CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 20 · Q1

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

Target: ~75s · ID EXAM-G20-1

Q 2/48CSCA Standardsets · Mock 20 · Q2

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$A = \{x|-2<x<1\}$ , $B = \{x|x>0\}$ : $A \cap B =$

Target: ~75s · ID EXAM-G20-2

Q 3/48CSCA Standardinequalities · Mock 20 · Q3

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

Target: ~75s · ID EXAM-G20-3

Q 4/48CSCA Standardinequalities · Mock 20 · Q4

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

Target: ~75s · ID EXAM-G20-4

Q 5/48CSCA Standardinequalities · Mock 20 · Q5

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

Target: ~75s · ID EXAM-G20-5

Q 6/48CSCA Standarddomain-range · Mock 20 · Q6

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Which function is the same as $y = |x|$ ?

Target: ~75s · ID EXAM-G20-6

Q 7/48CSCA Standarddomain-range · Mock 20 · Q7

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

Target: ~75s · ID EXAM-G20-7

Q 8/48CSCA Standarddomain-range · Mock 20 · Q8

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

Target: ~75s · ID EXAM-G20-8

Q 9/48CSCA Standardmonotonicity · Mock 20 · Q9

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

Target: ~75s · ID EXAM-G20-9

Q 10/48CSCA Standardeven-odd-functions · Mock 20 · Q10

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Which is an odd function?

Target: ~75s · ID EXAM-G20-10

Q 11/48CSCA Standardpower-functions · Mock 20 · Q11

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

Target: ~75s · ID EXAM-G20-11

Q 12/48CSCA Standardexponential-functions · Mock 20 · Q12

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G20-12

Q 13/48CSCA Standardexponential-functions · Mock 20 · Q13

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

Target: ~75s · ID EXAM-G20-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 20 · Q14

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Which logarithm statement is incorrect?

Target: ~75s · ID EXAM-G20-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 20 · Q15

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

Target: ~75s · ID EXAM-G20-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 20 · Q16

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G20-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 20 · Q17

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

Target: ~75s · ID EXAM-G20-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 20 · Q18

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

Target: ~75s · ID EXAM-G20-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 20 · Q19

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Minimum of $y = \cos 3x + 5$ is

Target: ~75s · ID EXAM-G20-19

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

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

Target: ~75s · ID EXAM-G20-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 20 · Q21

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$\sin 150^\circ =$

Target: ~75s · ID EXAM-G20-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 20 · Q22

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

Target: ~75s · ID EXAM-G20-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 20 · Q23

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G20-23

Q 24/48CSCA Standardinverse-functions · Mock 20 · Q24

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Inverse of $y = 10x + 5$ is

Target: ~75s · ID EXAM-G20-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 20 · Q25

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How many are arithmetic: $6,9,12,15$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

Target: ~75s · ID EXAM-G20-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 20 · Q26

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Arithmetic $a_1 = 2$ , $d = 1$ : then $a_{100} =$

Target: ~75s · ID EXAM-G20-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 20 · Q27

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Arithmetic $a_1 = 6, a_2 = 8$ : $a_5 =$

Target: ~75s · ID EXAM-G20-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 20 · Q28

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Arithmetic with $a_7 = 6$ : $S_{13} =$

Target: ~75s · ID EXAM-G20-28

Q 29/48CSCA Standardgeometric-sequences · Mock 20 · Q29

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Geometric $1,3,9$ : general term is

Target: ~75s · ID EXAM-G20-29

Q 30/48CSCA Standardgeometric-sequences · Mock 20 · Q30

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$\frac{1}{4}, -\frac{1}{16}, \frac{1}{64}, \ldots$ : $a_n =$

Target: ~75s · ID EXAM-G20-30

Q 31/48CSCA Standardgeometric-sequences · Mock 20 · Q31

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

Target: ~75s · ID EXAM-G20-31

Q 32/48CSCA Standardlines · Mock 20 · Q32

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Which line is perpendicular to $2x-2 = 0$ ?

Target: ~75s · ID EXAM-G20-32

Q 33/48CSCA Standardlines · Mock 20 · Q33

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Intersection of $y = -3x+5$ and $-2x-y+1 = 0$ :

Target: ~75s · ID EXAM-G20-33

Q 34/48CSCA Standardlines · Mock 20 · Q34

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Inclination $45^\circ$ : slope is

Target: ~75s · ID EXAM-G20-34

Q 35/48CSCA Standardlines · Mock 20 · Q35

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Slope $-5$ through $(-1,2)$ : equation is

Target: ~75s · ID EXAM-G20-35

Q 36/48CSCA Standardlines · Mock 20 · Q36

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Slope through $A(0,-4)$ , $B(3,0)$ :

Target: ~75s · ID EXAM-G20-36

Q 37/48CSCA Standardanalytic-geometry · Mock 20 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G20-37

Q 38/48CSCA Standardanalytic-geometry · Mock 20 · Q38

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

Target: ~75s · ID EXAM-G20-38

Q 39/48CSCA Standardanalytic-geometry · Mock 20 · Q39

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Distance $P(-3,-3)$ to $Q(-7,-8)$ is

Target: ~75s · ID EXAM-G20-39

Q 40/48CSCA Standardcircles · Mock 20 · Q40

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

Target: ~75s · ID EXAM-G20-40

Q 41/48CSCA Standardcircles · Mock 20 · Q41

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Circle $x^2+y^2-4x-8y+4 = 0$ : center and radius are

