CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 19 · Q1

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

Target: ~75s · ID EXAM-G19-1

Q 2/48CSCA Standardsets · Mock 19 · Q2

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$A = \{x|-5<x<-2\}$ , $B = \{x|x>-3\}$ : $A \cap B =$

Target: ~75s · ID EXAM-G19-2

Q 3/48CSCA Standardinequalities · Mock 19 · Q3

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

Target: ~75s · ID EXAM-G19-3

Q 4/48CSCA Standardinequalities · Mock 19 · Q4

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$x^2+6x+5 \ge 0$ : solution set is

Target: ~75s · ID EXAM-G19-4

Q 5/48CSCA Standardinequalities · Mock 19 · Q5

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

Target: ~75s · ID EXAM-G19-5

Q 6/48CSCA Standarddomain-range · Mock 19 · Q6

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

Target: ~75s · ID EXAM-G19-6

Q 7/48CSCA Standarddomain-range · Mock 19 · Q7

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

Target: ~75s · ID EXAM-G19-7

Q 8/48CSCA Standarddomain-range · Mock 19 · Q8

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

Target: ~75s · ID EXAM-G19-8

Q 9/48CSCA Standardmonotonicity · Mock 19 · Q9

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

Target: ~75s · ID EXAM-G19-9

Q 10/48CSCA Standardeven-odd-functions · Mock 19 · Q10

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

Target: ~75s · ID EXAM-G19-10

Q 11/48CSCA Standardpower-functions · Mock 19 · Q11

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The inverse function of $y = x^3+4$ $(x \in \mathbb{R})$ is

Target: ~75s · ID EXAM-G19-11

Q 12/48CSCA Standardexponential-functions · Mock 19 · Q12

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

Target: ~75s · ID EXAM-G19-12

Q 13/48CSCA Standardexponential-functions · Mock 19 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G19-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 19 · Q14

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

Target: ~75s · ID EXAM-G19-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 19 · Q15

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

Target: ~75s · ID EXAM-G19-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 19 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G19-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 19 · Q17

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Minimum of $y = \cos 8x + 3$ is

Target: ~75s · ID EXAM-G19-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 19 · Q18

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$\sin\alpha = -\frac{5}{13}$ , QIII: $\cos(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-G19-18

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

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

Target: ~75s · ID EXAM-G19-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 19 · Q20

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

Target: ~75s · ID EXAM-G19-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 19 · Q21

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$\sin 120^\circ =$

Target: ~75s · ID EXAM-G19-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 19 · Q22

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

Target: ~75s · ID EXAM-G19-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 19 · Q23

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

Target: ~75s · ID EXAM-G19-23

Q 24/48CSCA Standardinverse-functions · Mock 19 · Q24

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Inverse of $y = 9x - 6$ is

Target: ~75s · ID EXAM-G19-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 19 · Q25

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Arithmetic with $a_7 = 7$ : $S_{13} =$

Target: ~75s · ID EXAM-G19-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 19 · Q26

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Arithmetic $a_1 = 6$ , $d = -1$ : then $a_{50} =$

Target: ~75s · ID EXAM-G19-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 19 · Q27

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$2, a, 20$ arithmetic: $a =$

Target: ~75s · ID EXAM-G19-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 19 · Q28

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Arithmetic $a_1 = -9, a_2 = -14$ : $a_5 =$

Target: ~75s · ID EXAM-G19-28

Q 29/48CSCA Standardgeometric-sequences · Mock 19 · Q29

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

Target: ~75s · ID EXAM-G19-29

Q 30/48CSCA Standardgeometric-sequences · Mock 19 · Q30

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Geometric $a_1 = 48, a_4 = 6$ : $q =$

Target: ~75s · ID EXAM-G19-30

Q 31/48CSCA Standardgeometric-sequences · Mock 19 · Q31

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$\frac{1}{5}, -\frac{1}{25}, \frac{1}{125}, \ldots$ : $a_n =$

Target: ~75s · ID EXAM-G19-31

Q 32/48CSCA Standardlines · Mock 19 · Q32

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Inclination $60^\circ$ : slope is

Target: ~75s · ID EXAM-G19-32

Q 33/48CSCA Standardlines · Mock 19 · Q33

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Which line is perpendicular to $x+6 = 0$ ?

