CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 15 · Q1

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

Target: ~75s · ID EXAM-G15-1

Q 2/48CSCA Standardsets · Mock 15 · Q2

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

Target: ~75s · ID EXAM-G15-2

Q 3/48CSCA Standardinequalities · Mock 15 · Q3

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

Target: ~75s · ID EXAM-G15-3

Q 4/48CSCA Standardinequalities · Mock 15 · Q4

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$x^2-4x+3 \ge 0$ : solution set is

Target: ~75s · ID EXAM-G15-4

Q 5/48CSCA Standardinequalities · Mock 15 · Q5

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

Target: ~75s · ID EXAM-G15-5

Q 6/48CSCA Standarddomain-range · Mock 15 · Q6

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

Target: ~75s · ID EXAM-G15-6

Q 7/48CSCA Standarddomain-range · Mock 15 · Q7

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

Target: ~75s · ID EXAM-G15-7

Q 8/48CSCA Standarddomain-range · Mock 15 · Q8

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

Target: ~75s · ID EXAM-G15-8

Q 9/48CSCA Standardmonotonicity · Mock 15 · Q9

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

Target: ~75s · ID EXAM-G15-9

Q 10/48CSCA Standardeven-odd-functions · Mock 15 · Q10

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About $f(x) = x^4 + 6$ , which is correct?

Target: ~75s · ID EXAM-G15-10

Q 11/48CSCA Standardpower-functions · Mock 15 · Q11

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The inverse function of $y = x^3+7$ $(x \in \mathbb{R})$ is

Target: ~75s · ID EXAM-G15-11

Q 12/48CSCA Standardexponential-functions · Mock 15 · Q12

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

Target: ~75s · ID EXAM-G15-12

Q 13/48CSCA Standardexponential-functions · Mock 15 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G15-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 15 · Q14

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

Target: ~75s · ID EXAM-G15-14

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

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

Target: ~75s · ID EXAM-G15-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 15 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G15-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 15 · Q17

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

Target: ~75s · ID EXAM-G15-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 15 · Q18

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$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{2}{3}$ : $\tan\alpha =$

Target: ~75s · ID EXAM-G15-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 15 · Q19

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Minimum of $y = \cos 4x + 4$ is

Target: ~75s · ID EXAM-G15-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 15 · Q20

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$\cos\alpha = \frac{6}{10}$ , acute: $\tan\alpha =$

Target: ~75s · ID EXAM-G15-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 15 · Q21

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G15-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 15 · Q22

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

Target: ~75s · ID EXAM-G15-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 15 · Q23

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

Target: ~75s · ID EXAM-G15-23

Q 24/48CSCA Standardinverse-functions · Mock 15 · Q24

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Inverse of $y = 4x - 1$ is

Target: ~75s · ID EXAM-G15-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 15 · Q25

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

Target: ~75s · ID EXAM-G15-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 15 · Q26

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Arithmetic $a_1 = 4$ , $d = -1$ : then $a_{100} =$

Target: ~75s · ID EXAM-G15-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 15 · Q27

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Arithmetic $a_1 = 7, a_2 = 4$ : $a_5 =$

Target: ~75s · ID EXAM-G15-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 15 · Q28

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

Target: ~75s · ID EXAM-G15-28

Q 29/48CSCA Standardgeometric-sequences · Mock 15 · Q29

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

Target: ~75s · ID EXAM-G15-29

Q 30/48CSCA Standardgeometric-sequences · Mock 15 · Q30

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Geometric $a_1 = -24, a_4 = 192$ : $q =$

Target: ~75s · ID EXAM-G15-30

Q 31/48CSCA Standardgeometric-sequences · Mock 15 · Q31

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

Target: ~75s · ID EXAM-G15-31

Q 32/48CSCA Standardlines · Mock 15 · Q32

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

Target: ~75s · ID EXAM-G15-32

Q 33/48CSCA Standardlines · Mock 15 · Q33

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

Target: ~75s · ID EXAM-G15-33

Q 34/48CSCA Standardlines · Mock 15 · Q34

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Inclination $60^\circ$ : slope is

Target: ~75s · ID EXAM-G15-34

Q 35/48CSCA Standardlines · Mock 15 · Q35

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Slope $-3$ through $(-4,-2)$ : equation is

Target: ~75s · ID EXAM-G15-35

Q 36/48CSCA Standardlines · Mock 15 · Q36

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Slope through $A(-3,0)$ , $B(1,-2)$ :

Target: ~75s · ID EXAM-G15-36

Q 37/48CSCA Standardanalytic-geometry · Mock 15 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G15-37

Q 38/48CSCA Standardanalytic-geometry · Mock 15 · Q38

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Distance $P(1,3)$ to $Q(5,8)$ is

Target: ~75s · ID EXAM-G15-38

Q 39/48CSCA Standardanalytic-geometry · Mock 15 · Q39

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$P(-5,4)$ ; Q symmetric about the y-axis: Q =

Target: ~75s · ID EXAM-G15-39

Q 40/48CSCA Standardcircles · Mock 15 · Q40

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Circle center $(3,-1)$ , radius 5: equation is

Target: ~75s · ID EXAM-G15-40

Q 41/48CSCA Standardcircles · Mock 15 · Q41

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

Target: ~75s · ID EXAM-G15-41

Q 42/48CSCA Standardparabolas · Mock 15 · Q42

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Directrix of $y^2 = 12x$ is

Target: ~75s · ID EXAM-G15-42

Q 43/48CSCA Standardparabolas · Mock 15 · Q43

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About parabola $y^2 = 24x$ , which is correct?

