CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 01 · Q1

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

Target: ~75s · ID EXAM-G1-1

Q 2/48CSCA Standardsets · Mock 01 · Q2

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$A = \{x|-3<x<0\}$ , $B = \{x|x>-1\}$ : $A \cap B =$

Target: ~75s · ID EXAM-G1-2

Q 3/48CSCA Standardinequalities · Mock 01 · Q3

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

Target: ~75s · ID EXAM-G1-3

Q 4/48CSCA Standardinequalities · Mock 01 · Q4

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$\frac{2x-6}{x-5} \le 0$ : solution set is

Target: ~75s · ID EXAM-G1-4

Q 5/48CSCA Standardinequalities · Mock 01 · Q5

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

Target: ~75s · ID EXAM-G1-5

Q 6/48CSCA Standarddomain-range · Mock 01 · Q6

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

Target: ~75s · ID EXAM-G1-6

Q 7/48CSCA Standarddomain-range · Mock 01 · Q7

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

Target: ~75s · ID EXAM-G1-7

Q 8/48CSCA Standarddomain-range · Mock 01 · Q8

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The domain of $y = \sqrt{x-5}$ is

Target: ~75s · ID EXAM-G1-8

Q 9/48CSCA Standardmonotonicity · Mock 01 · Q9

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

Target: ~75s · ID EXAM-G1-9

Q 10/48CSCA Standardeven-odd-functions · Mock 01 · Q10

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

Target: ~75s · ID EXAM-G1-10

Q 11/48CSCA Standardpower-functions · Mock 01 · Q11

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

Target: ~75s · ID EXAM-G1-11

Q 12/48CSCA Standardexponential-functions · Mock 01 · Q12

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

Target: ~75s · ID EXAM-G1-12

Q 13/48CSCA Standardexponential-functions · Mock 01 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G1-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 01 · Q14

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

Target: ~75s · ID EXAM-G1-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 01 · Q15

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

Target: ~75s · ID EXAM-G1-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 01 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G1-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 01 · Q17

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

Target: ~75s · ID EXAM-G1-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 01 · Q18

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

Target: ~75s · ID EXAM-G1-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 01 · Q19

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

Target: ~75s · ID EXAM-G1-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 01 · Q20

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

Target: ~75s · ID EXAM-G1-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 01 · Q21

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$\sin 150^\circ =$

Target: ~75s · ID EXAM-G1-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 01 · Q22

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$\cos\alpha = \frac{3}{5}$ , acute: $\tan\alpha =$

Target: ~75s · ID EXAM-G1-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 01 · Q23

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

Target: ~75s · ID EXAM-G1-23

Q 24/48CSCA Standardinverse-functions · Mock 01 · Q24

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Inverse of $y = 4x - 9$ is

Target: ~75s · ID EXAM-G1-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 01 · Q25

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Arithmetic $a_1 = 6, a_2 = 2$ : $a_5 =$

Target: ~75s · ID EXAM-G1-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 01 · Q26

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Arithmetic $a_1 = 4$ , $d = -2$ : then $a_{50} =$

Target: ~75s · ID EXAM-G1-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 01 · Q27

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How many are arithmetic: $2,5,8,11$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

Target: ~75s · ID EXAM-G1-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 01 · Q28

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$-6, a, 12$ arithmetic: $a =$

Target: ~75s · ID EXAM-G1-28

Q 29/48CSCA Standardgeometric-sequences · Mock 01 · Q29

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

Target: ~75s · ID EXAM-G1-29

Q 30/48CSCA Standardgeometric-sequences · Mock 01 · Q30

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Geometric $a_1 = 1$ , $q = 2$ : $S_6 =$

Target: ~75s · ID EXAM-G1-30

Q 31/48CSCA Standardgeometric-sequences · Mock 01 · Q31

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

Target: ~75s · ID EXAM-G1-31

Q 32/48CSCA Standardlines · Mock 01 · Q32

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Slope $-2$ through $(0,-1)$ : equation is

Target: ~75s · ID EXAM-G1-32

Q 33/48CSCA Standardlines · Mock 01 · Q33

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Inclination $30^\circ$ : slope is

Target: ~75s · ID EXAM-G1-33

Q 34/48CSCA Standardlines · Mock 01 · Q34

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Intersection of $y = 2x-2$ and $3x-y-5 = 0$ :

Target: ~75s · ID EXAM-G1-34

Q 35/48CSCA Standardlines · Mock 01 · Q35

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Which line is perpendicular to $3x-4 = 0$ ?

Target: ~75s · ID EXAM-G1-35

Q 36/48CSCA Standardlines · Mock 01 · Q36

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Slope through $A(4,-4)$ , $B(1,-6)$ :

Target: ~75s · ID EXAM-G1-36

Q 37/48CSCA Standardanalytic-geometry · Mock 01 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G1-37

Q 38/48CSCA Standardanalytic-geometry · Mock 01 · Q38

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$|AB| = 5$ , $A(1,-4)$ , $B(x,0)$ : $x =$

Target: ~75s · ID EXAM-G1-38

Q 39/48CSCA Standardanalytic-geometry · Mock 01 · Q39

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$P(-3,-2)$ ; Q symmetric about the y-axis: Q =

Target: ~75s · ID EXAM-G1-39

Q 40/48CSCA Standardcircles · Mock 01 · Q40

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Circle center $(3,-2)$ , radius 4: equation is

Target: ~75s · ID EXAM-G1-40

Q 41/48CSCA Standardcircles · Mock 01 · Q41

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

Target: ~75s · ID EXAM-G1-41

Q 42/48CSCA Standardparabolas · Mock 01 · Q42

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About parabola $y^2 = 32x$ , which is correct?