Target: ~75s · ID EXAM-G20-41

Q 42/48CSCA Standardparabolas · Mock 20 · Q42

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Focus F of $y^2 = 16x$ ; P on parabola with x = 8: $|PF| =$

Target: ~75s · ID EXAM-G20-42

Q 43/48CSCA Standardparabolas · Mock 20 · Q43

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

Target: ~75s · ID EXAM-G20-43

Q 44/48CSCA Standardellipses · Mock 20 · Q44

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About ellipse $\frac{x^2}{16}+\frac{y^2}{25} = 1$ , correct is

Target: ~75s · ID EXAM-G20-44

Q 45/48CSCA Standardhyperbolas · Mock 20 · Q45

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

Target: ~75s · ID EXAM-G20-45

Q 46/48CSCA Standardprobability · Mock 20 · Q46

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

Target: ~75s · ID EXAM-G20-46

Q 47/48CSCA Standardvectors · Mock 20 · Q47

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

Target: ~75s · ID EXAM-G20-47

Q 48/48CSCA Standardcomplex-numbers · Mock 20 · Q48

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$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{1001} =$

Target: ~75s · ID EXAM-G20-48

Mock 20 paper

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

A={x∣−2<x<1}A = \{x|-2<x<1\}A={x∣−2<x<1}, B={x∣x>0}B = \{x|x>0\}B={x∣x>0}: A∩B=A \cap B =A∩B=

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

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

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

Which function is the same as y=∣x∣y = |x|y=∣x∣ ?

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

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

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

sin⁡135∘=\sin 135^\circ =sin135∘=

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

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

Minimum of y=cos⁡3x+5y = \cos 3x + 5y=cos3x+5 is

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

sin⁡150∘=\sin 150^\circ =sin150∘=

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

Which reduction equation is incorrect?

Inverse of y=10x+5y = 10x + 5y=10x+5 is

How many are arithmetic: 6,9,12,156,9,12,156,9,12,15 · 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 ?

Arithmetic a1=2a_1 = 2a1​=2, d=1d = 1d=1: then a100=a_{100} =a100​=

Arithmetic a1=6,a2=8a_1 = 6, a_2 = 8a1​=6,a2​=8: a5=a_5 =a5​=

Arithmetic with a7=6a_7 = 6a7​=6: S13=S_{13} =S13​=

Geometric 1,3,91,3,91,3,9: general term is

14,−116,164,…\frac{1}{4}, -\frac{1}{16}, \frac{1}{64}, \ldots41​,−161​,641​,…: an=a_n =an​=

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

Which line is perpendicular to 2x−2=02x-2 = 02x−2=0 ?

Intersection of y=−3x+5y = -3x+5y=−3x+5 and −2x−y+1=0-2x-y+1 = 0−2x−y+1=0:

Inclination 45∘45^\circ45∘: slope is

Slope −5-5−5 through (−1,2)(-1,2)(−1,2): equation is

Slope through A(0,−4)A(0,-4)A(0,−4) , B(3,0)B(3,0)B(3,0):

Which point is in the third quadrant?

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

Distance P(−3,−3)P(-3,-3)P(−3,−3) to Q(−7,−8)Q(-7,-8)Q(−7,−8) is

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

Circle x2+y2−4x−8y+4=0x^2+y^2-4x-8y+4 = 0x2+y2−4x−8y+4=0: center and radius are

Focus F of y2=16xy^2 = 16xy2=16x; P on parabola with x = 8: ∣PF∣=|PF| =∣PF∣=

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

About ellipse x216+y225=1\frac{x^2}{16}+\frac{y^2}{25} = 116x2​+25y2​=1, correct is

Foci of x236−y264=1\frac{x^2}{36} - \frac{y^2}{64} = 136x2​−64y2​=1 are

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

a=(5,5)a = (5,5)a=(5,5), b=(−10,−10)b = (-10,-10)b=(−10,−10): a and b are

z3=1z^3 = 1z3=1, z≠1z \ne 1z=1: 1+z+⋯+z1001=1+z+\cdots+z^{1001} =1+z+⋯+z1001=

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

$A = \{x|-2<x<1\}$ , $B = \{x|x>0\}$ : $A \cap B =$

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

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

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

Which function is the same as $y = |x|$ ?

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

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

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

$\sin 135^\circ =$

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

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

Minimum of $y = \cos 3x + 5$ is

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

$\sin 150^\circ =$

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

Inverse of $y = 10x + 5$ is

How many are arithmetic: $6,9,12,15$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

Arithmetic $a_1 = 2$ , $d = 1$ : then $a_{100} =$

Arithmetic $a_1 = 6, a_2 = 8$ : $a_5 =$

Arithmetic with $a_7 = 6$ : $S_{13} =$

Geometric $1,3,9$ : general term is

$\frac{1}{4}, -\frac{1}{16}, \frac{1}{64}, \ldots$ : $a_n =$

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

Which line is perpendicular to $2x-2 = 0$ ?

Intersection of $y = -3x+5$ and $-2x-y+1 = 0$ :

Inclination $45^\circ$ : slope is

Slope $-5$ through $(-1,2)$ : equation is

Slope through $A(0,-4)$ , $B(3,0)$ :

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

Distance $P(-3,-3)$ to $Q(-7,-8)$ is

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

Circle $x^2+y^2-4x-8y+4 = 0$ : center and radius are

Focus F of $y^2 = 16x$ ; P on parabola with x = 8: $|PF| =$

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

About ellipse $\frac{x^2}{16}+\frac{y^2}{25} = 1$ , correct is

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

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

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

$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{1001} =$