Diagnostic Test

Diagnostic Test
Diagnostic math test is a comprehensive assessment that evaluates a student’s current level of math proficiency. Designed to identify areas of strength and weakness, it provides valuable insights that can guide targeted instruction and personalized learning plans. This test is an essential tool for determining a student’s math level and understanding their readiness for more advanced math topics. The test is typically comprised of a range of math problems and exercises, covering fundamental concepts such as arithmetic, algebra, geometry, and more advanced topics such as calculus and statistics. With its ability to provide a precise assessment of a student’s math abilities, a diagnostic math test is a powerful tool for educators and learners alike. By identifying areas that need improvement and building on areas of strength, students can gain the confidence and skills needed to succeed in their math education and beyond.

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Categories

Absolute value equations and inequalities 0%

Circles 0%

Complex numbers 0%

Coordinate geometry 0%

Data analysis I 0%

Data analysis II 0%

Factors and divisibility and zeros of a function 0%

Isolation 0%

Linear functions 0%

Log 0%

Percentages and ratios 0%

Plane geometry 0%

Probability 0%

Quadratic equations 0%

Quadratic functions 0%

Simple Equations and Simplify Expression 0%

Solid geometry 0%

System of equations 0%

System of inequalities 0%

Trigonometry 0%

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Current

Review

Answered

Correct

Incorrect

Question 1 of 74

1. Question

Category: Simple Equations and Simplify Expression

$
\begin{aligned}
&\text { If } 2 x+3 y=8+3 y \\
&\text { then } x=\ldots \ldots .
\end{aligned}
$

$ 2 $

$ 3 $

$ 4 $

$ 8 $

Correct

Incorrect

Question 2 of 74

2. Question

Category: Simple Equations and Simplify Expression

$
\begin{aligned}
&\text { If } 2 x+3 a=8 \\
&\text { then } 4 x+6 a+5=\ldots \ldots
\end{aligned}
$

$ 21 $

$ 16 $

$ 13 $

$ 3 $

Correct

Incorrect

Question 3 of 74

3. Question

Category: System of equations

$
\begin{aligned}
&\text { If } \begin{array}{c}
2 x+3 y=7 \\
4 x+3 y=23 \\
\text { then } x+y=\ldots \ldots
\end{array}
\end{aligned}
$

$ 30 $

$ 16 $

$ 12 $

$ 5 $

Correct

Incorrect

Question 4 of 74

4. Question

Category: System of equations

$
\begin{aligned}
&\text { If } \begin{array}{c}
2 x+3 y=8 \\
x+ y=3 \\
\text { then } y=\ldots \ldots
\end{array}
\end{aligned}
$

$ 1 $

$ 2 $

$ 3 $

$ 5 $

Correct

Incorrect

Question 5 of 74

5. Question

Category: Simple Equations and Simplify Expression

$
\frac{3}{x-2}+\frac{4}{2(x-2)}=\ldots \ldots
$

$
\frac{5}{x-2}
$

$
\frac{10}{x-2}
$

$
\frac{11}{x-2}
$

$
\frac{11}{2 x-4}
$

Correct

Incorrect

Question 6 of 74

6. Question

Category: Simple Equations and Simplify Expression

$
\begin{aligned}
&\text { If the equations } 3 x+2 y=11\\
&\text { and } k x+8 y=3
\end{aligned}
$

$
\text { have no solution, find } k
$

$
\frac{3}{2}
$

6

9

12

Correct

Incorrect

Question 7 of 74

7. Question

Category: System of equations

$
\text { If the system of equations }
$

$
\begin{aligned}
&a x+b y=12 \\
&3 x+4 y=5
\end{aligned}
$

$
\text { has infinitely many solutions, find } \frac{a}{b}
$

$
\frac{3}{4}
$

$ \frac{4}{3} $

$ 12 $

$ 6 $

Correct

Incorrect

Question 8 of 74

8. Question

Category: Quadratic equations

$
\text { If }
$

$
(2 x+3)(a x+b)=8 x^{2}+c x+6
$

$
\text { then } c=\ldots \ldots
$

$ 4 $

$ 12 $

$ 16 $

$ 20 $

Correct

Incorrect

Question 9 of 74

9. Question

Category: Quadratic equations

$
\text { If }(x+c)(x+b)=x^{2}+m x+6
$

$
\text { then } m \text { is equal to }
$

$
\text { (} b, c \text { are two positive numbers)…. }
$

$
3 \text { or } 4
$

$ 7 \text { or } 8 $

$ 5 \text { or } 7 $

$ 2 \text { or } 3 $

Correct

Incorrect

Question 10 of 74

10. Question

Category: Isolation

$
\begin{aligned}
&\text { If } \frac{x+y}{z-y}=w \\
&\text { then } x=\ldots \ldots .
\end{aligned}
$

