Practice · Apr 2026 paper

Apr 2026 paper

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

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Correct / answered of 45

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Progress in this paper

Q 1/45CSCA Standardsets · Apr 2026 · Q2

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$A = \{x|3<x<5\}$ , $B = \{x|x>4\}$ : $A \cap B =$

Target: ~75s · ID EXAM-E3-2

Q 2/45CSCA Standardanalytic-geometry · Apr 2026 · Q3

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Which point is in the third quadrant?

Target: ~75s · ID EXAM-E3-3

Q 3/45CSCA Standardinequalities · Apr 2026 · Q4

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

Target: ~75s · ID EXAM-E3-4

Q 4/45CSCA Standardanalytic-geometry · Apr 2026 · Q6

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M has x-coordinate −4, distance 5 from x-axis: M =

Target: ~75s · ID EXAM-E3-6

Q 5/45CSCA Standardtrigonometric-functions · Apr 2026 · Q7

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$\sin 120° =$

Target: ~75s · ID EXAM-E3-7

Q 6/45CSCA Standardeven-odd-functions · Apr 2026 · Q8

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Which is an odd function?

Target: ~75s · ID EXAM-E3-8

Q 7/45CSCA Standardlines · Apr 2026 · Q9

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

Target: ~75s · ID EXAM-E3-9

Q 8/45CSCA Standardinverse-functions · Apr 2026 · Q10

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Inverse of $y = 10x + 3$ is

Target: ~75s · ID EXAM-E3-10

Q 9/45CSCA Standardmonotonicity · Apr 2026 · Q11

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Decreasing on $(-\infty,+\infty)$ :

Target: ~75s · ID EXAM-E3-11

Q 10/45CSCA Standardinequalities · Apr 2026 · Q12

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

Target: ~75s · ID EXAM-E3-12

Q 11/45CSCA Standardarithmetic-sequences · Apr 2026 · Q13

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$-1, a, 15$ arithmetic: $a =$

Target: ~75s · ID EXAM-E3-13

Q 12/45CSCA Standardlines · Apr 2026 · Q14

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Inclination 60°: slope is

Target: ~75s · ID EXAM-E3-14

Q 13/45CSCA Standardarithmetic-sequences · Apr 2026 · Q15

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Arithmetic $a_1 = 1, a_2 = 3$ : $a_5 =$

Target: ~75s · ID EXAM-E3-15

Q 14/45CSCA Standardtrigonometric-functions · Apr 2026 · Q16

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$P(x,y)$ , $|OP| = r$ : $\cos\alpha =$

Target: ~75s · ID EXAM-E3-16

Q 15/45CSCA Standardarithmetic-sequences · Apr 2026 · Q17

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$a_n = 2n-1$ : correct is

Target: ~75s · ID EXAM-E3-17

Q 16/45CSCA Standardanalytic-geometry · Apr 2026 · Q18

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$|AB| = 5$ , $A(0,3)$ , $B(x,-1)$ : $x =$

Target: ~75s · ID EXAM-E3-18

Q 17/45CSCA Standardlines · Apr 2026 · Q19

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Slope −3 through $(1,2)$ : equation is

Target: ~75s · ID EXAM-E3-19

Q 18/45CSCA Standardcircles · Apr 2026 · Q20

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Center $(-1,2)$ , radius 3: equation is

Target: ~75s · ID EXAM-E3-20

Q 19/45CSCA Standardtrigonometric-functions · Apr 2026 · Q21

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$\cos\alpha = \frac{2}{3}$ , acute: $\tan\alpha =$

Target: ~75s · ID EXAM-E3-21

Q 20/45CSCA Standardgeometric-sequences · Apr 2026 · Q22

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Geometric $a_1 = -48, a_4 = 6$ : $q =$

Target: ~75s · ID EXAM-E3-22

Q 21/45CSCA Standardcircles · Apr 2026 · Q23

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Through $A(2,2)$ , center $(2,0)$ : equation is

Target: ~75s · ID EXAM-E3-23

Q 22/45CSCA Standardinequalities · Apr 2026 · Q24

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Rationals, $a > b$ : correct is

