Practice · Dec 2025 paper

Dec 2025 paper

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

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Progress in this paper

Q 1/44CSCA Standardsets · Dec 2025 · Q1

Elapsed: 0:00

If sets $A = \{1,2\}$ , $B = \{1,2,3\}$ , then

Target: ~75s · ID EXAM-E1-1

Q 2/44CSCA Standardsets · Dec 2025 · Q2

Elapsed: 0:00

If sets $A = (-1,3)$ , $B = [2,4]$ , then $A \cap B =$

Target: ~75s · ID EXAM-E1-2

Q 3/44CSCA Standardinequalities · Dec 2025 · Q3

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The solution set of $x^2 - 5x + 4 < 0$ is

Target: ~75s · ID EXAM-E1-3

Q 4/44CSCA Standardarithmetic-sequences · Dec 2025 · Q5

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

Target: ~75s · ID EXAM-E1-5

Q 5/44CSCA Standardanalytic-geometry · Dec 2025 · Q6

Elapsed: 0:00

The point $(-1, 3-\pi)$ lies in which quadrant?

Target: ~75s · ID EXAM-E1-6

Q 6/44CSCA Standardtrigonometric-functions · Dec 2025 · Q7

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$(\sin(\frac{\pi}{4}) + \cos(\frac{\pi}{4})) \times \tan(\frac{\pi}{4}) =$

Target: ~75s · ID EXAM-E1-7

Q 7/44CSCA Standardeven-odd-functions · Dec 2025 · Q8

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Which is an odd function?

Target: ~75s · ID EXAM-E1-8

Q 8/44CSCA Standardpower-functions · Dec 2025 · Q9

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The inverse function of $y = x^3$ is

Target: ~75s · ID EXAM-E1-9

Q 9/44CSCA Standardmonotonicity · Dec 2025 · Q10

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Which function is strictly increasing?

Target: ~75s · ID EXAM-E1-10

Q 10/44CSCA Standardanalytic-geometry · Dec 2025 · Q11

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Which point lies in the third quadrant?

Target: ~75s · ID EXAM-E1-11

Q 11/44CSCA Standardinequalities · Dec 2025 · Q12

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The solution set of $\frac{x-1}{x-2} \le 1$ is

Target: ~75s · ID EXAM-E1-12

Q 12/44CSCA Standardarithmetic-sequences · Dec 2025 · Q13

Elapsed: 0:00

$a, b, c$ arithmetic with $a + c = 20$ : then $b =$

Target: ~75s · ID EXAM-E1-13

Q 13/44CSCA Standardlines · Dec 2025 · Q14

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The inclination angle of $y = \sqrt{3}x + 10$ is

Target: ~75s · ID EXAM-E1-14

Q 14/44CSCA Standardexponential-functions · Dec 2025 · Q15

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Which inequality is correct?

Target: ~75s · ID EXAM-E1-15

Q 15/44CSCA Standardtrigonometric-functions · Dec 2025 · Q16

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$P(1, y)$ on terminal side of $\alpha$ , $\tan\alpha = 2$ : then $y =$

Target: ~75s · ID EXAM-E1-16

Q 16/44CSCA Standardarithmetic-sequences · Dec 2025 · Q17

Elapsed: 0:00

Arithmetic $a_1 = 1, a_2 = 2$ : then $a_{2025} =$

Target: ~75s · ID EXAM-E1-17

Q 17/44CSCA Standardcircles · Dec 2025 · Q18

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

Target: ~75s · ID EXAM-E1-18

Q 18/44CSCA Standardtrigonometric-functions · Dec 2025 · Q19

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

Target: ~75s · ID EXAM-E1-19

Q 19/44CSCA Standarddomain-range · Dec 2025 · Q20

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Domain of $y = \sqrt{x-1}$ is

Target: ~75s · ID EXAM-E1-20

Q 20/44CSCA Standardcircles · Dec 2025 · Q21

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Circle $x^2+y^2+2x-2y = 0$ : radius is

