Practice · Jan 2026 paper

Jan 2026 paper

46 questions, in exam order. Answer, review the step-by-step solution, and log every miss.

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Progress in this paper

Q 1/46CSCA Standardsets · Jan 2026 · Q1

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

Target: ~75s · ID EXAM-E2-1

Q 2/46CSCA Standardsets · Jan 2026 · Q2

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$A = \{x | -2 \le x \le 2\}$ , $B = \{x | x > 0\}$ : $A \cup B =$

Target: ~75s · ID EXAM-E2-2

Q 3/46CSCA Standardinequalities · Jan 2026 · Q3

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

Target: ~75s · ID EXAM-E2-3

Q 4/46CSCA Standardarithmetic-sequences · Jan 2026 · Q4

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

Target: ~75s · ID EXAM-E2-4

Q 5/46CSCA Standarddomain-range · Jan 2026 · Q5

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

Target: ~75s · ID EXAM-E2-5

Q 6/46CSCA Standardanalytic-geometry · Jan 2026 · Q6

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

Target: ~75s · ID EXAM-E2-6

Q 7/46CSCA Standardeven-odd-functions · Jan 2026 · Q7

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About $f(x) = x^4 + 3$ , correct is

Target: ~75s · ID EXAM-E2-7

Q 8/46CSCA Standardinverse-functions · Jan 2026 · Q8

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Inverse of $y = x^3 + 3$ $(x \in \mathbb{R})$ is

Target: ~75s · ID EXAM-E2-8

Q 9/46CSCA Standardanalytic-geometry · Jan 2026 · Q9

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-E2-9

Q 10/46CSCA Standardmonotonicity · Jan 2026 · Q10

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About $y = |x|$ , correct is

Target: ~75s · ID EXAM-E2-10

Q 11/46CSCA Standardinequalities · Jan 2026 · Q11

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$\frac{2x+1}{x-2} \le 0$ : solution set is

Target: ~75s · ID EXAM-E2-11

Q 12/46CSCA Standardarithmetic-sequences · Jan 2026 · Q12

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Arithmetic mean of $2-\sqrt{3}$ and $2+\sqrt{3}$ is

Target: ~75s · ID EXAM-E2-12

Q 13/46CSCA Standardlines · Jan 2026 · Q13

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Line through $A(-2,3)$ , $B(3,1)$ : slope is

Target: ~75s · ID EXAM-E2-13

Q 14/46CSCA Standardlines · Jan 2026 · Q14

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Angle between x-axis and line through $P(1,3)$ : $\sin\alpha =$

Target: ~75s · ID EXAM-E2-14

Q 15/46CSCA Standardarithmetic-sequences · Jan 2026 · Q15

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How many are arithmetic: 7,13,19,25 · 2,4,7,11 · −1,−3,−5,−7 · 2,4,8,16?

Target: ~75s · ID EXAM-E2-15

Q 16/46CSCA Standardanalytic-geometry · Jan 2026 · Q16

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

Target: ~75s · ID EXAM-E2-16

Q 17/46CSCA Standardlines · Jan 2026 · Q17

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Inclination 45° through $(0,2)$ : equation is

Target: ~75s · ID EXAM-E2-17

Q 18/46CSCA Standardcircles · Jan 2026 · Q18

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Circle $x^2+y^2-4x-3 = 0$ : center and radius are

Target: ~75s · ID EXAM-E2-18

Q 19/46CSCA Standardtrigonometric-functions · Jan 2026 · Q19

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$\sin\alpha = \frac{4}{5}$ , second quadrant: correct is

Target: ~75s · ID EXAM-E2-19

Q 20/46CSCA Standardarithmetic-sequences · Jan 2026 · Q20

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Arithmetic $a_2 = 1, a_4 = 5$ : $a_1, d$ are

Target: ~75s · ID EXAM-E2-20

Q 21/46CSCA Standardinequalities · Jan 2026 · Q21

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$a, b, c$ reals. Correct is

Target: ~75s · ID EXAM-E2-21

Q 22/46CSCA Standardexponential-functions · Jan 2026 · Q22

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About $y = a^x$ : which is incorrect?