Target: ~75s · ID EXAM-E3-24

Q 23/45CSCA Standardexponential-functions · Apr 2026 · Q25

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$y = a^x$ decreasing: range of $a$ is

Target: ~75s · ID EXAM-E3-25

Q 24/45CSCA Standardtrigonometric-functions · Apr 2026 · Q26

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$\sin\alpha = \frac{3}{4}$ : $\cos 2\alpha =$

Target: ~75s · ID EXAM-E3-26

Q 25/45CSCA Standardlines · Apr 2026 · Q27

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Intersection of $3x-y+2=0$ , $4x-y+3=0$ :

Target: ~75s · ID EXAM-E3-27

Q 26/45CSCA Standardhyperbolas · Apr 2026 · Q28

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Hyperbola $\frac{x^2}{a^2}-\frac{y^2}{3} = 1$ , $e = 2$ : $a =$

Target: ~75s · ID EXAM-E3-28

Q 27/45CSCA Standardgeometric-sequences · Apr 2026 · Q29

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

Target: ~75s · ID EXAM-E3-29

Q 28/45CSCA Standardtrigonometric-functions · Apr 2026 · Q31

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Minimum of $y = \cos 5x + 4$ is

Target: ~75s · ID EXAM-E3-31

Q 29/45CSCA Standardpower-functions · Apr 2026 · Q32

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Parabola $y = ax^2$ through $(1,2)$ : $a =$

Target: ~75s · ID EXAM-E3-32

Q 30/45CSCA Standardlines · Apr 2026 · Q33

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Perpendicular to $-2x+y-2 = 0$ :

Target: ~75s · ID EXAM-E3-33

Q 31/45CSCA Standardtrigonometric-functions · Apr 2026 · Q34

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

Target: ~75s · ID EXAM-E3-34

Q 32/45CSCA Standardtrigonometric-functions · Apr 2026 · Q35

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$\cos 75° =$

Target: ~75s · ID EXAM-E3-35

Q 33/45CSCA Standarddomain-range · Apr 2026 · Q36

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$f$ domain $(-1,0)$ : domain of $f(x^2-1)$ is

Target: ~75s · ID EXAM-E3-36

Q 34/45CSCA Standardtrigonometric-functions · Apr 2026 · Q37

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

Target: ~75s · ID EXAM-E3-37

Q 35/45CSCA Standardtrigonometric-functions · Apr 2026 · Q38

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Which equation is correct?

Target: ~75s · ID EXAM-E3-38

Q 36/45CSCA Standardtrigonometric-functions · Apr 2026 · Q39

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Min positive period of $y = 2\tan(3x+\frac{\pi}{4})$ is

Target: ~75s · ID EXAM-E3-39

Q 37/45CSCA Standardellipses · Apr 2026 · Q40

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Ellipse, foci on y-axis, focal length 4, $e = \frac{2}{3}$ : equation is

Target: ~75s · ID EXAM-E3-40

Q 38/45CSCA Standardrecursive-sequences · Apr 2026 · Q41

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$a_n = (-1)^n\cdot2\cdot a_{n-1}$ , $a_1 = \frac{1}{3}$ : $a_4 =$

Target: ~75s · ID EXAM-E3-41

Q 39/45CSCA Standarddomain-range · Apr 2026 · Q42

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Domain of $y = \frac{1}{\lg|x-5|}$ is

Target: ~75s · ID EXAM-E3-42

Q 40/45CSCA Standardellipses · Apr 2026 · Q43

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Same foci as $\frac{x^2}{4}+\frac{y^2}{9} = 1$ , minor axis $4\sqrt{5}$ : equation is

Target: ~75s · ID EXAM-E3-43

Q 41/45CSCA Standardvectors · Apr 2026 · Q44

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Square ABCD, E midpoint of CD, $AB = a$ , $AD = b$ : $BE =$

Target: ~75s · ID EXAM-E3-44

Q 42/45CSCA Standardgeometric-sequences · Apr 2026 · Q45

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$2S_n = 3a_{n+1}-3$ : $S_n =$

