CSCA Preparation Platform Free Practice, Mocks & Syllabus

Q 1/48CSCA Standardsets · Mock 07 · Q1

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

Target: ~75s · ID EXAM-G7-1

Q 2/48CSCA Standardsets · Mock 07 · Q2

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$A = \{7,8,9,10,11\}$ : which is correct?

Target: ~75s · ID EXAM-G7-2

Q 3/48CSCA Standardinequalities · Mock 07 · Q3

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

Target: ~75s · ID EXAM-G7-3

Q 4/48CSCA Standardinequalities · Mock 07 · Q4

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$x^2+1x-6 \ge 0$ : solution set is

Target: ~75s · ID EXAM-G7-4

Q 5/48CSCA Standardinequalities · Mock 07 · Q5

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

Target: ~75s · ID EXAM-G7-5

Q 6/48CSCA Standarddomain-range · Mock 07 · Q6

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

Target: ~75s · ID EXAM-G7-6

Q 7/48CSCA Standarddomain-range · Mock 07 · Q7

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

Target: ~75s · ID EXAM-G7-7

Q 8/48CSCA Standarddomain-range · Mock 07 · Q8

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

Target: ~75s · ID EXAM-G7-8

Q 9/48CSCA Standardmonotonicity · Mock 07 · Q9

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

Target: ~75s · ID EXAM-G7-9

Q 10/48CSCA Standardeven-odd-functions · Mock 07 · Q10

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About $f(x) = x^4 + 8$ , which is correct?

Target: ~75s · ID EXAM-G7-10

Q 11/48CSCA Standardpower-functions · Mock 07 · Q11

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

Target: ~75s · ID EXAM-G7-11

Q 12/48CSCA Standardexponential-functions · Mock 07 · Q12

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

Target: ~75s · ID EXAM-G7-12

Q 13/48CSCA Standardexponential-functions · Mock 07 · Q13

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Given $a > b$ , which must hold?

Target: ~75s · ID EXAM-G7-13

Q 14/48CSCA Standardlogarithmic-functions · Mock 07 · Q14

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

Target: ~75s · ID EXAM-G7-14

Q 15/48CSCA Standardtrigonometric-functions · Mock 07 · Q15

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Minimum of $y = \cos 9x + 8$ is

Target: ~75s · ID EXAM-G7-15

Q 16/48CSCA Standardtrigonometric-functions · Mock 07 · Q16

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-G7-16

Q 17/48CSCA Standardtrigonometric-functions · Mock 07 · Q17

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

Target: ~75s · ID EXAM-G7-17

Q 18/48CSCA Standardtrigonometric-functions · Mock 07 · Q18

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

Target: ~75s · ID EXAM-G7-18

Q 19/48CSCA Standardtrigonometric-functions · Mock 07 · Q19

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

Target: ~75s · ID EXAM-G7-19

Q 20/48CSCA Standardtrigonometric-functions · Mock 07 · Q20

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

Target: ~75s · ID EXAM-G7-20

Q 21/48CSCA Standardtrigonometric-functions · Mock 07 · Q21

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$\sin 135^\circ =$

Target: ~75s · ID EXAM-G7-21

Q 22/48CSCA Standardtrigonometric-functions · Mock 07 · Q22

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

Target: ~75s · ID EXAM-G7-22

Q 23/48CSCA Standardtrigonometric-functions · Mock 07 · Q23

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

Target: ~75s · ID EXAM-G7-23

Q 24/48CSCA Standardinverse-functions · Mock 07 · Q24

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Inverse of $y = 2x - 4$ is

Target: ~75s · ID EXAM-G7-24

Q 25/48CSCA Standardarithmetic-sequences · Mock 07 · Q25

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$-1, a, 7$ arithmetic: $a =$

Target: ~75s · ID EXAM-G7-25

Q 26/48CSCA Standardarithmetic-sequences · Mock 07 · Q26

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

Target: ~75s · ID EXAM-G7-26

Q 27/48CSCA Standardarithmetic-sequences · Mock 07 · Q27

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Arithmetic with $a_7 = 5$ : $S_{13} =$

Target: ~75s · ID EXAM-G7-27

Q 28/48CSCA Standardarithmetic-sequences · Mock 07 · Q28

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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-G7-28

Q 29/48CSCA Standardgeometric-sequences · Mock 07 · Q29

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

Target: ~75s · ID EXAM-G7-29

Q 30/48CSCA Standardgeometric-sequences · Mock 07 · Q30

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

Target: ~75s · ID EXAM-G7-30

Q 31/48CSCA Standardgeometric-sequences · Mock 07 · Q31

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

Target: ~75s · ID EXAM-G7-31

Q 32/48CSCA Standardlines · Mock 07 · Q32

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

Target: ~75s · ID EXAM-G7-32

Q 33/48CSCA Standardlines · Mock 07 · Q33

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

Target: ~75s · ID EXAM-G7-33

Q 34/48CSCA Standardlines · Mock 07 · Q34

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Which line is perpendicular to $3x-6 = 0$ ?

