CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 12 · Q1

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$A = \{6,7,8,9,10\}$ : which is correct?

Target: ~75s · ID EXAM-G12-1

Q 2/48CSCA Standardsets · Mock 12 · Q2

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

Target: ~75s · ID EXAM-G12-2

Q 3/48CSCA Standardinequalities · Mock 12 · Q3

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$x^2+7x+12 > 0$ : solution set is

Target: ~75s · ID EXAM-G12-3

Q 4/48CSCA Standardinequalities · Mock 12 · Q4

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$a, b, c$ reals. Which is correct?

Target: ~75s · ID EXAM-G12-4

Q 5/48CSCA Standardinequalities · Mock 12 · Q5

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$x^2+2x-15 > 0$ : solution set is

Target: ~75s · ID EXAM-G12-5

Q 6/48CSCA Standarddomain-range · Mock 12 · Q6

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The domain of $y = \frac{1}{x+9}$ is

Target: ~75s · ID EXAM-G12-6

Q 7/48CSCA Standarddomain-range · Mock 12 · Q7

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The domain of $y = \sqrt{x-3}$ is

Target: ~75s · ID EXAM-G12-7

Q 8/48CSCA Standarddomain-range · Mock 12 · Q8

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The domain of $f(x) = \frac{1}{x} + \sqrt{8-x}$ is

Target: ~75s · ID EXAM-G12-8

Q 9/48CSCA Standardmonotonicity · Mock 12 · Q9

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

Target: ~75s · ID EXAM-G12-9

Q 10/48CSCA Standardeven-odd-functions · Mock 12 · Q10

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Which is an odd function?

Target: ~75s · ID EXAM-G12-10

Q 11/48CSCA Standardpower-functions · Mock 12 · Q11

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

Target: ~75s · ID EXAM-G12-11

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

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G12-12

Q 13/48CSCA Standardexponential-functions · Mock 12 · Q13

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

Target: ~75s · ID EXAM-G12-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 12 · Q14

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Which logarithm statement is incorrect?

Target: ~75s · ID EXAM-G12-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 12 · Q15

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Minimum of $y = \cos 7x + 3$ is

Target: ~75s · ID EXAM-G12-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 12 · Q16

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$\sin 150^\circ =$

Target: ~75s · ID EXAM-G12-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 12 · Q17

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

Target: ~75s · ID EXAM-G12-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 12 · Q18

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

Target: ~75s · ID EXAM-G12-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 12 · Q19

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

Target: ~75s · ID EXAM-G12-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 12 · Q20

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Minimum of $y = \cos 4x + 4$ is

Target: ~75s · ID EXAM-G12-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 12 · Q21

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$\sin 120^\circ =$

Target: ~75s · ID EXAM-G12-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 12 · Q22

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G12-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 12 · Q23

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

Target: ~75s · ID EXAM-G12-23

Q 24/48CSCA Standardinverse-functions · Mock 12 · Q24

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Inverse of $y = 10x + 2$ is

Target: ~75s · ID EXAM-G12-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 12 · Q25

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$-4, a, 10$ arithmetic: $a =$

Target: ~75s · ID EXAM-G12-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 12 · Q26

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Arithmetic $a_1 = 6$ , $d = -1$ : then $a_{101} =$

Target: ~75s · ID EXAM-G12-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 12 · Q27

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Arithmetic with $a_7 = 8$ : $S_{13} =$

Target: ~75s · ID EXAM-G12-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 12 · Q28

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How many are arithmetic: $6,9,12,15$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

Target: ~75s · ID EXAM-G12-28

Q 29/48CSCA Standardgeometric-sequences · Mock 12 · Q29

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

Target: ~75s · ID EXAM-G12-29

Q 30/48CSCA Standardgeometric-sequences · Mock 12 · Q30

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$\frac{1}{3}, -\frac{1}{9}, \frac{1}{27}, \ldots$ : $a_n =$