Target: ~75s · ID EXAM-E1-21

Q 21/44CSCA Standardgeometric-sequences · Dec 2025 · Q23

Elapsed: 0:00

Geometric 1, 2, 4: general term is

Target: ~75s · ID EXAM-E1-23

Q 22/44CSCA Standardexponential-functions · Dec 2025 · Q24

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Given $a > b$ , then

Target: ~75s · ID EXAM-E1-24

Q 23/44CSCA Standardanalytic-geometry · Dec 2025 · Q25

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

Target: ~75s · ID EXAM-E1-25

Q 24/44CSCA Standardexponential-functions · Dec 2025 · Q26

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Which describes $y = (\frac{1}{2})^x$ ?

Target: ~75s · ID EXAM-E1-26

Q 25/44CSCA Standardtrigonometric-functions · Dec 2025 · Q27

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$\sin\alpha = \frac{1}{4}$ : $\cos 2\alpha =$

Target: ~75s · ID EXAM-E1-27

Q 26/44CSCA Standardlines · Dec 2025 · Q28

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Intersection of $y = 2x+1$ and $x+y+1 = 0$ is

Target: ~75s · ID EXAM-E1-28

Q 27/44CSCA Standardhyperbolas · Dec 2025 · Q29

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Foci of $x^2 - y^2 = 1$ are

Target: ~75s · ID EXAM-E1-29

Q 28/44CSCA Standardtrigonometric-functions · Dec 2025 · Q31

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

Target: ~75s · ID EXAM-E1-31

Q 29/44CSCA Standardparabolas · Dec 2025 · Q32

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

Target: ~75s · ID EXAM-E1-32

Q 30/44CSCA Standardlines · Dec 2025 · Q33

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Which line is perpendicular to $x + y + 3 = 0$ ?

Target: ~75s · ID EXAM-E1-33

Q 31/44CSCA Standardtrigonometric-functions · Dec 2025 · Q34

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

Target: ~75s · ID EXAM-E1-34

Q 32/44CSCA Standardtrigonometric-functions · Dec 2025 · Q35

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Deduce $\cos(\frac{\pi}{12})$ =

Target: ~75s · ID EXAM-E1-35

Q 33/44CSCA Standarddomain-range · Dec 2025 · Q36

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

Target: ~75s · ID EXAM-E1-36

Q 34/44CSCA Standardtrigonometric-functions · Dec 2025 · Q37

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

Target: ~75s · ID EXAM-E1-37

Q 35/44CSCA Standardtrigonometric-functions · Dec 2025 · Q38

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Which reduction equation is incorrect?

Target: ~75s · ID EXAM-E1-38

Q 36/44CSCA Standardparabolas · Dec 2025 · Q39

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Directrix of $y^2 = -x$ is

Target: ~75s · ID EXAM-E1-39

Q 37/44CSCA Standardtrigonometric-functions · Dec 2025 · Q40

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$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{3}$ : $\tan\alpha =$

Target: ~75s · ID EXAM-E1-40

Q 38/44CSCA Standardrecursive-sequences · Dec 2025 · Q41

Elapsed: 0:00

$a_1 = 1$ , $a_n = \frac{1}{1+\frac{1}{a_{n-1}}}$ : $a_{100} =$

Target: ~75s · ID EXAM-E1-41

Q 39/44CSCA Standardlogarithmic-functions · Dec 2025 · Q42

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

Target: ~75s · ID EXAM-E1-42

Q 40/44CSCA Standardellipses · Dec 2025 · Q43

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About ellipse $\frac{x^2}{4} + \frac{y^2}{20} = 1$ , correct is