Target: ~75s · ID EXAM-G7-34

Q 35/48CSCA Standardlines · Mock 07 · Q35

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Inclination $45^\circ$ : slope is

Target: ~75s · ID EXAM-G7-35

Q 36/48CSCA Standardlines · Mock 07 · Q36

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Slope through $A(-2,5)$ , $B(-4,0)$ :

Target: ~75s · ID EXAM-G7-36

Q 37/48CSCA Standardanalytic-geometry · Mock 07 · Q37

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-G7-37

Q 38/48CSCA Standardanalytic-geometry · Mock 07 · Q38

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Distance $P(-3,-1)$ to $Q(-1,1)$ is

Target: ~75s · ID EXAM-G7-38

Q 39/48CSCA Standardanalytic-geometry · Mock 07 · Q39

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$P(1,-5)$ ; Q symmetric about the x-axis: Q =

Target: ~75s · ID EXAM-G7-39

Q 40/48CSCA Standardcircles · Mock 07 · Q40

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

Target: ~75s · ID EXAM-G7-40

Q 41/48CSCA Standardcircles · Mock 07 · Q41

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

Target: ~75s · ID EXAM-G7-41

Q 42/48CSCA Standardparabolas · Mock 07 · Q42

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

Target: ~75s · ID EXAM-G7-42

Q 43/48CSCA Standardparabolas · Mock 07 · Q43

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

Target: ~75s · ID EXAM-G7-43

Q 44/48CSCA Standardellipses · Mock 07 · Q44

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

Target: ~75s · ID EXAM-G7-44

Q 45/48CSCA Standardhyperbolas · Mock 07 · Q45

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

Target: ~75s · ID EXAM-G7-45

Q 46/48CSCA Standardprobability · Mock 07 · Q46

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Bag: 2 red, 4 blue. One draw. $P(\text{red}) =$

Target: ~75s · ID EXAM-G7-46

Q 47/48CSCA Standardvectors · Mock 07 · Q47

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$a = (5,4)$ , $b = (15,12)$ : a and b are

Target: ~75s · ID EXAM-G7-47

Q 48/48CSCA Standardcomplex-numbers · Mock 07 · Q48

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$(z-3i)(3-i) = 10$ : $z =$

Target: ~75s · ID EXAM-G7-48

Mock 07 paper

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

A={7,8,9,10,11}A = \{7,8,9,10,11\}A={7,8,9,10,11}: which is correct?

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

x2+1x−6≥0x^2+1x-6 \ge 0x2+1x−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−2y = \sqrt{x-2}y=x−2​ is

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

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

About f(x)=x4+8f(x) = x^4 + 8f(x)=x4+8 , 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?

Minimum of y=cos⁡9x+8y = \cos 9x + 8y=cos9x+8 is

Which reduction equation is incorrect?

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

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

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

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

sin⁡135∘=\sin 135^\circ =sin135∘=

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=

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

Inverse of y=2x−4y = 2x - 4y=2x−4 is

−1,a,7-1, a, 7−1,a,7 arithmetic: a=a =a=

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

Arithmetic with a7=5a_7 = 5a7​=5: S13=S_{13} =S13​=

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 ?

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

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

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

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

Slope 222 through (1,2)(1,2)(1,2): equation is

Which line is perpendicular to 3x−6=03x-6 = 03x−6=0 ?

Inclination 45∘45^\circ45∘: slope is

Slope through A(−2,5)A(-2,5)A(−2,5) , B(−4,0)B(-4,0)B(−4,0):

Which point is in the third quadrant?

Distance P(−3,−1)P(-3,-1)P(−3,−1) to Q(−1,1)Q(-1,1)Q(−1,1) is

P(1,−5)P(1,-5)P(1,−5); Q symmetric about the x-axis: Q =

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

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

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

About parabola y2=24xy^2 = 24xy2=24x, 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: 2 red, 4 blue. One draw. P(red)=P(\text{red}) =P(red)=

a=(5,4)a = (5,4)a=(5,4), b=(15,12)b = (15,12)b=(15,12): a and b are

(z−3i)(3−i)=10(z-3i)(3-i) = 10(z−3i)(3−i)=10: z=z =z=

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

$A = \{7,8,9,10,11\}$ : which is correct?

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

$x^2+1x-6 \ge 0$ : solution set is

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

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

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

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

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

About $f(x) = x^4 + 8$ , 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?

Minimum of $y = \cos 9x + 8$ is

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

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

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

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

$\sin 135^\circ =$

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

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

Inverse of $y = 2x - 4$ is

$-1, a, 7$ arithmetic: $a =$

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

Arithmetic with $a_7 = 5$ : $S_{13} =$

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

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

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

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

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

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

Which line is perpendicular to $3x-6 = 0$ ?

Inclination $45^\circ$ : slope is

Slope through $A(-2,5)$ , $B(-4,0)$ :

Distance $P(-3,-1)$ to $Q(-1,1)$ is

$P(1,-5)$ ; Q symmetric about the x-axis: Q =

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

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

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

About parabola $y^2 = 24x$ , 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: 2 red, 4 blue. One draw. $P(\text{red}) =$

$a = (5,4)$ , $b = (15,12)$ : a and b are

$(z-3i)(3-i) = 10$ : $z =$