Target: ~75s · ID EXAM-E3-45

Q 43/45CSCA Standardcomplex-numbers · Apr 2026 · Q46

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$(z-2i)(2-i) = 5$ : $z =$

Target: ~75s · ID EXAM-E3-46

Q 44/45CSCA Standardgeometric-sequences · Apr 2026 · Q47

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$S_n = \frac23 a_n + \frac13$ : $a_n =$

Target: ~75s · ID EXAM-E3-47

Q 45/45CSCA Standardprobability · Apr 2026 · Q48

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12 balls: P(red)=1/3, P(yellow or green)=5/12, P(black or yellow)=5/12: P(yellow, black, green) =

Target: ~75s · ID EXAM-E3-48

3 source-issue questions

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

Apr 2026 · Q1 · sets

$A = \{1,3,4,6,7\}$, $B = \{1,3,5\}$: correct is

Source issue: no option is correct (5 ∉ A).

Apr 2026 · Q5 · domain-range

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

Source issue: [−1, +∞) appears in no option.

Apr 2026 · Q30 · logarithmic-functions

$(\log_3 27)(\log_{64} 16) =$

Source issue: true value 2 appears in no option.

Apr 2026 paper

A={x∣3<x<5}A = \{x|3<x<5\}A={x∣3<x<5}, B={x∣x>4}B = \{x|x>4\}B={x∣x>4}: A∩B=A \cap B =A∩B=

Which point is in the third quadrant?

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

M has x-coordinate −4, distance 5 from x-axis: M =

sin⁡120°=\sin 120° =sin120°=

Which is an odd function?

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

Inverse of y=10x+3y = 10x + 3y=10x+3 is

Decreasing on (−∞,+∞)(-\infty,+\infty)(−∞,+∞):

2x+1x−1<0\frac{2x+1}{x-1} < 0x−12x+1​<0: solution set is

−1,a,15-1, a, 15−1,a,15 arithmetic: a=a =a=

Inclination 60°: slope is

Arithmetic a1=1,a2=3a_1 = 1, a_2 = 3a1​=1,a2​=3: a5=a_5 =a5​=

P(x,y)P(x,y)P(x,y), ∣OP∣=r|OP| = r∣OP∣=r: cos⁡α=\cos\alpha =cosα=

an=2n−1a_n = 2n-1an​=2n−1: correct is

∣AB∣=5|AB| = 5∣AB∣=5, A(0,3)A(0,3)A(0,3), B(x,−1)B(x,-1)B(x,−1): x=x =x=

Slope −3 through (1,2)(1,2)(1,2): equation is

Center (−1,2)(-1,2)(−1,2), radius 3: equation is

cos⁡α=23\cos\alpha = \frac{2}{3}cosα=32​, acute: tan⁡α=\tan\alpha =tanα=

Geometric a1=−48,a4=6a_1 = -48, a_4 = 6a1​=−48,a4​=6: q=q =q=

Through A(2,2)A(2,2)A(2,2), center (2,0)(2,0)(2,0): equation is

Rationals, a>ba > ba>b: correct is

y=axy = a^xy=ax decreasing: range of aaa is

sin⁡α=34\sin\alpha = \frac{3}{4}sinα=43​: cos⁡2α=\cos 2\alpha =cos2α=

Intersection of 3x−y+2=03x-y+2=03x−y+2=0, 4x−y+3=04x-y+3=04x−y+3=0:

Hyperbola x2a2−y23=1\frac{x^2}{a^2}-\frac{y^2}{3} = 1a2x2​−3y2​=1, e=2e = 2e=2: a=a =a=

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

Minimum of y=cos⁡5x+4y = \cos 5x + 4y=cos5x+4 is

Parabola y=ax2y = ax^2y=ax2 through (1,2)(1,2)(1,2): a=a =a=

Perpendicular to −2x+y−2=0-2x+y-2 = 0−2x+y−2=0:

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

cos⁡75°=\cos 75° =cos75°=

fff domain (−1,0)(-1,0)(−1,0): domain of f(x2−1)f(x^2-1)f(x2−1) is

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

Which equation is correct?