Target: ~75s · ID EXAM-E1-43

Q 41/44CSCA Standardlines · Dec 2025 · Q44

Elapsed: 0:00

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

Target: ~75s · ID EXAM-E1-44

Q 42/44CSCA Standardcomplex-numbers · Dec 2025 · Q46

Elapsed: 0:00

$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{999} =$

Target: ~75s · ID EXAM-E1-46

Q 43/44CSCA Standardarithmetic-sequences · Dec 2025 · Q47

Elapsed: 0:00

Arithmetic: $3(a_2+a_6)+2(a_6+a_{10}+a_{14}) = 24$ : $S_{13} =$

Target: ~75s · ID EXAM-E1-47

Q 44/44CSCA Standardprobability · Dec 2025 · Q48

Elapsed: 0:00

Zodiac: P(at least two of three share an animal) =

Target: ~75s · ID EXAM-E1-48

4 source-issue questions

These came in Dec 2025 paper but no option is correct as printed — read-only, not counted in your score.

Dec 2025 · Q4 · domain-range

The domain of $y = 1/(x+1)$ is

Source issue: no option shows the full domain (−∞, −1) ∪ (−1, ∞).

Dec 2025 · Q22 · trigonometric-functions

Acute $\alpha$, $\sin\alpha = \sqrt{3}/2$: $\tan\alpha =$

Source issue: tan 60° = √3 appears in no option.

Dec 2025 · Q30 · logarithmic-functions

$\log_2 32 + \log_3 32 =$

Source issue: likely a typo; unsolvable as written.

Dec 2025 · Q45 · vectors

P midpoint of AB: vector $OP =$

Source issue: correct (OA+OB)/2 absent; A and C duplicate.

Dec 2025 paper

If sets A={1,2}A = \{1,2\}A={1,2}, B={1,2,3}B = \{1,2,3\}B={1,2,3}, then

If sets A=(−1,3)A = (-1,3)A=(−1,3), B=[2,4]B = [2,4]B=[2,4], then A∩B=A \cap B =A∩B=

The solution set of x2−5x+4<0x^2 - 5x + 4 < 0x2−5x+4<0 is

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

The point (−1,3−π)(-1, 3-\pi)(−1,3−π) lies in which quadrant?

(sin⁡(π4)+cos⁡(π4))×tan⁡(π4)=(\sin(\frac{\pi}{4}) + \cos(\frac{\pi}{4})) \times \tan(\frac{\pi}{4}) =(sin(4π​)+cos(4π​))×tan(4π​)=

Which is an odd function?

The inverse function of y=x3y = x^3y=x3 is

Which function is strictly increasing?

Which point lies in the third quadrant?

The solution set of x−1x−2≤1\frac{x-1}{x-2} \le 1x−2x−1​≤1 is

a,b,ca, b, ca,b,c arithmetic with a+c=20a + c = 20a+c=20: then b=b =b=

The inclination angle of y=3x+10y = \sqrt{3}x + 10y=3​x+10 is

Which inequality is correct?

P(1,y)P(1, y)P(1,y) on terminal side of α\alphaα, tan⁡α=2\tan\alpha = 2tanα=2: then y=y =y=

Arithmetic a1=1,a2=2a_1 = 1, a_2 = 2a1​=1,a2​=2: then a2025=a_{2025} =a2025​=

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

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

Domain of y=x−1y = \sqrt{x-1}y=x−1​ is

Circle x2+y2+2x−2y=0x^2+y^2+2x-2y = 0x2+y2+2x−2y=0: radius is

Geometric 1, 2, 4: general term is

Given a>ba > ba>b, then

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

Which describes y=(12)xy = (\frac{1}{2})^xy=(21​)x?

sin⁡α=14\sin\alpha = \frac{1}{4}sinα=41​: cos⁡2α=\cos 2\alpha =cos2α=

Intersection of y=2x+1y = 2x+1y=2x+1 and x+y+1=0x+y+1 = 0x+y+1=0 is

Foci of x2−y2=1x^2 - y^2 = 1x2−y2=1 are

About y=cos⁡xy = \cos xy=cosx, which is correct?