$
wz-w y
$

$ wz-w$

$ w z-w y-y $

$ w z-w y+y $

Correct

Incorrect

Question 11 of 74

11. Question

Category: Isolation

$
\begin{aligned}
&\text { If } \frac{a+b}{c+d}=\frac{a}{d} \\
&\text { then } a=\ldots .
\end{aligned}
$

$
\frac{b c}{d}
$

$
\frac{b d}{c}
$

$
\frac{b d+b c}{d}
$

$
\frac{a(c+d)}{d}
$

Correct

Incorrect

Question 12 of 74

12. Question

Category: Quadratic equations

$
\text { Which of the following are }
$

$
\text { the values of } x \text { in the equation : }
$

$
x^{2}-8 x-20=0 ?
$

$
2,10
$

$ -2,10 $

$ 2,-10 $

$ -4,5 $

Correct

Incorrect

Question 13 of 74

13. Question

Category: Quadratic equations

$
\text { Which of the following are }
$

$
\text { the values of } x \text { it }
$

$
x^{2}-3 x-2=0 ?
$

$
1,2
$

$ 3 \pm \sqrt{17} $

$ \frac{-3 \pm \sqrt{17}}{2} $

$ \frac{3 \pm \sqrt{17}}{2} $

Correct

Incorrect

Question 14 of 74

14. Question

Category: Quadratic equations

$
\text { If } x^{2}-6 x+7=0
$

$
\text { then the solution }
$

$
\text { of the equation is …. }
$

$
7,1
$

$ 3 \pm \sqrt{8} $

$ 3 \pm \sqrt{2} $

$ -3 \pm \sqrt{2} $

Correct

Incorrect

Question 15 of 74

15. Question

Category: Quadratic equations

$
\text { If } k, l \text { are the two solutions }
$

$
\text { of the equation }
$

$
2 x^{2}-8 x+13=0
$

$
\text { then } k+l=\ldots
$

$
-4
$

$ 4 $

$ 8 $

$ -8 $

Correct

Incorrect

Question 16 of 74

16. Question

Category: Quadratic equations

$
\text { If the equation } x^{2}-8 x+k=0
$

$
\text { has two equal solutions, find } k
$

$ 16 $

$ 32 $

$ 64 $

$ 80 $

Correct

Incorrect

Question 17 of 74

17. Question

Category: Absolute value equations and inequalities

$
\begin{aligned}
&\text { If }|x-5|=3 \\
&\text { then } x=\ldots \ldots .
\end{aligned}
$

$
8 \text { only }
$

$
8 \text { or }-8
$

$
2 \text { or }-8
$

$
2 \text { or } 8
$

Correct

Incorrect

Question 18 of 74

18. Question

Category: Absolute value equations and inequalities

A

B

C

D

Correct

Incorrect

Question 19 of 74

19. Question

Category: Absolute value equations and inequalities

$
\text { If the accepted length of produced }
$

$
\text { item lies between } 3.2 \text { and } 3.6 \text {, }
$

$
\text { which of the following is a suitable }
$

$
\text { inequality to represent the accepted }
$

$
\text { length? }
$

$
|x| \leq 3.2
$

$ |x-3.2| \leq 3.6 $

$ |x-3.4| \leq 0.2 $

$ |x-3.4| \geq 0.2 $

Correct

Incorrect

Question 20 of 74

20. Question

Category: System of inequalities

$
\text {The solution of the inequality }
$

$
2 x+y \geq 3 \text { doesn’t contain }
$

$
\text {any points from the …. quad}
$

$
1^{s t}
$

$ 2^{n d} $

$ 3^{r d} $

$ 4^{t h} $

Correct

Incorrect

Question 21 of 74

21. Question

Category: System of inequalities

$
\text {The solution of the system of}
$

$
\text {inequalities}
$

$
\begin{aligned}
&y \geq 2 x+1 \\
&x+2 y \geq 3
\end{aligned}
$

$
\text {lies completely in the ….. quad. }
$

$
I
$

$ I,II $

$ II,III $

$ IV $

Correct

Incorrect

Question 22 of 74

22. Question

Category: Linear functions

$
\text { If } f(x)=3 x+8, f(m)=50 \text {, find } m
$

$ 14 $

$ 18 $

$ 24 $

$ 158 $

Correct

Incorrect

Question 23 of 74

23. Question

Category: Linear functions

$
\text { If } f(x) \text { is a linear function }
$

$
f(3)=8, f(5)=11
$

$
\text { then } f(7)=\ldots
$

$ 14 $

$ 15 $

$ 19 $

$ 21 $

Correct

Incorrect

Question 24 of 74

24. Question

Category: Linear functions

$
\begin{aligned}
&\text { If } f(x)=2 x+3, g(x)=3 x-1 \\
&\text { then } f(g(2))=\ldots \ldots .
\end{aligned}
$