Target: ~75s · ID EXAM-G15-43

Q 44/48CSCA Standardellipses · Mock 15 · Q44

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Ellipse $\frac{x^2}{64}+\frac{y^2}{60} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-G15-44

Q 45/48CSCA Standardhyperbolas · Mock 15 · Q45

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

Target: ~75s · ID EXAM-G15-45

Q 46/48CSCA Standardprobability · Mock 15 · Q46

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

Target: ~75s · ID EXAM-G15-46

Q 47/48CSCA Standardvectors · Mock 15 · Q47

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$a = (5,6)$ , $b = (10,12)$ : a and b are

Target: ~75s · ID EXAM-G15-47

Q 48/48CSCA Standardcomplex-numbers · Mock 15 · Q48

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$(z-4i)(1-i) = 2$ : $z =$

Target: ~75s · ID EXAM-G15-48

Mock 15 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:

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

x2−4x+3≥0x^2-4x+3 \ge 0x2−4x+3≥0: solution set is

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

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

The domain of y=x−2y = \sqrt{x-2}y=x−2​ 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+6f(x) = x^4 + 6f(x)=x4+6 , which is correct?

The inverse function of y=x3+7y = x^3+7y=x3+7 (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=−1517\cos\alpha = -\frac{15}{17}cosα=−1715​, QII: cos⁡(α2)=\cos(\frac{\alpha}{2}) =cos(2α​)=

Which reduction equation is incorrect?

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

cos⁡α−sin⁡αcos⁡α+sin⁡α=23\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{2}{3}cosα+sinαcosα−sinα​=32​: tan⁡α=\tan\alpha =tanα=

Minimum of y=cos⁡4x+4y = \cos 4x + 4y=cos4x+4 is

cos⁡α=610\cos\alpha = \frac{6}{10}cosα=106​, acute: tan⁡α=\tan\alpha =tanα=

sin⁡135∘=\sin 135^\circ =sin135∘=

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

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

Inverse of y=4x−1y = 4x - 1y=4x−1 is

How many are arithmetic: 3,−3,−9,−153,-3,-9,-153,−3,−9,−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=4a_1 = 4a1​=4, d=−1d = -1d=−1: then a100=a_{100} =a100​=

Arithmetic a1=7,a2=4a_1 = 7, a_2 = 4a1​=7,a2​=4: a5=a_5 =a5​=

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

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

Geometric a1=−24,a4=192a_1 = -24, a_4 = 192a1​=−24,a4​=192: q=q =q=

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

Which line is perpendicular to −x+0=0-x+0 = 0−x+0=0 ?

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

Inclination 60∘60^\circ60∘: slope is

Slope −3-3−3 through (−4,−2)(-4,-2)(−4,−2): equation is

Slope through A(−3,0)A(-3,0)A(−3,0) , B(1,−2)B(1,-2)B(1,−2):

Which point is in the third quadrant?

Distance P(1,3)P(1,3)P(1,3) to Q(5,8)Q(5,8)Q(5,8) is

P(−5,4)P(-5,4)P(−5,4); Q symmetric about the y-axis: Q =

Circle center (3,−1)(3,-1)(3,−1), radius 5: equation is

Through A(0,3)A(0,3)A(0,3), center (0,0)(0,0)(0,0): equation is

Directrix of y2=12xy^2 = 12xy2=12x is

About parabola y2=24xy^2 = 24xy2=24x, which is correct?

Ellipse x264+y260=1\frac{x^2}{64}+\frac{y^2}{60} = 164x2​+60y2​=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: 5 red, 5 blue. One draw. P(red)=P(\text{red}) =P(red)=

a=(5,6)a = (5,6)a=(5,6), b=(10,12)b = (10,12)b=(10,12): a and b are

(z−4i)(1−i)=2(z-4i)(1-i) = 2(z−4i)(1−i)=2: z=z =z=

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

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

$x^2-4x+3 \ge 0$ : solution set is

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

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

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

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

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

About $f(x) = x^4 + 6$ , which is correct?

The inverse function of $y = x^3+7$ $(x \in \mathbb{R})$ 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?

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

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

$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{2}{3}$ : $\tan\alpha =$

Minimum of $y = \cos 4x + 4$ is

$\cos\alpha = \frac{6}{10}$ , acute: $\tan\alpha =$

$\sin 135^\circ =$

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

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

Inverse of $y = 4x - 1$ is

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

Arithmetic $a_1 = 4$ , $d = -1$ : then $a_{100} =$

Arithmetic $a_1 = 7, a_2 = 4$ : $a_5 =$

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

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

Geometric $a_1 = -24, a_4 = 192$ : $q =$

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

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

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

Inclination $60^\circ$ : slope is

Slope $-3$ through $(-4,-2)$ : equation is

Slope through $A(-3,0)$ , $B(1,-2)$ :

Distance $P(1,3)$ to $Q(5,8)$ is

$P(-5,4)$ ; Q symmetric about the y-axis: Q =

Circle center $(3,-1)$ , radius 5: equation is

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

Directrix of $y^2 = 12x$ is

About parabola $y^2 = 24x$ , which is correct?

Ellipse $\frac{x^2}{64}+\frac{y^2}{60} = 1$ : $|PF_1|+|PF_2| =$

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

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

$a = (5,6)$ , $b = (10,12)$ : a and b are

$(z-4i)(1-i) = 2$ : $z =$