CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 03 · Q1

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$A = \{5,6,7,8,9\}$ : which is correct?

Target: ~75s · ID EXAM-G3-1

Q 2/48CSCA Standardsets · Mock 03 · Q2

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Survey of 40: 20 like A, 16 like B, 8 like both. Like only A:

Target: ~75s · ID EXAM-G3-2

Q 3/48CSCA Standardinequalities · Mock 03 · Q3

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

Target: ~75s · ID EXAM-G3-3

Q 4/48CSCA Standardinequalities · Mock 03 · Q4

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$x^2+7x+10 \ge 0$ : solution set is

Target: ~75s · ID EXAM-G3-4

Q 5/48CSCA Standardinequalities · Mock 03 · Q5

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$x^2-3x-4 > 0$ : solution set is

Target: ~75s · ID EXAM-G3-5

Q 6/48CSCA Standarddomain-range · Mock 03 · Q6

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

Target: ~75s · ID EXAM-G3-6

Q 7/48CSCA Standarddomain-range · Mock 03 · Q7

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

Target: ~75s · ID EXAM-G3-7

Q 8/48CSCA Standarddomain-range · Mock 03 · Q8

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

Target: ~75s · ID EXAM-G3-8

Q 9/48CSCA Standardmonotonicity · Mock 03 · Q9

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

Target: ~75s · ID EXAM-G3-9

Q 10/48CSCA Standardeven-odd-functions · Mock 03 · Q10

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

Target: ~75s · ID EXAM-G3-10

Q 11/48CSCA Standardpower-functions · Mock 03 · Q11

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

Target: ~75s · ID EXAM-G3-11

Q 12/48CSCA Standardexponential-functions · Mock 03 · Q12

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

Target: ~75s · ID EXAM-G3-12

Q 13/48CSCA Standardexponential-functions · Mock 03 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G3-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 03 · Q14

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

Target: ~75s · ID EXAM-G3-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 03 · Q15

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G3-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 03 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G3-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 03 · Q17

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

Target: ~75s · ID EXAM-G3-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 03 · Q18

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Minimum of $y = \cos 8x + 2$ is

Target: ~75s · ID EXAM-G3-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 03 · Q19

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

Target: ~75s · ID EXAM-G3-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 03 · Q20

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Minimum of $y = \cos 7x + 5$ is

Target: ~75s · ID EXAM-G3-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 03 · Q21

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$\sin 150^\circ =$

Target: ~75s · ID EXAM-G3-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 03 · Q22

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Minimum of $y = \cos 9x + 2$ is

Target: ~75s · ID EXAM-G3-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 03 · Q23

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

Target: ~75s · ID EXAM-G3-23

Q 24/48CSCA Standardinverse-functions · Mock 03 · Q24

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Inverse of $y = 2x - 9$ is

Target: ~75s · ID EXAM-G3-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 03 · Q25

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Arithmetic $a_1 = 5$ , $d = -2$ : then $a_{50} =$

Target: ~75s · ID EXAM-G3-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 03 · Q26

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Arithmetic $a_1 = 2$ , $d = -3$ : then $a_{100} =$

Target: ~75s · ID EXAM-G3-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 03 · Q27

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Arithmetic $a_1 = 2$ , $d = -3$ : then $a_{50} =$

Target: ~75s · ID EXAM-G3-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 03 · Q28

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Arithmetic $a_1 = 5$ , $d = 4$ : then $a_{101} =$

Target: ~75s · ID EXAM-G3-28

Q 29/48CSCA Standardgeometric-sequences · Mock 03 · Q29

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Geometric $1,2,4$ : general term is

Target: ~75s · ID EXAM-G3-29

Q 30/48CSCA Standardgeometric-sequences · Mock 03 · Q30

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Geometric $a_1 = 48, a_4 = -384$ : $q =$

Target: ~75s · ID EXAM-G3-30

Q 31/48CSCA Standardgeometric-sequences · Mock 03 · Q31

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

Target: ~75s · ID EXAM-G3-31

Q 32/48CSCA Standardlines · Mock 03 · Q32

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

Target: ~75s · ID EXAM-G3-32

Q 33/48CSCA Standardlines · Mock 03 · Q33

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

Target: ~75s · ID EXAM-G3-33

Q 34/48CSCA Standardlines · Mock 03 · Q34

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

Target: ~75s · ID EXAM-G3-34

Q 35/48CSCA Standardlines · Mock 03 · Q35

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Slope through $A(-1,-5)$ , $B(0,-10)$ :

Target: ~75s · ID EXAM-G3-35

Q 36/48CSCA Standardlines · Mock 03 · Q36

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Slope through $A(-4,-5)$ , $B(-7,-10)$ :

Target: ~75s · ID EXAM-G3-36

Q 37/48CSCA Standardanalytic-geometry · Mock 03 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G3-37

Q 38/48CSCA Standardanalytic-geometry · Mock 03 · Q38

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Distance $P(1,3)$ to $Q(6,2)$ is

Target: ~75s · ID EXAM-G3-38

Q 39/48CSCA Standardanalytic-geometry · Mock 03 · Q39

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

Target: ~75s · ID EXAM-G3-39

Q 40/48CSCA Standardcircles · Mock 03 · Q40

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Circle center $(5,4)$ , radius 2: equation is