Target: ~75s · ID EXAM-G12-30

Q 31/48CSCA Standardgeometric-sequences · Mock 12 · Q31

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

Target: ~75s · ID EXAM-G12-31

Q 32/48CSCA Standardlines · Mock 12 · Q32

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Intersection of $y = 3x-4$ and $-3x-y+2 = 0$ :

Target: ~75s · ID EXAM-G12-32

Q 33/48CSCA Standardlines · Mock 12 · Q33

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Slope $4$ through $(-2,-5)$ : equation is

Target: ~75s · ID EXAM-G12-33

Q 34/48CSCA Standardlines · Mock 12 · Q34

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

Target: ~75s · ID EXAM-G12-34

Q 35/48CSCA Standardlines · Mock 12 · Q35

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Inclination $60^\circ$ : slope is

Target: ~75s · ID EXAM-G12-35

Q 36/48CSCA Standardlines · Mock 12 · Q36

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Slope through $A(-4,1)$ , $B(-9,2)$ :

Target: ~75s · ID EXAM-G12-36

Q 37/48CSCA Standardanalytic-geometry · Mock 12 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G12-37

Q 38/48CSCA Standardanalytic-geometry · Mock 12 · Q38

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$P(2,4)$ ; Q symmetric about the x-axis: Q =

Target: ~75s · ID EXAM-G12-38

Q 39/48CSCA Standardanalytic-geometry · Mock 12 · Q39

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

Target: ~75s · ID EXAM-G12-39

Q 40/48CSCA Standardcircles · Mock 12 · Q40

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Circle center $(-4,4)$ , radius 2: equation is

Target: ~75s · ID EXAM-G12-40

Q 41/48CSCA Standardcircles · Mock 12 · Q41

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Through $A(-1,4)$ , center $(-1,0)$ : equation is

Target: ~75s · ID EXAM-G12-41

Q 42/48CSCA Standardparabolas · Mock 12 · Q42

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Directrix of $y^2 = 4x$ is

Target: ~75s · ID EXAM-G12-42

Q 43/48CSCA Standardparabolas · Mock 12 · Q43

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About parabola $y^2 = 12x$ , which is correct?

Target: ~75s · ID EXAM-G12-43

Q 44/48CSCA Standardellipses · Mock 12 · Q44

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

Target: ~75s · ID EXAM-G12-44

Q 45/48CSCA Standardhyperbolas · Mock 12 · Q45

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Foci of $\frac{x^2}{36} - \frac{y^2}{64} = 1$ are

Target: ~75s · ID EXAM-G12-45

Q 46/48CSCA Standardprobability · Mock 12 · Q46

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

Target: ~75s · ID EXAM-G12-46

Q 47/48CSCA Standardvectors · Mock 12 · Q47

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$a = (1,3)$ , $b = (3,9)$ : a and b are

Target: ~75s · ID EXAM-G12-47

Q 48/48CSCA Standardcomplex-numbers · Mock 12 · Q48

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$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{999} =$

Target: ~75s · ID EXAM-G12-48

Mock 12 paper

A={6,7,8,9,10}A = \{6,7,8,9,10\}A={6,7,8,9,10}: which is correct?

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

x2+7x+12>0x^2+7x+12 > 0x2+7x+12>0: solution set is

a,b,ca, b, ca,b,c reals. Which is correct?

x2+2x−15>0x^2+2x-15 > 0x2+2x−15>0: solution set is

The domain of y=1x+9y = \frac{1}{x+9}y=x+91​ is

The domain of y=x−3y = \sqrt{x-3}y=x−3​ is

The domain of f(x)=1x+8−xf(x) = \frac{1}{x} + \sqrt{8-x}f(x)=x1​+8−x​ is

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

Which is an odd function?

The inverse function of y=x3+3y = x^3+3y=x3+3 (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?

Minimum of y=cos⁡7x+3y = \cos 7x + 3y=cos7x+3 is

sin⁡150∘=\sin 150^\circ =sin150∘=

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

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

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

Minimum of y=cos⁡4x+4y = \cos 4x + 4y=cos4x+4 is

sin⁡120∘=\sin 120^\circ =sin120∘=

Which reduction equation is incorrect?