$ 5 $

$ 7 $

$ 13 $

$ 20 $

Correct

Incorrect

Question 25 of 74

25. Question

Category: Quadratic functions

$
\text { Which of the following represent }
$

$
\text { the form of the quadratic function }
$

$
\text { representing its vertex }
$

$
\text { as a constant or coefficient? }
$

$
y=x^{2}+3 x+4
$

$ y=x(x+2)+5 $

$ y=(x+3)^{2}+4 $

$ y=-(x-2)(x-4) $

Correct

Incorrect

Question 26 of 74

26. Question

Category: Quadratic functions

$
\text {What is the vertex of the function }
$

$
y=(x-3)(x-5) ?
$

$
(3,5)
$

$ (-3,-5) $

$ (4,1) $

$ (4,-1) $

Correct

Incorrect

Question 27 of 74

27. Question

Category: Quadratic functions

$
\text { What is the minimum value of }
$

$
\text { the function } f(x)=x^{2}-8 x+30 ?
$

$ 30 $

$ 14 $

$ 8 $

$ 4 $

Correct

Incorrect

Question 28 of 74

28. Question

Category: Quadratic functions

$
\text { If the height in meters of a projected}
$

$
\text { body at any time } t^{\prime \prime} \text { seconds}
$

$
\text { given by }h=-2 t^{2}+18 t+44
$

$
\text { then the time needed to reach}
$

$
\text { the ground is …… seconds. }
$

2

4

9

11

Correct

Incorrect

Question 29 of 74

29. Question

Category: Factors and divisibility and zeros of a function

$
\text { If } x-3 \text { is a factor of the function }
$

$
f(x)=x^{3}-x^{2}-4 x+b
$

$
\text { what is } b \text { ? }
$

$ -6 $

$ -5 $

$ 5 $

$ 11 $

Correct

Incorrect

Question 30 of 74

30. Question

Category: Factors and divisibility and zeros of a function

$
\text { If } g(x) \text { is a function, } g(3)=11
$

$
\text { which of the following is true? }
$

$
g(11)=3
$

$ g(x) \text { is divisible by } x-3 $

$ \text { when } g(x) \text { is divided by } x-3 \text { the remainder is } 11 $

$ \text { when } g(x) \text { is divided by } x-11 \text { the remainder is } 3 $

Correct

Incorrect

Question 31 of 74

31. Question

Category: Factors and divisibility and zeros of a function

A

B

C

D

Correct

Incorrect

Question 32 of 74

32. Question

Category: Factors and divisibility and zeros of a function

A

B

C

D

Correct

Incorrect

Question 33 of 74

33. Question

Category: Factors and divisibility and zeros of a function

$
\begin{aligned}
&\text { If } \frac{x^{2}-3 x+8}{x-2}=a x+b+\frac{c}{x-2}\\
&\text { then } a, b, c \text { are: }
\end{aligned}
$