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

Which line is perpendicular to x+y+3=0x + y + 3 = 0x+y+3=0?

cos⁡α=−12\cos\alpha = -\frac{1}{2}cosα=−21​, α∈(π2,π)\alpha \in (\frac{\pi}{2},\pi)α∈(2π​,π): sin⁡(α2)=\sin(\frac{\alpha}{2}) =sin(2α​)=

Deduce cos⁡(π12)\cos(\frac{\pi}{12})cos(12π​) =

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

Acute α\alphaα, cos⁡α=12\cos\alpha = \frac{1}{2}cosα=21​: sin⁡(α2)=\sin(\frac{\alpha}{2}) =sin(2α​)=

Which reduction equation is incorrect?

Directrix of y2=−xy^2 = -xy2=−x is

cos⁡α−sin⁡αcos⁡α+sin⁡α=13\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{3}cosα+sinαcosα−sinα​=31​: tan⁡α=\tan\alpha =tanα=

a1=1a_1 = 1a1​=1, an=11+1an−1a_n = \frac{1}{1+\frac{1}{a_{n-1}}}an​=1+an−1​1​1​: a100=a_{100} =a100​=

About y=log⁡axy = \log_a xy=loga​x, which is correct?

About ellipse x24+y220=1\frac{x^2}{4} + \frac{y^2}{20} = 14x2​+20y2​=1, correct 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:

z3=1z^3 = 1z3=1, z≠1z \ne 1z=1: 1+z+⋯+z999=1+z+\cdots+z^{999} =1+z+⋯+z999=

Arithmetic: 3(a2+a6)+2(a6+a10+a14)=243(a_2+a_6)+2(a_6+a_{10}+a_{14}) = 243(a2​+a6​)+2(a6​+a10​+a14​)=24: S13=S_{13} =S13​=

Zodiac: P(at least two of three share an animal) =

If sets $A = \{1,2\}$ , $B = \{1,2,3\}$ , then

If sets $A = (-1,3)$ , $B = [2,4]$ , then $A \cap B =$

The solution set of $x^2 - 5x + 4 < 0$ is

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

The point $(-1, 3-\pi)$ lies in which quadrant?

$(\sin(\frac{\pi}{4}) + \cos(\frac{\pi}{4})) \times \tan(\frac{\pi}{4}) =$

The inverse function of $y = x^3$ is

The solution set of $\frac{x-1}{x-2} \le 1$ is

$a, b, c$ arithmetic with $a + c = 20$ : then $b =$

The inclination angle of $y = \sqrt{3}x + 10$ is

$P(1, y)$ on terminal side of $\alpha$ , $\tan\alpha = 2$ : then $y =$

Arithmetic $a_1 = 1, a_2 = 2$ : then $a_{2025} =$

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

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

Domain of $y = \sqrt{x-1}$ is

Circle $x^2+y^2+2x-2y = 0$ : radius is

Given $a > b$ , then

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

Which describes $y = (\frac{1}{2})^x$ ?

$\sin\alpha = \frac{1}{4}$ : $\cos 2\alpha =$

Intersection of $y = 2x+1$ and $x+y+1 = 0$ is

Foci of $x^2 - y^2 = 1$ are

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

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

Which line is perpendicular to $x + y + 3 = 0$ ?

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

Deduce $\cos(\frac{\pi}{12})$ =

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

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

Directrix of $y^2 = -x$ is

$\frac{\cos\alpha-\sin\alpha}{\cos\alpha+\sin\alpha} = \frac{1}{3}$ : $\tan\alpha =$

$a_1 = 1$ , $a_n = \frac{1}{1+\frac{1}{a_{n-1}}}$ : $a_{100} =$

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

About ellipse $\frac{x^2}{4} + \frac{y^2}{20} = 1$ , correct is

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

$z^3 = 1$ , $z \ne 1$ : $1+z+\cdots+z^{999} =$

Arithmetic: $3(a_2+a_6)+2(a_6+a_{10}+a_{14}) = 24$ : $S_{13} =$