CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 05 · Q1

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

Target: ~75s · ID EXAM-G5-1

Q 2/48CSCA Standardsets · Mock 05 · Q2

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$A = \{x|-5<x<0\}$ , $B = \{x|x>-1\}$ : $A \cap B =$

Target: ~75s · ID EXAM-G5-2

Q 3/48CSCA Standardinequalities · Mock 05 · Q3

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

Target: ~75s · ID EXAM-G5-3

Q 4/48CSCA Standardinequalities · Mock 05 · Q4

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$\frac{2x-8}{x-6} \le 0$ : solution set is

Target: ~75s · ID EXAM-G5-4

Q 5/48CSCA Standardinequalities · Mock 05 · Q5

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$x^2+8x+15 > 0$ : solution set is

Target: ~75s · ID EXAM-G5-5

Q 6/48CSCA Standarddomain-range · Mock 05 · Q6

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

Target: ~75s · ID EXAM-G5-6

Q 7/48CSCA Standarddomain-range · Mock 05 · Q7

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The domain of $y = \sqrt{x-4}$ is

Target: ~75s · ID EXAM-G5-7

Q 8/48CSCA Standarddomain-range · Mock 05 · Q8

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

Target: ~75s · ID EXAM-G5-8

Q 9/48CSCA Standardmonotonicity · Mock 05 · Q9

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

Target: ~75s · ID EXAM-G5-9

Q 10/48CSCA Standardeven-odd-functions · Mock 05 · Q10

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

Target: ~75s · ID EXAM-G5-10

Q 11/48CSCA Standardpower-functions · Mock 05 · Q11

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The inverse function of $y = x^3+9$ $(x \in \mathbb{R})$ is

Target: ~75s · ID EXAM-G5-11

Q 12/48CSCA Standardexponential-functions · Mock 05 · Q12

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

Target: ~75s · ID EXAM-G5-12

Q 13/48CSCA Standardexponential-functions · Mock 05 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G5-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 05 · Q14

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

Target: ~75s · ID EXAM-G5-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 05 · Q15

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

Target: ~75s · ID EXAM-G5-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 05 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G5-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 05 · Q17

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

Target: ~75s · ID EXAM-G5-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 05 · Q18

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

Target: ~75s · ID EXAM-G5-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 05 · Q19

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Minimum of $y = \cos 2x + 7$ is

Target: ~75s · ID EXAM-G5-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 05 · Q20

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

Target: ~75s · ID EXAM-G5-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 05 · Q21

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G5-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 05 · Q22

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

Target: ~75s · ID EXAM-G5-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 05 · Q23

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$\cos\alpha = -\frac{1}{2}$ , QII: $\sin(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-G5-23

Q 24/48CSCA Standardinverse-functions · Mock 05 · Q24

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Inverse of $y = 6x - 3$ is

Target: ~75s · ID EXAM-G5-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 05 · Q25

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How many are arithmetic: $4,7,10,13$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

Target: ~75s · ID EXAM-G5-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 05 · Q26

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

Target: ~75s · ID EXAM-G5-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 05 · Q27

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Arithmetic $a_1 = -4, a_2 = -8$ : $a_5 =$

Target: ~75s · ID EXAM-G5-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 05 · Q28

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Arithmetic with $a_7 = 1$ : $S_{13} =$

Target: ~75s · ID EXAM-G5-28

Q 29/48CSCA Standardgeometric-sequences · Mock 05 · Q29

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

Target: ~75s · ID EXAM-G5-29

Q 30/48CSCA Standardgeometric-sequences · Mock 05 · Q30

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

Target: ~75s · ID EXAM-G5-30

Q 31/48CSCA Standardgeometric-sequences · Mock 05 · Q31

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

Target: ~75s · ID EXAM-G5-31

Q 32/48CSCA Standardlines · Mock 05 · Q32

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Which line is perpendicular to $x+5 = 0$ ?

Target: ~75s · ID EXAM-G5-32

Q 33/48CSCA Standardlines · Mock 05 · Q33

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

Target: ~75s · ID EXAM-G5-33

Q 34/48CSCA Standardlines · Mock 05 · Q34

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Inclination $45^\circ$ : slope is

Target: ~75s · ID EXAM-G5-34

Q 35/48CSCA Standardlines · Mock 05 · Q35

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

Target: ~75s · ID EXAM-G5-35

Q 36/48CSCA Standardlines · Mock 05 · Q36

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Slope through $A(5,-2)$ , $B(6,3)$ :

Target: ~75s · ID EXAM-G5-36

Q 37/48CSCA Standardanalytic-geometry · Mock 05 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G5-37

Q 38/48CSCA Standardanalytic-geometry · Mock 05 · Q38

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$|AB| = 5$ , $A(-2,-3)$ , $B(x,1)$ : $x =$

Target: ~75s · ID EXAM-G5-38

Q 39/48CSCA Standardanalytic-geometry · Mock 05 · Q39

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

Target: ~75s · ID EXAM-G5-39

Q 40/48CSCA Standardcircles · Mock 05 · Q40

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

Target: ~75s · ID EXAM-G5-40

Q 41/48CSCA Standardcircles · Mock 05 · Q41

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Circle $x^2+y^2-4x-2y+1 = 0$ : center and radius are

Target: ~75s · ID EXAM-G5-41

Q 42/48CSCA Standardparabolas · Mock 05 · Q42

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Focus F of $y^2 = 12x$ ; P on parabola with x = 5: $|PF| =$

Target: ~75s · ID EXAM-G5-42

Q 43/48CSCA Standardparabolas · Mock 05 · Q43

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About parabola $y^2 = 8x$ , which is correct?

