CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 06 · Q1

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$A = \{5,6,7,8,9\}$ : which is correct?

Target: ~75s · ID EXAM-G6-1

Q 2/48CSCA Standardsets · Mock 06 · Q2

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Survey of 50: 25 like A, 20 like B, 10 like both. Like only A:

Target: ~75s · ID EXAM-G6-2

Q 3/48CSCA Standardinequalities · Mock 06 · Q3

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$x^2+3x-4 > 0$ : solution set is

Target: ~75s · ID EXAM-G6-3

Q 4/48CSCA Standardinequalities · Mock 06 · Q4

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$x^2-11x+28 > 0$ : solution set is

Target: ~75s · ID EXAM-G6-4

Q 5/48CSCA Standardinequalities · Mock 06 · Q5

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$x^2-2x-3 > 0$ : solution set is

Target: ~75s · ID EXAM-G6-5

Q 6/48CSCA Standarddomain-range · Mock 06 · Q6

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The domain of $y = \frac{1}{x+7}$ is

Target: ~75s · ID EXAM-G6-6

Q 7/48CSCA Standarddomain-range · Mock 06 · Q7

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The domain of $y = \sqrt{x-8}$ is

Target: ~75s · ID EXAM-G6-7

Q 8/48CSCA Standarddomain-range · Mock 06 · Q8

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Which function is the same as $y = |x|$ ?

Target: ~75s · ID EXAM-G6-8

Q 9/48CSCA Standardmonotonicity · Mock 06 · Q9

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Which function is strictly increasing on $(-\infty,+\infty)$ ?

Target: ~75s · ID EXAM-G6-9

Q 10/48CSCA Standardeven-odd-functions · Mock 06 · Q10

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Which is an odd function?

Target: ~75s · ID EXAM-G6-10

Q 11/48CSCA Standardpower-functions · Mock 06 · Q11

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The inverse function of $y = x^3+2$ $(x \in \mathbb{R})$ is

Target: ~75s · ID EXAM-G6-11

Q 12/48CSCA Standardexponential-functions · Mock 06 · Q12

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G6-12

Q 13/48CSCA Standardexponential-functions · Mock 06 · Q13

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The function $y = a^x$ is decreasing. The range of $a$ is

Target: ~75s · ID EXAM-G6-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 06 · Q14

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Which logarithm statement is incorrect?

Target: ~75s · ID EXAM-G6-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 06 · Q15

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$\sin\alpha = \frac{5}{13}$ , second quadrant: $\cos\alpha =$

Target: ~75s · ID EXAM-G6-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 06 · Q16

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G6-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 06 · Q17

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$\cos\alpha = -\frac{3}{5}$ , QII: $\cos(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-G6-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 06 · Q18

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Minimum of $y = \cos 2x + 8$ is

Target: ~75s · ID EXAM-G6-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 06 · Q19

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$\cos\alpha = -\frac{7}{25}$ , QII: $\sin(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-G6-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 06 · Q20

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$\sin\alpha = \frac{3}{5}$ , second quadrant: $\cos\alpha =$

Target: ~75s · ID EXAM-G6-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 06 · Q21

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$\sin 120^\circ =$

Target: ~75s · ID EXAM-G6-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 06 · Q22

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$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{3}$ : $\tan\alpha =$

Target: ~75s · ID EXAM-G6-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 06 · Q23

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Minimum of $y = \cos 3x + 5$ is

Target: ~75s · ID EXAM-G6-23

Q 24/48CSCA Standardinverse-functions · Mock 06 · Q24

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Inverse of $y = 10x + 2$ is

Target: ~75s · ID EXAM-G6-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 06 · Q25

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Arithmetic $a_1 = 3, a_2 = 2$ : $a_5 =$

Target: ~75s · ID EXAM-G6-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 06 · Q26

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Arithmetic $a_1 = 5$ , $d = -3$ : then $a_{100} =$

