CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 09 · Q1

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$A = \{9,10,11,12,13\}$ : which is correct?

Target: ~75s · ID EXAM-G9-1

Q 2/48CSCA Standardsets · Mock 09 · Q2

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

Target: ~75s · ID EXAM-G9-2

Q 3/48CSCA Standardinequalities · Mock 09 · Q3

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

Target: ~75s · ID EXAM-G9-3

Q 4/48CSCA Standardinequalities · Mock 09 · Q4

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$\frac{2x+6}{x-1} \le 0$ : solution set is

Target: ~75s · ID EXAM-G9-4

Q 5/48CSCA Standardinequalities · Mock 09 · Q5

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$x^2-1x-2 > 0$ : solution set is

Target: ~75s · ID EXAM-G9-5

Q 6/48CSCA Standarddomain-range · Mock 09 · Q6

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The domain of $y = \frac{1}{x+8}$ is

Target: ~75s · ID EXAM-G9-6

Q 7/48CSCA Standarddomain-range · Mock 09 · Q7

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The domain of $y = \sqrt{x-6}$ is

Target: ~75s · ID EXAM-G9-7

Q 8/48CSCA Standarddomain-range · Mock 09 · Q8

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The domain of $f(x) = \frac{1}{x} + \sqrt{9-x}$ is

Target: ~75s · ID EXAM-G9-8

Q 9/48CSCA Standardmonotonicity · Mock 09 · Q9

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

Target: ~75s · ID EXAM-G9-9

Q 10/48CSCA Standardeven-odd-functions · Mock 09 · Q10

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About $f(x) = x^4 + 2$ , which is correct?

Target: ~75s · ID EXAM-G9-10

Q 11/48CSCA Standardpower-functions · Mock 09 · Q11

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

Target: ~75s · ID EXAM-G9-11

Q 12/48CSCA Standardexponential-functions · Mock 09 · Q12

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

Target: ~75s · ID EXAM-G9-12

Q 13/48CSCA Standardexponential-functions · Mock 09 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G9-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 09 · Q14

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About $y = \log_a x$ , which is correct?

Target: ~75s · ID EXAM-G9-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 09 · Q15

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$\cos\alpha = -\frac{1}{2}$ , QII: $\sin(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-G9-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 09 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G9-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 09 · Q17

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Minimum of $y = \cos 2x + 4$ is

Target: ~75s · ID EXAM-G9-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 09 · Q18

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

Target: ~75s · ID EXAM-G9-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 09 · Q19

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$\cos\alpha = -\frac{15}{17}$ , QII: $\cos(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-G9-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 09 · Q20

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$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{4}$ : $\tan\alpha =$

Target: ~75s · ID EXAM-G9-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 09 · Q21

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G9-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 09 · Q22

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$\sin\alpha = \frac{1}{4}$ : $\cos 2\alpha =$

Target: ~75s · ID EXAM-G9-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 09 · Q23

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$\sin\alpha = \frac{8}{17}$ , second quadrant: $\cos\alpha =$

Target: ~75s · ID EXAM-G9-23

Q 24/48CSCA Standardinverse-functions · Mock 09 · Q24

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Inverse of $y = 9x - 1$ is

Target: ~75s · ID EXAM-G9-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 09 · Q25

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Arithmetic with $a_7 = 3$ : $S_{13} =$

Target: ~75s · ID EXAM-G9-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 09 · Q26

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Arithmetic $a_1 = 7$ , $d = 1$ : then $a_{100} =$

Target: ~75s · ID EXAM-G9-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 09 · Q27

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$13, a, 17$ arithmetic: $a =$

Target: ~75s · ID EXAM-G9-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 09 · Q28

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Arithmetic $a_1 = -1, a_2 = 1$ : $a_5 =$

Target: ~75s · ID EXAM-G9-28

Q 29/48CSCA Standardgeometric-sequences · Mock 09 · Q29

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Geometric $1,5,25$ : general term is

Target: ~75s · ID EXAM-G9-29

Q 30/48CSCA Standardgeometric-sequences · Mock 09 · Q30

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Geometric $a_1 = 1$ , $q = 2$ : $S_5 =$

Target: ~75s · ID EXAM-G9-30

Q 31/48CSCA Standardgeometric-sequences · Mock 09 · Q31

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$\frac{1}{2}, -\frac{1}{4}, \frac{1}{8}, \ldots$ : $a_n =$

Target: ~75s · ID EXAM-G9-31

Q 32/48CSCA Standardlines · Mock 09 · Q32

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Inclination $30^\circ$ : slope is

Target: ~75s · ID EXAM-G9-32

Q 33/48CSCA Standardlines · Mock 09 · Q33

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Which line is perpendicular to $x+5 = 0$ ?