Target: ~75s · ID EXAM-G1-42

Q 43/48CSCA Standardparabolas · Mock 01 · Q43

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

Target: ~75s · ID EXAM-G1-43

Q 44/48CSCA Standardellipses · Mock 01 · Q44

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Ellipse $\frac{x^2}{77}+\frac{y^2}{81} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-G1-44

Q 45/48CSCA Standardhyperbolas · Mock 01 · Q45

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

Target: ~75s · ID EXAM-G1-45

Q 46/48CSCA Standardprobability · Mock 01 · Q46

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Bag: 3 red, 2 blue. One draw. $P(\text{red}) =$

Target: ~75s · ID EXAM-G1-46

Q 47/48CSCA Standardvectors · Mock 01 · Q47

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$a = (4,2)$ , $b = (12,6)$ : a and b are

Target: ~75s · ID EXAM-G1-47

Q 48/48CSCA Standardcomplex-numbers · Mock 01 · Q48

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

Target: ~75s · ID EXAM-G1-48

Mock 01 paper

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

A={x∣−3<x<0}A = \{x|-3<x<0\}A={x∣−3<x<0}, B={x∣x>−1}B = \{x|x>-1\}B={x∣x>−1}: A∩B=A \cap B =A∩B=

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

2x−6x−5≤0\frac{2x-6}{x-5} \le 0x−52x−6​≤0: solution set is

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

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

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

The domain of y=x−5y = \sqrt{x-5}y=x−5​ 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+3y = x^3+3y=x3+3 (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?

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

Which reduction equation is incorrect?

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

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

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

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

sin⁡150∘=\sin 150^\circ =sin150∘=

cos⁡α=35\cos\alpha = \frac{3}{5}cosα=53​, acute: tan⁡α=\tan\alpha =tanα=

Minimum of y=cos⁡3x+7y = \cos 3x + 7y=cos3x+7 is

Inverse of y=4x−9y = 4x - 9y=4x−9 is

Arithmetic a1=6,a2=2a_1 = 6, a_2 = 2a1​=6,a2​=2: a5=a_5 =a5​=

Arithmetic a1=4a_1 = 4a1​=4, d=−2d = -2d=−2: then a50=a_{50} =a50​=

How many are arithmetic: 2,5,8,112,5,8,112,5,8,11 · 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 ?

−6,a,12-6, a, 12−6,a,12 arithmetic: a=a =a=

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

Geometric a1=1a_1 = 1a1​=1, q=2q = 2q=2: S6=S_6 =S6​=

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

Slope −2-2−2 through (0,−1)(0,-1)(0,−1): equation is

Inclination 30∘30^\circ30∘: slope is

Intersection of y=2x−2y = 2x-2y=2x−2 and 3x−y−5=03x-y-5 = 03x−y−5=0:

Which line is perpendicular to 3x−4=03x-4 = 03x−4=0 ?

Slope through A(4,−4)A(4,-4)A(4,−4) , B(1,−6)B(1,-6)B(1,−6):

Which point is in the third quadrant?

∣AB∣=5|AB| = 5∣AB∣=5, A(1,−4)A(1,-4)A(1,−4), B(x,0)B(x,0)B(x,0): x=x =x=

P(−3,−2)P(-3,-2)P(−3,−2); Q symmetric about the y-axis: Q =

Circle center (3,−2)(3,-2)(3,−2), radius 4: equation is

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

About parabola y2=32xy^2 = 32xy2=32x, which is correct?

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

Ellipse x277+y281=1\frac{x^2}{77}+\frac{y^2}{81} = 177x2​+81y2​=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, 2 blue. One draw. P(red)=P(\text{red}) =P(red)=

a=(4,2)a = (4,2)a=(4,2), b=(12,6)b = (12,6)b=(12,6): a and b are

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

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

$A = \{x|-3<x<0\}$ , $B = \{x|x>-1\}$ : $A \cap B =$

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

$\frac{2x-6}{x-5} \le 0$ : solution set is

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

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

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

The domain of $y = \sqrt{x-5}$ is

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

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

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

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

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

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

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

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

$\sin 150^\circ =$

$\cos\alpha = \frac{3}{5}$ , acute: $\tan\alpha =$

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

Inverse of $y = 4x - 9$ is

Arithmetic $a_1 = 6, a_2 = 2$ : $a_5 =$

Arithmetic $a_1 = 4$ , $d = -2$ : then $a_{50} =$

How many are arithmetic: $2,5,8,11$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

$-6, a, 12$ arithmetic: $a =$

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

Geometric $a_1 = 1$ , $q = 2$ : $S_6 =$

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

Slope $-2$ through $(0,-1)$ : equation is

Inclination $30^\circ$ : slope is

Intersection of $y = 2x-2$ and $3x-y-5 = 0$ :

Which line is perpendicular to $3x-4 = 0$ ?

Slope through $A(4,-4)$ , $B(1,-6)$ :

$|AB| = 5$ , $A(1,-4)$ , $B(x,0)$ : $x =$

$P(-3,-2)$ ; Q symmetric about the y-axis: Q =

Circle center $(3,-2)$ , radius 4: equation is

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

About parabola $y^2 = 32x$ , which is correct?

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

Ellipse $\frac{x^2}{77}+\frac{y^2}{81} = 1$ : $|PF_1|+|PF_2| =$

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

Bag: 3 red, 2 blue. One draw. $P(\text{red}) =$

$a = (4,2)$ , $b = (12,6)$ : a and b are

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