Target: ~75s · ID EXAM-G6-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 06 · Q27

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How many are arithmetic: $2,-3,-8,-13$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

Target: ~75s · ID EXAM-G6-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 06 · Q28

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$9, a, 25$ arithmetic: $a =$

Target: ~75s · ID EXAM-G6-28

Q 29/48CSCA Standardgeometric-sequences · Mock 06 · Q29

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Geometric $1,4,16$ : general term is

Target: ~75s · ID EXAM-G6-29

Q 30/48CSCA Standardgeometric-sequences · Mock 06 · Q30

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Geometric $1,2,4$ : general term is

Target: ~75s · ID EXAM-G6-30

Q 31/48CSCA Standardgeometric-sequences · Mock 06 · Q31

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Geometric $1,3,9$ : general term is

Target: ~75s · ID EXAM-G6-31

Q 32/48CSCA Standardlines · Mock 06 · Q32

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Slope $1$ through $(1,-2)$ : equation is

Target: ~75s · ID EXAM-G6-32

Q 33/48CSCA Standardlines · Mock 06 · Q33

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Inclination $45^\circ$ : slope is

Target: ~75s · ID EXAM-G6-33

Q 34/48CSCA Standardlines · Mock 06 · Q34

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Intersection of $y = x+5$ and $2x-y-4 = 0$ :

Target: ~75s · ID EXAM-G6-34

Q 35/48CSCA Standardlines · Mock 06 · Q35

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Which line is perpendicular to $-3x+9 = 0$ ?

Target: ~75s · ID EXAM-G6-35

Q 36/48CSCA Standardlines · Mock 06 · Q36

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Slope through $A(2,2)$ , $B(-2,3)$ :

Target: ~75s · ID EXAM-G6-36

Q 37/48CSCA Standardanalytic-geometry · Mock 06 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G6-37

Q 38/48CSCA Standardanalytic-geometry · Mock 06 · Q38

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Distance $P(-4,-5)$ to $Q(-6,-2)$ is

Target: ~75s · ID EXAM-G6-38

Q 39/48CSCA Standardanalytic-geometry · Mock 06 · Q39

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Distance $P(2,-1)$ to $Q(-3,-5)$ is

Target: ~75s · ID EXAM-G6-39

Q 40/48CSCA Standardcircles · Mock 06 · Q40

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Circle center $(-5,-1)$ , radius 3: equation is

Target: ~75s · ID EXAM-G6-40

Q 41/48CSCA Standardcircles · Mock 06 · Q41

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Through $A(-2,2)$ , center $(-2,0)$ : equation is

Target: ~75s · ID EXAM-G6-41

Q 42/48CSCA Standardparabolas · Mock 06 · Q42

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Directrix of $y^2 = 16x$ is

Target: ~75s · ID EXAM-G6-42

Q 43/48CSCA Standardparabolas · Mock 06 · Q43

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About parabola $y^2 = 36x$ , which is correct?

Target: ~75s · ID EXAM-G6-43

Q 44/48CSCA Standardellipses · Mock 06 · Q44

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About ellipse $\frac{x^2}{9}+\frac{y^2}{25} = 1$ , correct is

Target: ~75s · ID EXAM-G6-44

Q 45/48CSCA Standardhyperbolas · Mock 06 · Q45

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Foci of $\frac{x^2}{9} - \frac{y^2}{16} = 1$ are

Target: ~75s · ID EXAM-G6-45

Q 46/48CSCA Standardprobability · Mock 06 · Q46

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A fair die rolled once. $P(\ ext{even}) =$

Target: ~75s · ID EXAM-G6-46

Q 47/48CSCA Standardvectors · Mock 06 · Q47

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$a = (4,3)$ , $b = (12,9)$ : a and b are

Target: ~75s · ID EXAM-G6-47

Q 48/48CSCA Standardcomplex-numbers · Mock 06 · Q48

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$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{1000} =$

Target: ~75s · ID EXAM-G6-48

Mock 06 paper

A={5,6,7,8,9}A = \{5,6,7,8,9\}A={5,6,7,8,9}: which is correct?