Target: ~75s · ID EXAM-G19-33

Q 34/48CSCA Standardlines · Mock 19 · Q34

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Slope $-4$ through $(0,-4)$ : equation is

Target: ~75s · ID EXAM-G19-34

Q 35/48CSCA Standardlines · Mock 19 · Q35

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Intersection of $y = x-1$ and $2x-y+3 = 0$ :

Target: ~75s · ID EXAM-G19-35

Q 36/48CSCA Standardlines · Mock 19 · Q36

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Slope through $A(2,-2)$ , $B(1,0)$ :

Target: ~75s · ID EXAM-G19-36

Q 37/48CSCA Standardanalytic-geometry · Mock 19 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G19-37

Q 38/48CSCA Standardanalytic-geometry · Mock 19 · Q38

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Distance $P(-4,-1)$ to $Q(0,-5)$ is

Target: ~75s · ID EXAM-G19-38

Q 39/48CSCA Standardanalytic-geometry · Mock 19 · Q39

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$P(-1,-2)$ ; Q symmetric about the x-axis: Q =

Target: ~75s · ID EXAM-G19-39

Q 40/48CSCA Standardcircles · Mock 19 · Q40

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

Target: ~75s · ID EXAM-G19-40

Q 41/48CSCA Standardcircles · Mock 19 · Q41

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Circle center $(-1,-4)$ , radius 6: equation is

Target: ~75s · ID EXAM-G19-41

Q 42/48CSCA Standardparabolas · Mock 19 · Q42

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

Target: ~75s · ID EXAM-G19-42

Q 43/48CSCA Standardparabolas · Mock 19 · Q43

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

Target: ~75s · ID EXAM-G19-43

Q 44/48CSCA Standardellipses · Mock 19 · Q44

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Ellipse $\frac{x^2}{12}+\frac{y^2}{16} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-G19-44

Q 45/48CSCA Standardhyperbolas · Mock 19 · Q45

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

Target: ~75s · ID EXAM-G19-45

Q 46/48CSCA Standardprobability · Mock 19 · Q46

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Bag: 3 red, 5 blue. One draw. $P(\text{red}) =$

Target: ~75s · ID EXAM-G19-46

Q 47/48CSCA Standardvectors · Mock 19 · Q47

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$a = (3,1)$ , $b = (6,2)$ : a and b are

Target: ~75s · ID EXAM-G19-47

Q 48/48CSCA Standardcomplex-numbers · Mock 19 · Q48

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$(z-3i)(3-i) = 10$ : $z =$

Target: ~75s · ID EXAM-G19-48

Mock 19 paper

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

A={x∣−5<x<−2}A = \{x|-5<x<-2\}A={x∣−5<x<−2}, B={x∣x>−3}B = \{x|x>-3\}B={x∣x>−3}: A∩B=A \cap B =A∩B=

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

x2+6x+5≥0x^2+6x+5 \ge 0x2+6x+5≥0: solution set is

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

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

The domain of y=x−1y = \sqrt{x-1}y=x−1​ is

The domain of y=x−7y = \sqrt{x-7}y=x−7​ 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+4y = x^3+4y=x3+4 (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=−725\cos\alpha = -\frac{7}{25}cosα=−257​, QII: sin⁡(α2)=\sin(\frac{\alpha}{2}) =sin(2α​)=

Which reduction equation is incorrect?