Min positive period of y=2tan⁡(3x+π4)y = 2\tan(3x+\frac{\pi}{4})y=2tan(3x+4π​) is

Ellipse, foci on y-axis, focal length 4, e=23e = \frac{2}{3}e=32​: equation is

an=(−1)n⋅2⋅an−1a_n = (-1)^n\cdot2\cdot a_{n-1}an​=(−1)n⋅2⋅an−1​, a1=13a_1 = \frac{1}{3}a1​=31​: a4=a_4 =a4​=

Domain of y=1lg⁡∣x−5∣y = \frac{1}{\lg|x-5|}y=lg∣x−5∣1​ is

Same foci as x24+y29=1\frac{x^2}{4}+\frac{y^2}{9} = 14x2​+9y2​=1, minor axis 454\sqrt{5}45​: equation is

Square ABCD, E midpoint of CD, AB=aAB = aAB=a, AD=bAD = bAD=b: BE=BE =BE=

2Sn=3an+1−32S_n = 3a_{n+1}-32Sn​=3an+1​−3: Sn=S_n =Sn​=

(z−2i)(2−i)=5(z-2i)(2-i) = 5(z−2i)(2−i)=5: z=z =z=

Sn=23an+13S_n = \frac23 a_n + \frac13Sn​=32​an​+31​: an=a_n =an​=

12 balls: P(red)=1/3, P(yellow or green)=5/12, P(black or yellow)=5/12: P(yellow, black, green) =

$A = \{x|3<x<5\}$ , $B = \{x|x>4\}$ : $A \cap B =$

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

$\sin 120° =$

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

Inverse of $y = 10x + 3$ is

Decreasing on $(-\infty,+\infty)$ :

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

$-1, a, 15$ arithmetic: $a =$

Arithmetic $a_1 = 1, a_2 = 3$ : $a_5 =$

$P(x,y)$ , $|OP| = r$ : $\cos\alpha =$

$a_n = 2n-1$ : correct is

$|AB| = 5$ , $A(0,3)$ , $B(x,-1)$ : $x =$

Slope −3 through $(1,2)$ : equation is

Center $(-1,2)$ , radius 3: equation is

$\cos\alpha = \frac{2}{3}$ , acute: $\tan\alpha =$

Geometric $a_1 = -48, a_4 = 6$ : $q =$

Through $A(2,2)$ , center $(2,0)$ : equation is

Rationals, $a > b$ : correct is

$y = a^x$ decreasing: range of $a$ is

$\sin\alpha = \frac{3}{4}$ : $\cos 2\alpha =$

Intersection of $3x-y+2=0$ , $4x-y+3=0$ :

Hyperbola $\frac{x^2}{a^2}-\frac{y^2}{3} = 1$ , $e = 2$ : $a =$

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

Minimum of $y = \cos 5x + 4$ is

Parabola $y = ax^2$ through $(1,2)$ : $a =$

Perpendicular to $-2x+y-2 = 0$ :

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

$\cos 75° =$

$f$ domain $(-1,0)$ : domain of $f(x^2-1)$ is

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

Min positive period of $y = 2\tan(3x+\frac{\pi}{4})$ is

Ellipse, foci on y-axis, focal length 4, $e = \frac{2}{3}$ : equation is

$a_n = (-1)^n\cdot2\cdot a_{n-1}$ , $a_1 = \frac{1}{3}$ : $a_4 =$

Domain of $y = \frac{1}{\lg|x-5|}$ is

Same foci as $\frac{x^2}{4}+\frac{y^2}{9} = 1$ , minor axis $4\sqrt{5}$ : equation is

Square ABCD, E midpoint of CD, $AB = a$ , $AD = b$ : $BE =$

$2S_n = 3a_{n+1}-3$ : $S_n =$

$(z-2i)(2-i) = 5$ : $z =$

$S_n = \frac23 a_n + \frac13$ : $a_n =$