Survey of 50: 25 like A, 20 like B, 10 like both. Like only A:

x2+3x−4>0x^2+3x-4 > 0x2+3x−4>0: solution set is

x2−11x+28>0x^2-11x+28 > 0x2−11x+28>0: solution set is

x2−2x−3>0x^2-2x-3 > 0x2−2x−3>0: solution set is

The domain of y=1x+7y = \frac{1}{x+7}y=x+71​ is

The domain of y=x−8y = \sqrt{x-8}y=x−8​ is

Which function is the same as y=∣x∣y = |x|y=∣x∣ ?

Which function is strictly increasing on (−∞,+∞)(-\infty,+\infty)(−∞,+∞) ?

Which is an odd function?

The inverse function of y=x3+2y = x^3+2y=x3+2 (x∈R)(x \in \mathbb{R})(x∈R) is

Given a>ba > ba>b , which must hold?

The function y=axy = a^xy=ax is decreasing. The range of aaa is

Which logarithm statement is incorrect?

sin⁡α=513\sin\alpha = \frac{5}{13}sinα=135​, second quadrant: cos⁡α=\cos\alpha =cosα=

sin⁡135∘=\sin 135^\circ =sin135∘=

cos⁡α=−35\cos\alpha = -\frac{3}{5}cosα=−53​, QII: cos⁡(α2)=\cos(\frac{\alpha}{2}) =cos(2α​)=

Minimum of y=cos⁡2x+8y = \cos 2x + 8y=cos2x+8 is

cos⁡α=−725\cos\alpha = -\frac{7}{25}cosα=−257​, QII: sin⁡(α2)=\sin(\frac{\alpha}{2}) =sin(2α​)=

sin⁡α=35\sin\alpha = \frac{3}{5}sinα=53​, second quadrant: cos⁡α=\cos\alpha =cosα=

sin⁡120∘=\sin 120^\circ =sin120∘=

cos⁡α−sin⁡αcos⁡α+sin⁡α=13\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{3}cosα+sinαcosα−sinα​=31​: tan⁡α=\tan\alpha =tanα=

Minimum of y=cos⁡3x+5y = \cos 3x + 5y=cos3x+5 is

Inverse of y=10x+2y = 10x + 2y=10x+2 is

Arithmetic a1=3,a2=2a_1 = 3, a_2 = 2a1​=3,a2​=2: a5=a_5 =a5​=

Arithmetic a1=5a_1 = 5a1​=5, d=−3d = -3d=−3: then a100=a_{100} =a100​=

How many are arithmetic: 2,−3,−8,−132,-3,-8,-132,−3,−8,−13 · 2,4,7,112,4,7,112,4,7,11 · 3,3,3,33,3,3,33,3,3,3 · 2,4,8,162,4,8,162,4,8,16 ?

9,a,259, a, 259,a,25 arithmetic: a=a =a=

Geometric 1,4,161,4,161,4,16: general term is

Geometric 1,2,41,2,41,2,4: general term is

Geometric 1,3,91,3,91,3,9: general term is

Slope 111 through (1,−2)(1,-2)(1,−2): equation is

Inclination 45∘45^\circ45∘: slope is

Intersection of y=x+5y = x+5y=x+5 and 2x−y−4=02x-y-4 = 02x−y−4=0:

Which line is perpendicular to −3x+9=0-3x+9 = 0−3x+9=0 ?

Slope through A(2,2)A(2,2)A(2,2) , B(−2,3)B(-2,3)B(−2,3):

Which point is in the third quadrant?