Minimum of y=cos⁡8x+3y = \cos 8x + 3y=cos8x+3 is

sin⁡α=−513\sin\alpha = -\frac{5}{13}sinα=−135​, QIII: cos⁡(α2)=\cos(\frac{\alpha}{2}) =cos(2α​)=

cos⁡α=−35\cos\alpha = -\frac{3}{5}cosα=−53​, 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⁡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=

Inverse of y=9x−6y = 9x - 6y=9x−6 is

Arithmetic with a7=7a_7 = 7a7​=7: S13=S_{13} =S13​=

Arithmetic a1=6a_1 = 6a1​=6, d=−1d = -1d=−1: then a50=a_{50} =a50​=

2,a,202, a, 202,a,20 arithmetic: a=a =a=

Arithmetic a1=−9,a2=−14a_1 = -9, a_2 = -14a1​=−9,a2​=−14: a5=a_5 =a5​=

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

Geometric a1=48,a4=6a_1 = 48, a_4 = 6a1​=48,a4​=6: q=q =q=

15,−125,1125,…\frac{1}{5}, -\frac{1}{25}, \frac{1}{125}, \ldots51​,−251​,1251​,…: an=a_n =an​=

Inclination 60∘60^\circ60∘: slope is

Which line is perpendicular to x+6=0x+6 = 0x+6=0 ?

Slope −4-4−4 through (0,−4)(0,-4)(0,−4): equation is

Intersection of y=x−1y = x-1y=x−1 and 2x−y+3=02x-y+3 = 02x−y+3=0:

Slope through A(2,−2)A(2,-2)A(2,−2) , B(1,0)B(1,0)B(1,0):

Which point is in the third quadrant?

Distance P(−4,−1)P(-4,-1)P(−4,−1) to Q(0,−5)Q(0,-5)Q(0,−5) is

P(−1,−2)P(-1,-2)P(−1,−2); Q symmetric about the x-axis: Q =

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

Circle center (−1,−4)(-1,-4)(−1,−4), radius 6: equation is

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

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

Ellipse x212+y216=1\frac{x^2}{12}+\frac{y^2}{16} = 112x2​+16y2​=1: ∣PF1∣+∣PF2∣=|PF_1|+|PF_2| =∣PF1​∣+∣PF2​∣=

Foci of x264−y236=1\frac{x^2}{64} - \frac{y^2}{36} = 164x2​−36y2​=1 are

Bag: 3 red, 5 blue. One draw. P(red)=P(\text{red}) =P(red)=

a=(3,1)a = (3,1)a=(3,1), b=(6,2)b = (6,2)b=(6,2): a and b are

(z−3i)(3−i)=10(z-3i)(3-i) = 10(z−3i)(3−i)=10: z=z =z=

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

$A = \{x|-5<x<-2\}$ , $B = \{x|x>-3\}$ : $A \cap B =$

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

$x^2+6x+5 \ge 0$ : solution set is

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

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

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

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

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

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

The inverse function of $y = x^3+4$ $(x \in \mathbb{R})$ 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?

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

Minimum of $y = \cos 8x + 3$ is

$\sin\alpha = -\frac{5}{13}$ , QIII: $\cos(\frac{\alpha}{2}) =$

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

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

$\sin 120^\circ =$

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

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

Inverse of $y = 9x - 6$ is

Arithmetic with $a_7 = 7$ : $S_{13} =$

Arithmetic $a_1 = 6$ , $d = -1$ : then $a_{50} =$

$2, a, 20$ arithmetic: $a =$

Arithmetic $a_1 = -9, a_2 = -14$ : $a_5 =$

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

Geometric $a_1 = 48, a_4 = 6$ : $q =$

$\frac{1}{5}, -\frac{1}{25}, \frac{1}{125}, \ldots$ : $a_n =$

Inclination $60^\circ$ : slope is

Which line is perpendicular to $x+6 = 0$ ?

Slope $-4$ through $(0,-4)$ : equation is

Intersection of $y = x-1$ and $2x-y+3 = 0$ :

Slope through $A(2,-2)$ , $B(1,0)$ :

Distance $P(-4,-1)$ to $Q(0,-5)$ is

$P(-1,-2)$ ; Q symmetric about the x-axis: Q =

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

Circle center $(-1,-4)$ , radius 6: equation is

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

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

Ellipse $\frac{x^2}{12}+\frac{y^2}{16} = 1$ : $|PF_1|+|PF_2| =$

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

Bag: 3 red, 5 blue. One draw. $P(\text{red}) =$

$a = (3,1)$ , $b = (6,2)$ : a and b are

$(z-3i)(3-i) = 10$ : $z =$