Target: ~75s · ID EXAM-E2-22

Q 23/46CSCA Standardtrigonometric-functions · Jan 2026 · Q23

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$\sin\alpha = \frac{3}{5}$ , first quadrant: $\sin 2\alpha =$

Target: ~75s · ID EXAM-E2-23

Q 24/46CSCA Standardlines · Jan 2026 · Q24

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Intersection of $3x-y+8 = 0$ , $x+2y-9 = 0$ :

Target: ~75s · ID EXAM-E2-24

Q 25/46CSCA Standardhyperbolas · Jan 2026 · Q25

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Hyperbola $\frac{x^2}{64} - \frac{y^2}{16} = 1$ : correct is

Target: ~75s · ID EXAM-E2-25

Q 26/46CSCA Standardpower-functions · Jan 2026 · Q26

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Which inequality is correct?

Target: ~75s · ID EXAM-E2-26

Q 27/46CSCA Standardcircles · Jan 2026 · Q27

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Center $(-3,2)$ , radius 4: equation is

Target: ~75s · ID EXAM-E2-27

Q 28/46CSCA Standardlogarithmic-functions · Jan 2026 · Q28

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Which log statement is incorrect?

Target: ~75s · ID EXAM-E2-28

Q 29/46CSCA Standardtrigonometric-functions · Jan 2026 · Q29

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About $y = \sin x$ : incorrect is

Target: ~75s · ID EXAM-E2-29

Q 30/46CSCA Standardparabolas · Jan 2026 · Q30

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Focus F of $y^2 = 4x$ ; P on parabola with x = 4: $|PF| =$

Target: ~75s · ID EXAM-E2-30

Q 31/46CSCA Standardlines · Jan 2026 · Q31

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$l_1: ax+(a-1)y+3=0 \perp l_2: 2x+ay-1=0$ : $a =$

Target: ~75s · ID EXAM-E2-31

Q 32/46CSCA Standardanalytic-geometry · Jan 2026 · Q32

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Distance $P(-1,2)$ to $Q(3,1)$ :

Target: ~75s · ID EXAM-E2-32

Q 33/46CSCA Standardtrigonometric-functions · Jan 2026 · Q33

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$\cos\alpha = -\frac{\sqrt{5}}{5}$ , QII: $\sin(\frac{\pi}{6}+\alpha) =$

Target: ~75s · ID EXAM-E2-33

Q 34/46CSCA Standarddomain-range · Jan 2026 · Q34

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Which pair is the same function?

Target: ~75s · ID EXAM-E2-34

Q 35/46CSCA Standardtrigonometric-functions · Jan 2026 · Q35

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$\sin\alpha = -\frac{12}{13}$ , QIII: $\cos(\frac{\alpha}{2}) =$

Target: ~75s · ID EXAM-E2-35

Q 36/46CSCA Standardtrigonometric-functions · Jan 2026 · Q36

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

Target: ~75s · ID EXAM-E2-36

Q 37/46CSCA Standardtrigonometric-functions · Jan 2026 · Q37

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Which is correct?

Target: ~75s · ID EXAM-E2-37

Q 38/46CSCA Standardtrigonometric-functions · Jan 2026 · Q38

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About $y = \tan x$ : correct is

Target: ~75s · ID EXAM-E2-38

Q 39/46CSCA Standardgeneral-term · Jan 2026 · Q39

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$-\frac{1}{5}, \frac{1}{7}, -\frac{1}{9}, \frac{1}{11}, \ldots$ : $a_n =$

Target: ~75s · ID EXAM-E2-39

Q 40/46CSCA Standardlogarithmic-functions · Jan 2026 · Q40

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$f(x) = 2 + \log_a(x-3)$ passes fixed point P:

Target: ~75s · ID EXAM-E2-40

Q 41/46CSCA Standardparabolas · Jan 2026 · Q41

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Directrix of $y^2 = -x$ is

Target: ~75s · ID EXAM-E2-41

Q 42/46CSCA Standardellipses · Jan 2026 · Q42

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Ellipse $\frac{x^2}{4} + \frac{y^2}{2} = 1$ : $|PF_1|+|PF_2| =$

Target: ~75s · ID EXAM-E2-42

Q 43/46CSCA Standardvectors · Jan 2026 · Q43

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With $AB, BC, CD$ given: collinear triple is

Target: ~75s · ID EXAM-E2-43

Q 44/46CSCA Standardlines · Jan 2026 · Q44

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Line ⊥ $x+2y+4=0$ through intersection of $x+y+1=0$ , $2x+y-1=0$ :

