LFM Pure and Mechanics

brazil-enem 2010 Q175 Simplifying Surd Expressions View

Question 175
Um cubo tem aresta de 3 cm. A diagonal do cubo, em cm, é
(A) $3\sqrt{2}$ (B) $3\sqrt{3}$ (C) $6\sqrt{2}$ (D) $6\sqrt{3}$ (E) $9\sqrt{2}$

brazil-enem 2012 Q168 Evaluating Expressions Using Index Laws View

Among other research objects, Allometry studies the relationship between measurements of different parts of the human body. For example, according to Allometry, the area A of the body surface of a person relates to their mass $m$ by the formula $A = k \cdot \mathrm{~m}^{\frac{2}{3}}$, where $k$ is a positive constant.
If during the period from childhood to adulthood of an individual their mass is multiplied by 8, by how much will the area of body surface be multiplied?
(A) $\sqrt[3]{16}$
(B) 4
(C) $\sqrt{24}$
(D) 8
(E) 64

brazil-enem 2015 Q170 Evaluating Expressions Using Index Laws View

QUESTION 170
The value of $2^{10}$ is
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192

brazil-enem 2015 Q175 Simplifying Surd Expressions View

QUESTION 175
The value of $\sqrt{144} + \sqrt{25}$ is
(A) 13
(B) 15
(C) 17
(D) 19
(E) 21

brazil-enem 2024 Q177 Evaluating Expressions Using Index Laws View

The value of $2^{10}$ is:
(A) 512
(B) 1024
(C) 2048
(D) 4096
(E) 8192

cmi-entrance 2023 QA5 4 marks Ordering and Comparing Surd or Numerical Values View

Statements
(17) $4 < \sqrt { 5 + 5 \sqrt { 5 } }$. (18) $\log _ { 2 } 11 < \frac { 1 + \log _ { 2 } 61 } { 2 }$. (19) $( 2023 ) ^ { 2023 } < ( 2023 ! ) ^ { 2 }$. (20) $92 ^ { 100 } + 93 ^ { 100 } < 94 ^ { 100 }$.

csat-suneung 2005 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $3 ^ { \frac { 2 } { 3 } } \times 9 ^ { \frac { 3 } { 2 } } \div 27 ^ { \frac { 8 } { 9 } }$? [2 points]
(1) 1
(2) $\sqrt { 3 }$
(3) 3
(4) $3 \sqrt { 3 }$
(5) 9

csat-suneung 2005 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $3 ^ { \frac { 2 } { 3 } } \times 9 ^ { \frac { 3 } { 2 } } \div 27 ^ { \frac { 8 } { 9 } }$? [2 points]
(1) 1
(2) $\sqrt { 3 }$
(3) 3
(4) $3 \sqrt { 3 }$
(5) 9

csat-suneung 2006 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $5 ^ { \frac { 2 } { 3 } } \times 25 ^ { - \frac { 5 } { 6 } }$? [2 points]
(1) $\frac { 1 } { 25 }$
(2) $\frac { 1 } { 5 }$
(3) 1
(4) 5
(5) 25

csat-suneung 2006 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $5 ^ { \frac { 2 } { 3 } } \times 25 ^ { - \frac { 5 } { 6 } }$? [2 points]
(1) $\frac { 1 } { 25 }$
(2) $\frac { 1 } { 5 }$
(3) 1
(4) 5
(5) 25

csat-suneung 2008 Q4 3 marks Evaluating Expressions Using Index Laws View

When $a = \sqrt { 2 } , b ^ { 3 } = \sqrt { 3 }$, what is the value of $( a b ) ^ { 2 }$? (Here, $b$ is a real number.) [3 points]
(1) $2 \cdot 3 ^ { \frac { 1 } { 3 } }$
(2) $2 \cdot 3 ^ { \frac { 2 } { 3 } }$
(3) $2 ^ { \frac { 1 } { 2 } } \cdot 3 ^ { \frac { 1 } { 3 } }$
(4) $3 \cdot 2 ^ { \frac { 1 } { 3 } }$
(5) $3 \cdot 2 ^ { \frac { 2 } { 3 } }$

csat-suneung 2009 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $9 ^ { \frac { 3 } { 2 } } \times 27 ^ { - \frac { 2 } { 3 } }$? [2 points]
(1) $\frac { 1 } { 3 }$
(2) 1
(3) $\sqrt { 3 }$
(4) 3
(5) $3 \sqrt { 3 }$

csat-suneung 2009 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $9 ^ { \frac { 3 } { 2 } } \times 27 ^ { - \frac { 2 } { 3 } }$? [2 points]
(1) $\frac { 1 } { 3 }$
(2) 1
(3) $\sqrt { 3 }$
(4) 3
(5) $3 \sqrt { 3 }$

csat-suneung 2010 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $27 ^ { \frac { 1 } { 3 } } + \log _ { 2 } 4$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

csat-suneung 2010 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $27 ^ { \frac { 1 } { 3 } } + \log _ { 2 } 4$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

csat-suneung 2013 Q26 4 marks Number-Theoretic Reasoning with Indices View

For natural numbers $n$ with $2 \leq n \leq 100$, find the number of values of $n$ such that $\left( \sqrt[3]{3^5} \right)^{\frac{1}{2}}$ is the $n$-th root of some natural number. [4 points]

csat-suneung 2014 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $8 ^ { \frac { 2 } { 3 } } \times 9 ^ { \frac { 1 } { 2 } }$? [2 points]
(1) 4
(2) 6
(3) 8
(4) 10
(5) 12

csat-suneung 2015 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $5 \times 8 ^ { \frac { 1 } { 3 } }$? [2 points]
(1) 10
(2) 15
(3) 20
(4) 25
(5) 30

csat-suneung 2015 Q15 4 marks Exponential Inequalities and Counting Solutions View

What is the sum of all natural numbers $x$ that satisfy the exponential inequality $\left( \frac { 1 } { 5 } \right) ^ { 1 - 2 x } \leq 5 ^ { x + 4 }$? [4 points]
(1) 11
(2) 12
(3) 13
(4) 14
(5) 15

csat-suneung 2016 Q3 2 marks Evaluating Expressions Using Index Laws View

What is the value of $8 ^ { \frac { 1 } { 3 } } + 27 ^ { \frac { 2 } { 3 } }$? [2 points]
(1) 8
(2) 9
(3) 10
(4) 11
(5) 12

csat-suneung 2017 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $8 \times 2 ^ { - 2 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16

csat-suneung 2018 Q1 2 marks Evaluating Expressions Using Index Laws View

Find the value of $2 \times 16 ^ { \frac { 1 } { 4 } }$. [2 points]
(1) 2
(2) 4
(3) 6
(4) 8
(5) 10

csat-suneung 2019 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $2 ^ { - 1 } \times 16 ^ { \frac { 1 } { 2 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

csat-suneung 2020 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $16 \times 2 ^ { - 3 }$? [2 points]
(1) 1
(2) 2
(3) 4
(4) 8
(5) 16

csat-suneung 2021 Q1 2 marks Evaluating Expressions Using Index Laws View

What is the value of $3 ^ { 0 } \times 8 ^ { \frac { 2 } { 3 } }$? [2 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

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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