Target: ~75s · ID EXAM-G3-40

Q 41/48CSCA Standardcircles · Mock 03 · Q41

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

Target: ~75s · ID EXAM-G3-41

Q 42/48CSCA Standardparabolas · Mock 03 · Q42

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Directrix of $y^2 = -8x$ is

Target: ~75s · ID EXAM-G3-42

Q 43/48CSCA Standardparabolas · Mock 03 · Q43

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

Target: ~75s · ID EXAM-G3-43

Q 44/48CSCA Standardellipses · Mock 03 · Q44

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Ellipse $\frac{x^2}{36}+\frac{y^2}{32} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-G3-44

Q 45/48CSCA Standardhyperbolas · Mock 03 · Q45

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

Target: ~75s · ID EXAM-G3-45

Q 46/48CSCA Standardprobability · Mock 03 · Q46

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

Target: ~75s · ID EXAM-G3-46

Q 47/48CSCA Standardvectors · Mock 03 · Q47

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

Target: ~75s · ID EXAM-G3-47

Q 48/48CSCA Standardcomplex-numbers · Mock 03 · Q48

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$(z-1i)(5-i) = 26$ : $z =$

Target: ~75s · ID EXAM-G3-48

Mock 03 paper

A={5,6,7,8,9}A = \{5,6,7,8,9\}A={5,6,7,8,9}: which is correct?

Survey of 40: 20 like A, 16 like B, 8 like both. Like only A:

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

x2+7x+10≥0x^2+7x+10 \ge 0x2+7x+10≥0: solution set is

x2−3x−4>0x^2-3x-4 > 0x2−3x−4>0: solution set is

The domain of y=1x+1y = \frac{1}{x+1}y=x+11​ 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)(−∞,+∞) ?

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

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

Which reduction equation is incorrect?

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

Minimum of y=cos⁡8x+2y = \cos 8x + 2y=cos8x+2 is

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

Minimum of y=cos⁡7x+5y = \cos 7x + 5y=cos7x+5 is

sin⁡150∘=\sin 150^\circ =sin150∘=

Minimum of y=cos⁡9x+2y = \cos 9x + 2y=cos9x+2 is

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

Inverse of y=2x−9y = 2x - 9y=2x−9 is

Arithmetic a1=5a_1 = 5a1​=5, d=−2d = -2d=−2: then a50=a_{50} =a50​=

Arithmetic a1=2a_1 = 2a1​=2, d=−3d = -3d=−3: then a100=a_{100} =a100​=

Arithmetic a1=2a_1 = 2a1​=2, d=−3d = -3d=−3: then a50=a_{50} =a50​=

Arithmetic a1=5a_1 = 5a1​=5, d=4d = 4d=4: then a101=a_{101} =a101​=

Geometric 1,2,41,2,41,2,4: general term is

Geometric a1=48,a4=−384a_1 = 48, a_4 = -384a1​=48,a4​=−384: q=q =q=

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

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

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

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

Slope through A(−1,−5)A(-1,-5)A(−1,−5) , B(0,−10)B(0,-10)B(0,−10):

Slope through A(−4,−5)A(-4,-5)A(−4,−5) , B(−7,−10)B(-7,-10)B(−7,−10):

Which point is in the third quadrant?

Distance P(1,3)P(1,3)P(1,3) to Q(6,2)Q(6,2)Q(6,2) is

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

Circle center (5,4)(5,4)(5,4), radius 2: equation is

Through A(5,5)A(5,5)A(5,5), center (5,0)(5,0)(5,0): equation is

Directrix of y2=−8xy^2 = -8xy2=−8x is

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

Ellipse x236+y232=1\frac{x^2}{36}+\frac{y^2}{32} = 136x2​+32y2​=1: ∣PF1∣+∣PF2∣=|PF_1|+|PF_2| =∣PF1​∣+∣PF2​∣=

Foci of x29−y216=1\frac{x^2}{9} - \frac{y^2}{16} = 19x2​−16y2​=1 are

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

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

(z−1i)(5−i)=26(z-1i)(5-i) = 26(z−1i)(5−i)=26: z=z =z=

$A = \{5,6,7,8,9\}$ : which is correct?

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

$x^2+7x+10 \ge 0$ : solution set is

$x^2-3x-4 > 0$ : solution set is

The domain of $y = \frac{1}{x+1}$ 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 $(-\infty,+\infty)$ ?

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

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

$\sin 135^\circ =$

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

Minimum of $y = \cos 8x + 2$ is

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

Minimum of $y = \cos 7x + 5$ is

$\sin 150^\circ =$

Minimum of $y = \cos 9x + 2$ is

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

Inverse of $y = 2x - 9$ is

Arithmetic $a_1 = 5$ , $d = -2$ : then $a_{50} =$

Arithmetic $a_1 = 2$ , $d = -3$ : then $a_{100} =$

Arithmetic $a_1 = 2$ , $d = -3$ : then $a_{50} =$

Arithmetic $a_1 = 5$ , $d = 4$ : then $a_{101} =$

Geometric $1,2,4$ : general term is

Geometric $a_1 = 48, a_4 = -384$ : $q =$

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

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

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

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

Slope through $A(-1,-5)$ , $B(0,-10)$ :

Slope through $A(-4,-5)$ , $B(-7,-10)$ :

Distance $P(1,3)$ to $Q(6,2)$ is

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

Circle center $(5,4)$ , radius 2: equation is

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

Directrix of $y^2 = -8x$ is

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

Ellipse $\frac{x^2}{36}+\frac{y^2}{32} = 1$ : $|PF_1|+|PF_2| =$

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

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

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

$(z-1i)(5-i) = 26$ : $z =$