CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 18 · Q1

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

Target: ~75s · ID EXAM-G18-1

Q 2/48CSCA Standardsets · Mock 18 · Q2

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

Target: ~75s · ID EXAM-G18-2

Q 3/48CSCA Standardinequalities · Mock 18 · Q3

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$x^2-1x-12 > 0$ : solution set is

Target: ~75s · ID EXAM-G18-3

Q 4/48CSCA Standardinequalities · Mock 18 · Q4

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$x^2+8x+15 > 0$ : solution set is

Target: ~75s · ID EXAM-G18-4

Q 5/48CSCA Standardinequalities · Mock 18 · Q5

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$x^2-4x-5 > 0$ : solution set is

Target: ~75s · ID EXAM-G18-5

Q 6/48CSCA Standarddomain-range · Mock 18 · Q6

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The domain of $y = \frac{1}{x-2}$ is

Target: ~75s · ID EXAM-G18-6

Q 7/48CSCA Standarddomain-range · Mock 18 · Q7

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The domain of $y = \sqrt{x-7}$ is

Target: ~75s · ID EXAM-G18-7

Q 8/48CSCA Standarddomain-range · Mock 18 · Q8

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The domain of $f(x) = \frac{1}{x} + \sqrt{5-x}$ is

Target: ~75s · ID EXAM-G18-8

Q 9/48CSCA Standardmonotonicity · Mock 18 · Q9

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

Target: ~75s · ID EXAM-G18-9

Q 10/48CSCA Standardeven-odd-functions · Mock 18 · Q10

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Which is an odd function?

Target: ~75s · ID EXAM-G18-10

Q 11/48CSCA Standardpower-functions · Mock 18 · Q11

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The inverse function of $y = x^3+1$ $(x \in \mathbb{R})$ is

Target: ~75s · ID EXAM-G18-11

Q 12/48CSCA Standardexponential-functions · Mock 18 · Q12

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G18-12

Q 13/48CSCA Standardexponential-functions · Mock 18 · Q13

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

Target: ~75s · ID EXAM-G18-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 18 · Q14

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Which logarithm statement is incorrect?

Target: ~75s · ID EXAM-G18-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 18 · Q15

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G18-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 18 · Q16

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$\sin\alpha = \frac{3}{5}$ : $\cos 2\alpha =$

Target: ~75s · ID EXAM-G18-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 18 · Q17

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$\sin 120^\circ =$

Target: ~75s · ID EXAM-G18-17

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

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

Target: ~75s · ID EXAM-G18-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 18 · Q19

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

Target: ~75s · ID EXAM-G18-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 18 · Q20

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$\sin 150^\circ =$

Target: ~75s · ID EXAM-G18-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 18 · Q21

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$\cos\alpha = \frac{5}{13}$ , acute: $\tan\alpha =$

Target: ~75s · ID EXAM-G18-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 18 · Q22

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

Target: ~75s · ID EXAM-G18-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 18 · Q23

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

Target: ~75s · ID EXAM-G18-23

Q 24/48CSCA Standardinverse-functions · Mock 18 · Q24

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Inverse of $y = 10x + 7$ is

Target: ~75s · ID EXAM-G18-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 18 · Q25

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Arithmetic $a_1 = 3$ , $d = -4$ : then $a_{100} =$

Target: ~75s · ID EXAM-G18-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 18 · Q26

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Arithmetic $a_1 = 5$ , $d = 4$ : then $a_{100} =$

Target: ~75s · ID EXAM-G18-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 18 · Q27

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Arithmetic $a_1 = 4$ , $d = 4$ : then $a_{101} =$

Target: ~75s · ID EXAM-G18-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 18 · Q28

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Arithmetic $a_1 = 5$ , $d = -5$ : then $a_{101} =$

Target: ~75s · ID EXAM-G18-28

Q 29/48CSCA Standardgeometric-sequences · Mock 18 · Q29

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

Target: ~75s · ID EXAM-G18-29

Q 30/48CSCA Standardgeometric-sequences · Mock 18 · Q30

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

Target: ~75s · ID EXAM-G18-30

Q 31/48CSCA Standardgeometric-sequences · Mock 18 · Q31

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Geometric $a_1 = -24, a_4 = 3$ : $q =$