Target: ~75s · ID EXAM-E2-44

Q 45/46CSCA Standardcomplex-numbers · Jan 2026 · Q45

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$z$ on line $x-y=0$ , root of $x^2+mx+4=0$ : $m =$

Target: ~75s · ID EXAM-E2-45

Q 46/46CSCA Standardgeometric-sequences · Jan 2026 · Q46

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$\frac{1}{a_n} + \frac{2}{a_{n+1}} = 0$ , $b_n = |a_n|$ : $S_n$ of $b_n$ is

Target: ~75s · ID EXAM-E2-46

1 source-issue questions

These came in Jan 2026 paper but no option is correct as printed — read-only, not counted in your score.

Jan 2026 · Q47 · probability

Running apps survey: P(two picked students prefer different apps) =

Source issue: the question states no app-preference numbers — unsolvable as written.

Jan 2026 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≤2}A = \{x | -2 \le x \le 2\}A={x∣−2≤x≤2}, B={x∣x>0}B = \{x | x > 0\}B={x∣x>0}: A∪B=A \cup B =A∪B=

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

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

Domain of f(x)=1x+1−xf(x) = \frac{1}{x} + \sqrt{1-x}f(x)=x1​+1−x​ is

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

About f(x)=x4+3f(x) = x^4 + 3f(x)=x4+3, correct is

Inverse of y=x3+3y = x^3 + 3y=x3+3 (x∈R)(x \in \mathbb{R})(x∈R) is

Which point is in the third quadrant?

About y=∣x∣y = |x|y=∣x∣, correct is

2x+1x−2≤0\frac{2x+1}{x-2} \le 0x−22x+1​≤0: solution set is

Arithmetic mean of 2−32-\sqrt{3}2−3​ and 2+32+\sqrt{3}2+3​ is

Line through A(−2,3)A(-2,3)A(−2,3), B(3,1)B(3,1)B(3,1): slope is

Angle between x-axis and line through P(1,3)P(1,3)P(1,3): sin⁡α=\sin\alpha =sinα=

How many are arithmetic: 7,13,19,25 · 2,4,7,11 · −1,−3,−5,−7 · 2,4,8,16?

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

Inclination 45° through (0,2)(0,2)(0,2): equation is

Circle x2+y2−4x−3=0x^2+y^2-4x-3 = 0x2+y2−4x−3=0: center and radius are

sin⁡α=45\sin\alpha = \frac{4}{5}sinα=54​, second quadrant: correct is

Arithmetic a2=1,a4=5a_2 = 1, a_4 = 5a2​=1,a4​=5: a1,da_1, da1​,d are

a,b,ca, b, ca,b,c reals. Correct is

About y=axy = a^xy=ax: which is incorrect?

sin⁡α=35\sin\alpha = \frac{3}{5}sinα=53​, first quadrant: sin⁡2α=\sin 2\alpha =sin2α=

Intersection of 3x−y+8=03x-y+8 = 03x−y+8=0, x+2y−9=0x+2y-9 = 0x+2y−9=0:

Hyperbola x264−y216=1\frac{x^2}{64} - \frac{y^2}{16} = 164x2​−16y2​=1: correct is

Which inequality is correct?

Center (−3,2)(-3,2)(−3,2), radius 4: equation is

Which log statement is incorrect?

About y=sin⁡xy = \sin xy=sinx: incorrect is

Focus F of y2=4xy^2 = 4xy2=4x; P on parabola with x = 4: ∣PF∣=|PF| =∣PF∣=

l1:ax+(a−1)y+3=0⊥l2:2x+ay−1=0l_1: ax+(a-1)y+3=0 \perp l_2: 2x+ay-1=0l1​:ax+(a−1)y+3=0⊥l2​:2x+ay−1=0: a=a =a=

Distance P(−1,2)P(-1,2)P(−1,2) to Q(3,1)Q(3,1)Q(3,1):

cos⁡α=−55\cos\alpha = -\frac{\sqrt{5}}{5}cosα=−55​​, QII: sin⁡(π6+α)=\sin(\frac{\pi}{6}+\alpha) =sin(6π​+α)=

Which pair is the same function?

sin⁡α=−1213\sin\alpha = -\frac{12}{13}sinα=−1312​, 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​)=

Which is correct?