Distance P(−4,−5)P(-4,-5)P(−4,−5) to Q(−6,−2)Q(-6,-2)Q(−6,−2) is

Distance P(2,−1)P(2,-1)P(2,−1) to Q(−3,−5)Q(-3,-5)Q(−3,−5) is

Circle center (−5,−1)(-5,-1)(−5,−1), radius 3: equation is

Through A(−2,2)A(-2,2)A(−2,2), center (−2,0)(-2,0)(−2,0): equation is

Directrix of y2=16xy^2 = 16xy2=16x is

About parabola y2=36xy^2 = 36xy2=36x, which is correct?

About ellipse x29+y225=1\frac{x^2}{9}+\frac{y^2}{25} = 19x2​+25y2​=1, correct is

Foci of x29−y216=1\frac{x^2}{9} - \frac{y^2}{16} = 19x2​−16y2​=1 are

A fair die rolled once. P( exteven)=P(\ ext{even}) =P( exteven)=

a=(4,3)a = (4,3)a=(4,3), b=(12,9)b = (12,9)b=(12,9): a and b are

z3=1z^3 = 1z3=1, z≠1z \ne 1z=1: 1+z+⋯+z1000=1+z+\cdots+z^{1000} =1+z+⋯+z1000=

$A = \{5,6,7,8,9\}$ : which is correct?

$x^2+3x-4 > 0$ : solution set is

$x^2-11x+28 > 0$ : solution set is

$x^2-2x-3 > 0$ : solution set is

The domain of $y = \frac{1}{x+7}$ is

The domain of $y = \sqrt{x-8}$ is

Which function is the same as $y = |x|$ ?

Which function is strictly increasing on $(-\infty,+\infty)$ ?

The inverse function of $y = x^3+2$ $(x \in \mathbb{R})$ is

Given $a > b$ , which must hold?

The function $y = a^x$ is decreasing. The range of $a$ is

$\sin\alpha = \frac{5}{13}$ , second quadrant: $\cos\alpha =$

$\sin 135^\circ =$

$\cos\alpha = -\frac{3}{5}$ , QII: $\cos(\frac{\alpha}{2}) =$

Minimum of $y = \cos 2x + 8$ is

$\cos\alpha = -\frac{7}{25}$ , QII: $\sin(\frac{\alpha}{2}) =$

$\sin\alpha = \frac{3}{5}$ , second quadrant: $\cos\alpha =$

$\sin 120^\circ =$

$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{3}$ : $\tan\alpha =$

Minimum of $y = \cos 3x + 5$ is

Inverse of $y = 10x + 2$ is

Arithmetic $a_1 = 3, a_2 = 2$ : $a_5 =$

Arithmetic $a_1 = 5$ , $d = -3$ : then $a_{100} =$

How many are arithmetic: $2,-3,-8,-13$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

$9, a, 25$ arithmetic: $a =$

Geometric $1,4,16$ : general term is

Geometric $1,2,4$ : general term is

Geometric $1,3,9$ : general term is

Slope $1$ through $(1,-2)$ : equation is

Inclination $45^\circ$ : slope is

Intersection of $y = x+5$ and $2x-y-4 = 0$ :

Which line is perpendicular to $-3x+9 = 0$ ?

Slope through $A(2,2)$ , $B(-2,3)$ :

Distance $P(-4,-5)$ to $Q(-6,-2)$ is

Distance $P(2,-1)$ to $Q(-3,-5)$ is

Circle center $(-5,-1)$ , radius 3: equation is

Through $A(-2,2)$ , center $(-2,0)$ : equation is

Directrix of $y^2 = 16x$ is

About parabola $y^2 = 36x$ , which is correct?

About ellipse $\frac{x^2}{9}+\frac{y^2}{25} = 1$ , correct is

Foci of $\frac{x^2}{9} - \frac{y^2}{16} = 1$ are

A fair die rolled once. $P(\ ext{even}) =$

$a = (4,3)$ , $b = (12,9)$ : a and b are

$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{1000} =$