }$

turkey-yks 2020 Q2 Number-Theoretic Reasoning with Indices View

For a project, 16 schools were selected from each of Turkey's 81 provinces, and a message was sent to each school's principal. Then, each school's principal sent this message to 35 teachers in their school.
Accordingly, what is the total number of principals and teachers to whom this message was sent?
A) $4^{6}$
B) $5^{6}$
C) $6^{6}$
D) $7 \cdot 5^{5}$
E) $8^{6}$

turkey-yks 2020 Q3 Solving Exponential or Index Equations View

For integers $x$ and $y$
$$9 ^ { x } - 3 ^ { 2 x - 2 } = 2 ^ { y } \cdot 3 ^ { 6 }$$
the equality is satisfied. Accordingly, what is the sum $x + y$?
A) 3
B) 4
C) 5
D) 6
E) 7

turkey-yks 2020 Q3 Simplifying Surd Expressions View

When the numbers $\sqrt{5}, \sqrt{8}, \sqrt{12}, \sqrt{18}, \sqrt{20}$ and $\sqrt{27}$ are placed in the boxes below, with each box containing a different number, A, B, and C become whole numbers.
Accordingly, what is the sum $\mathrm{A} + \mathrm{B} + \mathrm{C}$?
A) 40
B) 44
C) 48
D) 52
E) 56

turkey-yks 2021 Q1 Number-Theoretic Reasoning with Indices View

For distinct natural numbers $a$, $b$, and $c$,
$$\frac { 6 ^ { a } \cdot 15 ^ { b } } { 9 ^ { b } \cdot 10 ^ { c } }$$
is equal to an integer. Accordingly, which of the following orderings is correct?
A) $a < b < c$
B) $b < a < c$
C) $b < c < a$
D) $c < a < b$
E) $c < b < a$

turkey-yks 2021 Q4 Simplifying Surd Expressions View

Mert, who performs operations with radical numbers, instead of multiplying the number $\sqrt{10} + \sqrt{6}$ by its conjugate $\sqrt{10} - \sqrt{6}$, mistakenly divided it.
Accordingly, how much greater is the number Mert found than the number he should have found?
A) $\sqrt{12}$ B) $\sqrt{15}$ C) $\sqrt{18}$ D) $\sqrt{20}$ E) $\sqrt{30}$

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LFM Pure and Mechanics

Indices and Surds 107

Exponential Functions 100

Laws of Logarithms 200

Exponential Equations & Modelling 58

Arithmetic Sequences and Series 271

Geometric Sequences and Series 203

Differentiation from First Principles 37

Tangents, normals and gradients 93

Stationary points and optimisation 384

Applied differentiation 164

Indefinite & Definite Integrals 533

Areas Between Curves 83

Areas by integration 109

Volumes of Revolution 61

Numerical integration 32

Vectors Introduction & 2D 204

Vectors 3D & Lines 233

Travel graphs 11

SUVAT in 2D & Gravity 6

Constant acceleration (SUVAT) 32

Variable acceleration (1D) 40

Variable acceleration (vectors) 26

Forces, equilibrium and resultants 9

Newton's laws and connected particles 18

Pulley systems 5

Motion on a slope 4

Friction 10

Momentum and Collisions 15

Moments 13

Parametric curves and Cartesian conversion 11

Parametric differentiation 15

Parametric integration 4

Projectiles 40