Target: ~75s · ID EXAM-G9-33

Q 34/48CSCA Standardlines · Mock 09 · Q34

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Slope $5$ through $(-1,-3)$ : equation is

Target: ~75s · ID EXAM-G9-34

Q 35/48CSCA Standardlines · Mock 09 · Q35

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

Target: ~75s · ID EXAM-G9-35

Q 36/48CSCA Standardlines · Mock 09 · Q36

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Slope through $A(1,3)$ , $B(5,-1)$ :

Target: ~75s · ID EXAM-G9-36

Q 37/48CSCA Standardanalytic-geometry · Mock 09 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G9-37

Q 38/48CSCA Standardanalytic-geometry · Mock 09 · Q38

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$|AB| = 10$ , $A(0,4)$ , $B(x,12)$ : $x =$

Target: ~75s · ID EXAM-G9-38

Q 39/48CSCA Standardanalytic-geometry · Mock 09 · Q39

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$P(-1,5)$ ; Q symmetric about the x-axis: Q =

Target: ~75s · ID EXAM-G9-39

Q 40/48CSCA Standardcircles · Mock 09 · Q40

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Circle center $(5,-2)$ , radius 3: equation is

Target: ~75s · ID EXAM-G9-40

Q 41/48CSCA Standardcircles · Mock 09 · Q41

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

Target: ~75s · ID EXAM-G9-41

Q 42/48CSCA Standardparabolas · Mock 09 · Q42

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Directrix of $y^2 = 8x$ is

Target: ~75s · ID EXAM-G9-42

Q 43/48CSCA Standardparabolas · Mock 09 · Q43

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About parabola $y^2 = 4x$ , which is correct?

Target: ~75s · ID EXAM-G9-43

Q 44/48CSCA Standardellipses · Mock 09 · Q44

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Ellipse $\frac{x^2}{21}+\frac{y^2}{25} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-G9-44

Q 45/48CSCA Standardhyperbolas · Mock 09 · Q45

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

Target: ~75s · ID EXAM-G9-45

Q 46/48CSCA Standardprobability · Mock 09 · Q46

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Bag: 6 red, 3 blue. One draw. $P(\text{red}) =$

Target: ~75s · ID EXAM-G9-46

Q 47/48CSCA Standardvectors · Mock 09 · Q47

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$a = (1,6)$ , $b = (3,18)$ : a and b are

Target: ~75s · ID EXAM-G9-47

Q 48/48CSCA Standardcomplex-numbers · Mock 09 · Q48

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$(z-5i)(1-i) = 2$ : $z =$

Target: ~75s · ID EXAM-G9-48

Mock 09 paper

A={9,10,11,12,13}A = \{9,10,11,12,13\}A={9,10,11,12,13}: which is correct?

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

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

2x+6x−1≤0\frac{2x+6}{x-1} \le 0x−12x+6​≤0: solution set is

x2−1x−2>0x^2-1x-2 > 0x2−1x−2>0: solution set is

The domain of y=1x+8y = \frac{1}{x+8}y=x+81​ is

The domain of y=x−6y = \sqrt{x-6}y=x−6​ is

The domain of f(x)=1x+9−xf(x) = \frac{1}{x} + \sqrt{9-x}f(x)=x1​+9−x​ is

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

About f(x)=x4+2f(x) = x^4 + 2f(x)=x4+2 , which is correct?

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

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

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

About y=log⁡axy = \log_a xy=loga​x , which is correct?

cos⁡α=−12\cos\alpha = -\frac{1}{2}cosα=−21​, QII: sin⁡(α2)=\sin(\frac{\alpha}{2}) =sin(2α​)=

Which reduction equation is incorrect?

Minimum of y=cos⁡2x+4y = \cos 2x + 4y=cos2x+4 is

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

cos⁡α=−1517\cos\alpha = -\frac{15}{17}cosα=−1715​, QII: cos⁡(α2)=\cos(\frac{\alpha}{2}) =cos(2α​)=

cos⁡α−sin⁡αcos⁡α+sin⁡α=14\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{4}cosα+sinαcosα−sinα​=41​: tan⁡α=\tan\alpha =tanα=

sin⁡135∘=\sin 135^\circ =sin135∘=

sin⁡α=14\sin\alpha = \frac{1}{4}sinα=41​: cos⁡2α=\cos 2\alpha =cos2α=

sin⁡α=817\sin\alpha = \frac{8}{17}sinα=178​, second quadrant: cos⁡α=\cos\alpha =cosα=