About y=tan⁡xy = \tan xy=tanx: correct is

−15,17,−19,111,…-\frac{1}{5}, \frac{1}{7}, -\frac{1}{9}, \frac{1}{11}, \ldots−51​,71​,−91​,111​,…: an=a_n =an​=

f(x)=2+log⁡a(x−3)f(x) = 2 + \log_a(x-3)f(x)=2+loga​(x−3) passes fixed point P:

Directrix of y2=−xy^2 = -xy2=−x is

Ellipse x24+y22=1\frac{x^2}{4} + \frac{y^2}{2} = 14x2​+2y2​=1: ∣PF1∣+∣PF2∣=|PF_1|+|PF_2| =∣PF1​∣+∣PF2​∣=

With AB,BC,CDAB, BC, CDAB,BC,CD given: collinear triple is

Line ⊥ x+2y+4=0x+2y+4=0x+2y+4=0 through intersection of x+y+1=0x+y+1=0x+y+1=0, 2x+y−1=02x+y-1=02x+y−1=0:

zzz on line x−y=0x-y=0x−y=0, root of x2+mx+4=0x^2+mx+4=0x2+mx+4=0: m=m =m=

1an+2an+1=0\frac{1}{a_n} + \frac{2}{a_{n+1}} = 0an​1​+an+1​2​=0, bn=∣an∣b_n = |a_n|bn​=∣an​∣: SnS_nSn​ of bnb_nbn​ is

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

$A = \{x | -2 \le x \le 2\}$ , $B = \{x | x > 0\}$ : $A \cup B =$

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

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

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

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

About $f(x) = x^4 + 3$ , correct is

Inverse of $y = x^3 + 3$ $(x \in \mathbb{R})$ is

About $y = |x|$ , correct is

$\frac{2x+1}{x-2} \le 0$ : solution set is

Arithmetic mean of $2-\sqrt{3}$ and $2+\sqrt{3}$ is

Line through $A(-2,3)$ , $B(3,1)$ : slope is

Angle between x-axis and line through $P(1,3)$ : $\sin\alpha =$

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

Inclination 45° through $(0,2)$ : equation is

Circle $x^2+y^2-4x-3 = 0$ : center and radius are

$\sin\alpha = \frac{4}{5}$ , second quadrant: correct is

Arithmetic $a_2 = 1, a_4 = 5$ : $a_1, d$ are

$a, b, c$ reals. Correct is

About $y = a^x$ : which is incorrect?

$\sin\alpha = \frac{3}{5}$ , first quadrant: $\sin 2\alpha =$

Intersection of $3x-y+8 = 0$ , $x+2y-9 = 0$ :

Hyperbola $\frac{x^2}{64} - \frac{y^2}{16} = 1$ : correct is

Center $(-3,2)$ , radius 4: equation is

About $y = \sin x$ : incorrect is

Focus F of $y^2 = 4x$ ; P on parabola with x = 4: $|PF| =$

$l_1: ax+(a-1)y+3=0 \perp l_2: 2x+ay-1=0$ : $a =$

Distance $P(-1,2)$ to $Q(3,1)$ :

$\cos\alpha = -\frac{\sqrt{5}}{5}$ , QII: $\sin(\frac{\pi}{6}+\alpha) =$

$\sin\alpha = -\frac{12}{13}$ , QIII: $\cos(\frac{\alpha}{2}) =$

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

About $y = \tan x$ : correct is

$-\frac{1}{5}, \frac{1}{7}, -\frac{1}{9}, \frac{1}{11}, \ldots$ : $a_n =$

$f(x) = 2 + \log_a(x-3)$ passes fixed point P:

Directrix of $y^2 = -x$ is

Ellipse $\frac{x^2}{4} + \frac{y^2}{2} = 1$ : $|PF_1|+|PF_2| =$

With $AB, BC, CD$ given: collinear triple is

Line ⊥ $x+2y+4=0$ through intersection of $x+y+1=0$ , $2x+y-1=0$ :

$z$ on line $x-y=0$ , root of $x^2+mx+4=0$ : $m =$

$\frac{1}{a_n} + \frac{2}{a_{n+1}} = 0$ , $b_n = |a_n|$ : $S_n$ of $b_n$ is