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

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

−4,a,10-4, a, 10−4,a,10 arithmetic: a=a =a=

Arithmetic a1=6a_1 = 6a1​=6, d=−1d = -1d=−1: then a101=a_{101} =a101​=

Arithmetic with a7=8a_7 = 8a7​=8: S13=S_{13} =S13​=

How many are arithmetic: 6,9,12,156,9,12,156,9,12,15 · 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 ?

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

13,−19,127,…\frac{1}{3}, -\frac{1}{9}, \frac{1}{27}, \ldots31​,−91​,271​,…: an=a_n =an​=

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

Intersection of y=3x−4y = 3x-4y=3x−4 and −3x−y+2=0-3x-y+2 = 0−3x−y+2=0:

Slope 444 through (−2,−5)(-2,-5)(−2,−5): equation is

Which line is perpendicular to x+9=0x+9 = 0x+9=0 ?

Inclination 60∘60^\circ60∘: slope is

Slope through A(−4,1)A(-4,1)A(−4,1) , B(−9,2)B(-9,2)B(−9,2):

Which point is in the third quadrant?

P(2,4)P(2,4)P(2,4); Q symmetric about the x-axis: Q =

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

Circle center (−4,4)(-4,4)(−4,4), radius 2: equation is

Through A(−1,4)A(-1,4)A(−1,4), center (−1,0)(-1,0)(−1,0): equation is

Directrix of y2=4xy^2 = 4xy2=4x is

About parabola y2=12xy^2 = 12xy2=12x, which is correct?

About ellipse x225+y29=1\frac{x^2}{25}+\frac{y^2}{9} = 125x2​+9y2​=1, correct is

Foci of x236−y264=1\frac{x^2}{36} - \frac{y^2}{64} = 136x2​−64y2​=1 are

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

a=(1,3)a = (1,3)a=(1,3), b=(3,9)b = (3,9)b=(3,9): a and b are

z3=1z^3 = 1z3=1, z≠1z \ne 1z=1: 1+z+⋯+z999=1+z+\cdots+z^{999} =1+z+⋯+z999=

$A = \{6,7,8,9,10\}$ : which is correct?

$x^2+7x+12 > 0$ : solution set is

$a, b, c$ reals. Which is correct?

$x^2+2x-15 > 0$ : solution set is

The domain of $y = \frac{1}{x+9}$ is

The domain of $y = \sqrt{x-3}$ is

The domain of $f(x) = \frac{1}{x} + \sqrt{8-x}$ is

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

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

Given $a > b$ , which must hold?

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

Minimum of $y = \cos 7x + 3$ is

$\sin 150^\circ =$

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

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

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

Minimum of $y = \cos 4x + 4$ is

$\sin 120^\circ =$

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

Inverse of $y = 10x + 2$ is

$-4, a, 10$ arithmetic: $a =$

Arithmetic $a_1 = 6$ , $d = -1$ : then $a_{101} =$

Arithmetic with $a_7 = 8$ : $S_{13} =$

How many are arithmetic: $6,9,12,15$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

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

$\frac{1}{3}, -\frac{1}{9}, \frac{1}{27}, \ldots$ : $a_n =$

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

Intersection of $y = 3x-4$ and $-3x-y+2 = 0$ :

Slope $4$ through $(-2,-5)$ : equation is

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

Inclination $60^\circ$ : slope is

Slope through $A(-4,1)$ , $B(-9,2)$ :

$P(2,4)$ ; Q symmetric about the x-axis: Q =

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

Circle center $(-4,4)$ , radius 2: equation is

Through $A(-1,4)$ , center $(-1,0)$ : equation is

Directrix of $y^2 = 4x$ is

About parabola $y^2 = 12x$ , which is correct?

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

Foci of $\frac{x^2}{36} - \frac{y^2}{64} = 1$ are

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

$a = (1,3)$ , $b = (3,9)$ : a and b are

$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{999} =$