Target: ~75s · ID EXAM-G18-31

Q 32/48CSCA Standardlines · Mock 18 · Q32

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Slope through $A(-4,-2)$ , $B(-7,-5)$ :

Target: ~75s · ID EXAM-G18-32

Q 33/48CSCA Standardlines · Mock 18 · Q33

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Slope through $A(-4,-3)$ , $B(-7,-2)$ :

Target: ~75s · ID EXAM-G18-33

Q 34/48CSCA Standardlines · Mock 18 · Q34

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Slope through $A(1,-1)$ , $B(2,-5)$ :

Target: ~75s · ID EXAM-G18-34

Q 35/48CSCA Standardlines · Mock 18 · Q35

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Slope through $A(-4,-2)$ , $B(-3,-1)$ :

Target: ~75s · ID EXAM-G18-35

Q 36/48CSCA Standardlines · Mock 18 · Q36

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Slope through $A(5,0)$ , $B(4,-1)$ :

Target: ~75s · ID EXAM-G18-36

Q 37/48CSCA Standardanalytic-geometry · Mock 18 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G18-37

Q 38/48CSCA Standardanalytic-geometry · Mock 18 · Q38

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Distance $P(0,-2)$ to $Q(-3,-3)$ is

Target: ~75s · ID EXAM-G18-38

Q 39/48CSCA Standardanalytic-geometry · Mock 18 · Q39

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Distance $P(-2,-1)$ to $Q(-5,-6)$ is

Target: ~75s · ID EXAM-G18-39

Q 40/48CSCA Standardcircles · Mock 18 · Q40

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Circle center $(2,-1)$ , radius 5: equation is

Target: ~75s · ID EXAM-G18-40

Q 41/48CSCA Standardcircles · Mock 18 · Q41

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Through $A(-3,5)$ , center $(-3,0)$ : equation is

Target: ~75s · ID EXAM-G18-41

Q 42/48CSCA Standardparabolas · Mock 18 · Q42

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Directrix of $y^2 = 4x$ is

Target: ~75s · ID EXAM-G18-42

Q 43/48CSCA Standardparabolas · Mock 18 · Q43

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

Target: ~75s · ID EXAM-G18-43

Q 44/48CSCA Standardellipses · Mock 18 · Q44

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

Target: ~75s · ID EXAM-G18-44

Q 45/48CSCA Standardhyperbolas · Mock 18 · Q45

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

Target: ~75s · ID EXAM-G18-45

Q 46/48CSCA Standardprobability · Mock 18 · Q46

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

Target: ~75s · ID EXAM-G18-46

Q 47/48CSCA Standardvectors · Mock 18 · Q47

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$a = (5,3)$ , $b = (-10,-6)$ : a and b are

Target: ~75s · ID EXAM-G18-47

Q 48/48CSCA Standardcomplex-numbers · Mock 18 · Q48

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

Target: ~75s · ID EXAM-G18-48

Mock 18 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:

x2−1x−12>0x^2-1x-12 > 0x2−1x−12>0: solution set is

x2+8x+15>0x^2+8x+15 > 0x2+8x+15>0: solution set is

x2−4x−5>0x^2-4x-5 > 0x2−4x−5>0: solution set is

The domain of y=1x−2y = \frac{1}{x-2}y=x−21​ is

The domain of y=x−7y = \sqrt{x-7}y=x−7​ is

The domain of f(x)=1x+5−xf(x) = \frac{1}{x} + \sqrt{5-x}f(x)=x1​+5−x​ is

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

Which is an odd function?