Target: ~75s · ID EXAM-G5-43

Q 44/48CSCA Standardellipses · Mock 05 · Q44

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Ellipse $\frac{x^2}{5}+\frac{y^2}{9} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-G5-44

Q 45/48CSCA Standardhyperbolas · Mock 05 · Q45

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

Target: ~75s · ID EXAM-G5-45

Q 46/48CSCA Standardprobability · Mock 05 · Q46

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

Target: ~75s · ID EXAM-G5-46

Q 47/48CSCA Standardvectors · Mock 05 · Q47

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$a = (1,2)$ , $b = (2,4)$ : a and b are

Target: ~75s · ID EXAM-G5-47

Q 48/48CSCA Standardcomplex-numbers · Mock 05 · Q48

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$(z-3i)(4-i) = 17$ : $z =$

Target: ~75s · ID EXAM-G5-48

Mock 05 paper

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

A={x∣−5<x<0}A = \{x|-5<x<0\}A={x∣−5<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−8x−6≤0\frac{2x-8}{x-6} \le 0x−62x−8​≤0: solution set is

x2+8x+15>0x^2+8x+15 > 0x2+8x+15>0: solution set is

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

The domain of y=x−4y = \sqrt{x-4}y=x−4​ is

The domain of y=1x−2y = \frac{1}{x-2}y=x−21​ 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+9y = x^3+9y=x3+9 (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: 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⁡2x+7y = \cos 2x + 7y=cos2x+7 is

cos⁡α=35\cos\alpha = \frac{3}{5}cosα=53​, 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=−12\cos\alpha = -\frac{1}{2}cosα=−21​, QII: sin⁡(α2)=\sin(\frac{\alpha}{2}) =sin(2α​)=

Inverse of y=6x−3y = 6x - 3y=6x−3 is

How many are arithmetic: 4,7,10,134,7,10,134,7,10,13 · 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=−3d = -3d=−3: then a50=a_{50} =a50​=

Arithmetic a1=−4,a2=−8a_1 = -4, a_2 = -8a1​=−4,a2​=−8: a5=a_5 =a5​=

Arithmetic with a7=1a_7 = 1a7​=1: S13=S_{13} =S13​=

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​=

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

Which line is perpendicular to x+5=0x+5 = 0x+5=0 ?

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

Inclination 45∘45^\circ45∘: slope is

Slope 222 through (1,−5)(1,-5)(1,−5): equation is

Slope through A(5,−2)A(5,-2)A(5,−2) , B(6,3)B(6,3)B(6,3):

Which point is in the third quadrant?

∣AB∣=5|AB| = 5∣AB∣=5, A(−2,−3)A(-2,-3)A(−2,−3), B(x,1)B(x,1)B(x,1): x=x =x=

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

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

Circle x2+y2−4x−2y+1=0x^2+y^2-4x-2y+1 = 0x2+y2−4x−2y+1=0: center and radius are

Focus F of y2=12xy^2 = 12xy2=12x; P on parabola with x = 5: ∣PF∣=|PF| =∣PF∣=

About parabola y2=8xy^2 = 8xy2=8x, which is correct?

Ellipse x25+y29=1\frac{x^2}{5}+\frac{y^2}{9} = 15x2​+9y2​=1: ∣PF1∣+∣PF2∣=|PF_1|+|PF_2| =∣PF1​∣+∣PF2​∣=

Foci of x216−y29=1\frac{x^2}{16} - \frac{y^2}{9} = 116x2​−9y2​=1 are

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

a=(1,2)a = (1,2)a=(1,2), b=(2,4)b = (2,4)b=(2,4): a and b are

(z−3i)(4−i)=17(z-3i)(4-i) = 17(z−3i)(4−i)=17: z=z =z=

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

$A = \{x|-5<x<0\}$ , $B = \{x|x>-1\}$ : $A \cap B =$

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

$\frac{2x-8}{x-6} \le 0$ : solution set is

$x^2+8x+15 > 0$ : solution set is

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

The domain of $y = \sqrt{x-4}$ is

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

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

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

The inverse function of $y = x^3+9$ $(x \in \mathbb{R})$ 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: $\cos(\frac{\alpha}{2}) =$

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

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

Minimum of $y = \cos 2x + 7$ is

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

$\sin 135^\circ =$

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

$\cos\alpha = -\frac{1}{2}$ , QII: $\sin(\frac{\alpha}{2}) =$

Inverse of $y = 6x - 3$ is

How many are arithmetic: $4,7,10,13$ · $2,4,7,11$ · $3,3,3,3$ · $2,4,8,16$ ?

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

Arithmetic $a_1 = -4, a_2 = -8$ : $a_5 =$

Arithmetic with $a_7 = 1$ : $S_{13} =$

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

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

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

Which line is perpendicular to $x+5 = 0$ ?

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

Inclination $45^\circ$ : slope is

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

Slope through $A(5,-2)$ , $B(6,3)$ :

$|AB| = 5$ , $A(-2,-3)$ , $B(x,1)$ : $x =$

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

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

Circle $x^2+y^2-4x-2y+1 = 0$ : center and radius are

Focus F of $y^2 = 12x$ ; P on parabola with x = 5: $|PF| =$

About parabola $y^2 = 8x$ , which is correct?

Ellipse $\frac{x^2}{5}+\frac{y^2}{9} = 1$ : $|PF_1|+|PF_2| =$

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

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

$a = (1,2)$ , $b = (2,4)$ : a and b are

$(z-3i)(4-i) = 17$ : $z =$