Inverse of y=9x−1y = 9x - 1y=9x−1 is

Arithmetic with a7=3a_7 = 3a7​=3: S13=S_{13} =S13​=

Arithmetic a1=7a_1 = 7a1​=7, d=1d = 1d=1: then a100=a_{100} =a100​=

13,a,1713, a, 1713,a,17 arithmetic: a=a =a=

Arithmetic a1=−1,a2=1a_1 = -1, a_2 = 1a1​=−1,a2​=1: a5=a_5 =a5​=

Geometric 1,5,251,5,251,5,25: general term is

Geometric a1=1a_1 = 1a1​=1, q=2q = 2q=2: S5=S_5 =S5​=

12,−14,18,…\frac{1}{2}, -\frac{1}{4}, \frac{1}{8}, \ldots21​,−41​,81​,…: an=a_n =an​=

Inclination 30∘30^\circ30∘: slope is

Which line is perpendicular to x+5=0x+5 = 0x+5=0 ?

Slope 555 through (−1,−3)(-1,-3)(−1,−3): equation is

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

Slope through A(1,3)A(1,3)A(1,3) , B(5,−1)B(5,-1)B(5,−1):

Which point is in the third quadrant?

∣AB∣=10|AB| = 10∣AB∣=10, A(0,4)A(0,4)A(0,4), B(x,12)B(x,12)B(x,12): x=x =x=

P(−1,5)P(-1,5)P(−1,5); Q symmetric about the x-axis: Q =

Circle center (5,−2)(5,-2)(5,−2), radius 3: equation is

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

Directrix of y2=8xy^2 = 8xy2=8x is

About parabola y2=4xy^2 = 4xy2=4x, which is correct?

Ellipse x221+y225=1\frac{x^2}{21}+\frac{y^2}{25} = 121x2​+25y2​=1: ∣PF1∣+∣PF2∣=|PF_1|+|PF_2| =∣PF1​∣+∣PF2​∣=

Foci of x216−y29=1\frac{x^2}{16} - \frac{y^2}{9} = 116x2​−9y2​=1 are

Bag: 6 red, 3 blue. One draw. P(red)=P(\text{red}) =P(red)=

a=(1,6)a = (1,6)a=(1,6), b=(3,18)b = (3,18)b=(3,18): a and b are

(z−5i)(1−i)=2(z-5i)(1-i) = 2(z−5i)(1−i)=2: z=z =z=

$A = \{9,10,11,12,13\}$ : which is correct?

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

$\frac{2x+6}{x-1} \le 0$ : solution set is

$x^2-1x-2 > 0$ : solution set is

The domain of $y = \frac{1}{x+8}$ is

The domain of $y = \sqrt{x-6}$ is

The domain of $f(x) = \frac{1}{x} + \sqrt{9-x}$ is

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

About $f(x) = x^4 + 2$ , which is correct?

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

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

Given $a > b$ , which must hold?

About $y = \log_a x$ , which is correct?

$\cos\alpha = -\frac{1}{2}$ , QII: $\sin(\frac{\alpha}{2}) =$

Minimum of $y = \cos 2x + 4$ is

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

$\cos\alpha = -\frac{15}{17}$ , QII: $\cos(\frac{\alpha}{2}) =$

$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{4}$ : $\tan\alpha =$

$\sin 135^\circ =$

$\sin\alpha = \frac{1}{4}$ : $\cos 2\alpha =$

$\sin\alpha = \frac{8}{17}$ , second quadrant: $\cos\alpha =$

Inverse of $y = 9x - 1$ is

Arithmetic with $a_7 = 3$ : $S_{13} =$

Arithmetic $a_1 = 7$ , $d = 1$ : then $a_{100} =$

$13, a, 17$ arithmetic: $a =$

Arithmetic $a_1 = -1, a_2 = 1$ : $a_5 =$

Geometric $1,5,25$ : general term is

Geometric $a_1 = 1$ , $q = 2$ : $S_5 =$

$\frac{1}{2}, -\frac{1}{4}, \frac{1}{8}, \ldots$ : $a_n =$

Inclination $30^\circ$ : slope is

Which line is perpendicular to $x+5 = 0$ ?

Slope $5$ through $(-1,-3)$ : equation is

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

Slope through $A(1,3)$ , $B(5,-1)$ :

$|AB| = 10$ , $A(0,4)$ , $B(x,12)$ : $x =$

$P(-1,5)$ ; Q symmetric about the x-axis: Q =

Circle center $(5,-2)$ , radius 3: equation is

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

Directrix of $y^2 = 8x$ is

About parabola $y^2 = 4x$ , which is correct?

Ellipse $\frac{x^2}{21}+\frac{y^2}{25} = 1$ : $|PF_1|+|PF_2| =$

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

Bag: 6 red, 3 blue. One draw. $P(\text{red}) =$

$a = (1,6)$ , $b = (3,18)$ : a and b are

$(z-5i)(1-i) = 2$ : $z =$