The inverse function of y=x3+1y = x^3+1y=x3+1 (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⁡135∘=\sin 135^\circ =sin135∘=

sin⁡α=35\sin\alpha = \frac{3}{5}sinα=53​: cos⁡2α=\cos 2\alpha =cos2α=

sin⁡120∘=\sin 120^\circ =sin120∘=

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=

sin⁡150∘=\sin 150^\circ =sin150∘=

cos⁡α=513\cos\alpha = \frac{5}{13}cosα=135​, acute: tan⁡α=\tan\alpha =tanα=

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

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

Inverse of y=10x+7y = 10x + 7y=10x+7 is

Arithmetic a1=3a_1 = 3a1​=3, d=−4d = -4d=−4: then a100=a_{100} =a100​=

Arithmetic a1=5a_1 = 5a1​=5, d=4d = 4d=4: then a100=a_{100} =a100​=

Arithmetic a1=4a_1 = 4a1​=4, d=4d = 4d=4: then a101=a_{101} =a101​=

Arithmetic a1=5a_1 = 5a1​=5, d=−5d = -5d=−5: then a101=a_{101} =a101​=

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

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

Geometric a1=−24,a4=3a_1 = -24, a_4 = 3a1​=−24,a4​=3: q=q =q=

Slope through A(−4,−2)A(-4,-2)A(−4,−2) , B(−7,−5)B(-7,-5)B(−7,−5):

Slope through A(−4,−3)A(-4,-3)A(−4,−3) , B(−7,−2)B(-7,-2)B(−7,−2):

Slope through A(1,−1)A(1,-1)A(1,−1) , B(2,−5)B(2,-5)B(2,−5):

Slope through A(−4,−2)A(-4,-2)A(−4,−2) , B(−3,−1)B(-3,-1)B(−3,−1):

Slope through A(5,0)A(5,0)A(5,0) , B(4,−1)B(4,-1)B(4,−1):

Which point is in the third quadrant?

Distance P(0,−2)P(0,-2)P(0,−2) to Q(−3,−3)Q(-3,-3)Q(−3,−3) is

Distance P(−2,−1)P(-2,-1)P(−2,−1) to Q(−5,−6)Q(-5,-6)Q(−5,−6) is

Circle center (2,−1)(2,-1)(2,−1), radius 5: equation is

Through A(−3,5)A(-3,5)A(−3,5), center (−3,0)(-3,0)(−3,0): equation is

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

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

About ellipse x225+y29=1\frac{x^2}{25}+\frac{y^2}{9} = 125x2​+9y2​=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=(5,3)a = (5,3)a=(5,3), b=(−10,−6)b = (-10,-6)b=(−10,−6): 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=

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

$x^2-1x-12 > 0$ : solution set is

$x^2+8x+15 > 0$ : solution set is

$x^2-4x-5 > 0$ : solution set is

The domain of $y = \frac{1}{x-2}$ is

The domain of $y = \sqrt{x-7}$ is

The domain of $f(x) = \frac{1}{x} + \sqrt{5-x}$ is

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

The inverse function of $y = x^3+1$ $(x \in \mathbb{R})$ is

Given $a > b$ , which must hold?

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

$\sin 135^\circ =$

$\sin\alpha = \frac{3}{5}$ : $\cos 2\alpha =$

$\sin 120^\circ =$

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

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

$\sin 150^\circ =$

$\cos\alpha = \frac{5}{13}$ , acute: $\tan\alpha =$

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

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

Inverse of $y = 10x + 7$ is

Arithmetic $a_1 = 3$ , $d = -4$ : then $a_{100} =$

Arithmetic $a_1 = 5$ , $d = 4$ : then $a_{100} =$

Arithmetic $a_1 = 4$ , $d = 4$ : then $a_{101} =$

Arithmetic $a_1 = 5$ , $d = -5$ : then $a_{101} =$

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

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

Geometric $a_1 = -24, a_4 = 3$ : $q =$

Slope through $A(-4,-2)$ , $B(-7,-5)$ :

Slope through $A(-4,-3)$ , $B(-7,-2)$ :

Slope through $A(1,-1)$ , $B(2,-5)$ :

Slope through $A(-4,-2)$ , $B(-3,-1)$ :

Slope through $A(5,0)$ , $B(4,-1)$ :

Distance $P(0,-2)$ to $Q(-3,-3)$ is

Distance $P(-2,-1)$ to $Q(-5,-6)$ is

Circle center $(2,-1)$ , radius 5: equation is

Through $A(-3,5)$ , center $(-3,0)$ : equation is

Directrix of $y^2 = 4x$ is

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

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

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

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

$a = (5,3)$ , $b = (-10,-6)$ : a and b are

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