$
2,8,7
$

$ 1,-1,6 $

$ 1,1,6 $

$ 2,3,6 $

Correct

Incorrect

Question 34 of 74

34. Question

Category: Coordinate geometry

$
\text {Which of the following is }
$

$
\text {the slope of the line whose equation}
$

$
\text{is }3 x-4 y=11 ?
$

$
\frac{3}{4}
$

$ \frac{-3}{4} $

$ \frac{4}{3} $

$ 3 $

Correct

Incorrect

Question 35 of 74

35. Question

Category: Coordinate geometry

$
\text { Which of the following is }
$

$
\text { the equation of the line which passes }
$

$
\text { through }(1,3) \text { and }(-1,8) ?
$

$
y-8=x+1
$

$ -2 y+5 x=1 $

$ 2 y+5 x=11 $

$ 2 y+5 x=-1 $

Correct

Incorrect

Question 36 of 74

36. Question

Category: Coordinate geometry

$
\text {Which of the following}
$

$
\text {is the equation}
$

$
\text {of a line passes through the point }
$

$
(2,3)
$ $
\text {and is perpendicular to the line }
$

$
\text {whose equation is } 2 x+3 y=8 ?
$

$
3 x=2 y
$

$ 3 x-2 y=8 $

$ 3 x+2 y=8 $

$ -3 x+2 y=8 $

Correct

Incorrect

Question 37 of 74

37. Question

Category: Coordinate geometry

$
\text { If } A B C D \text { is a square where }
$

$
\text { the coordinates of } A \text { are }(3,7)
$

$
\text { and } B \text { are }(3,12) \text {, }
$

$
\text { what is the area of the square? }
$

$ 4 $

$ 5 $

$ 20 $

$ 25 $

Correct

Incorrect

Question 38 of 74

38. Question

Category: Coordinate geometry

A

B

C

D

Correct

Incorrect

Question 39 of 74

39. Question

Category: Plane geometry

A

B

C

D

Correct

Incorrect

Question 40 of 74

40. Question

Category: Plane geometry

$
\text { The length of a rectangle is } 8 \text { inches }
$

$
\text { and its perimeter is } 20 \text { inches, }
$

$
\text { then its area is …. square inches }
$

$ 16 $

$ 24 $

$ 32 $

$ 36 $

Correct

Incorrect

Question 41 of 74

41. Question

Category: Plane geometry

$
\text { In } \Delta A B C
$

$
\text { if } A B=8 \mathrm{~cm}, B C=5 \mathrm{~cm}
$

$
\text { which of the following }
$

$
\text { could be the length of } A C \text { ? }
$

$ 2 $

$ 3 $

$ 11 $

$ 13 $

Correct

Incorrect

Question 42 of 74

42. Question

Category: Plane geometry

A

B

C

D

Correct

Incorrect

Question 43 of 74

43. Question

Category: Plane geometry

$
\text {A square whose area is } 32 \text { square}
$

$
\text {inches so its diagonal length is}
$

$
\text {….. inches}
$

$ 4 $

$ 4 \sqrt{2} $

$ 8 $

$ 8 \sqrt{2} $

Correct

Incorrect

Question 44 of 74

44. Question

Category: Plane geometry

A

B

C

D

Correct

Incorrect

Question 45 of 74

45. Question

Category: Plane geometry

A

B

C

D

Correct

Incorrect

Question 46 of 74

46. Question

Category: Solid geometry

$
\text {A rectangular box of dimensions }
$

$
3,4,12 \mathrm{~cm} \text { its diagonal length}
$

$
\text {is …. } \mathrm{cm}
$

$ 5 $

$ 5 \sqrt{2} $

$ 12 $

$ 13 $

Correct

Incorrect

Question 47 of 74

47. Question

Category: Solid geometry

$
\text { A cylinder with radius } 8 \mathrm{~cm}
$

$
\text { and height } 5 \mathrm{~cm} \text {, so its volume}
$

$
\text { is } \ldots \mathrm{cm}^{3}
$

$
320 \pi
$

$ 200 \pi $

$ 160 \pi $

$ 64 \pi $

Correct

Incorrect

Question 48 of 74

48. Question

Category: Circles

A

B

C

D

Correct

Incorrect

Question 49 of 74

49. Question

Category: Circles

$
\text { Which of the following is equation}
$

$
\text { of the circle whose center is }(3,4)
$

$
\text { and its radius is 7 untis?}
$

$
(x-3)^{2}+(y-4)^{2}=14
$

$ (x-3)^{2}+(y-4)^{2}=49 $

$ (x+3)^{2}+(y+4)^{2}=49 $

$ (x-3)^{2}+(y-4)^{2}=7 $

Correct

Incorrect

Question 50 of 74

50. Question

Category: Circles

$
\text {Which of the following is }
$

$
\text {the radius of the circle }
$

$
x^{2}+y^{2}-2 x-8 y+1=0 ?
$

$ 4 $

$ 5 $

$ 6 $

$ 8 $

Correct

Incorrect

Question 51 of 74

51. Question

Category: Circles

$
\text {What is the area of the circle whose}
$

$
\text {equation is: }
$

$
2 x^{2}+2 y^{2}-4 x+20 y+8=0 ?
$

$
11 \pi
$

$ 22 \pi $

$ 44 \pi $

$ 50 \pi $

Correct

Incorrect

Question 52 of 74

52. Question

Category: Trigonometry

$
\text { If } \sin A=\frac{3}{5}, \text { then } \tan A=\ldots
$

$
\frac{3}{4}
$

$ \frac{4}{5} $

$ \frac{4}{3} $

$ \frac{5}{3} $

Correct

Incorrect

Question 53 of 74

53. Question

Category: Trigonometry

$
\text { If } \sin 2 x=\cos x \text {, then } x=\ldots
$

$
\pi
$

$ \frac{\pi}{2} $

$ \frac{\pi}{3} $

$ \frac{\pi}{6} $

Correct

Incorrect

Question 54 of 74

54. Question

Category: Trigonometry

A

B

C

D

Correct

Incorrect

Question 55 of 74

55. Question

Category: Complex numbers

$
2 i+3 i^{2}+4 i^{3}=\ldots \ldots
$

$
-3+2 i
$

$ -3-2 i $

$ 3-2 i $

$ 3+2 i $

Correct

Incorrect

Question 56 of 74

56. Question

Category: Complex numbers

$
\sqrt{-25}+\sqrt{-36}=\ldots \ldots
$

$
\sqrt{-61}
$

$ \sqrt{-100} $

$ \sqrt{-121} $

$ \sqrt{-131} $

Correct

Incorrect

Question 57 of 74

57. Question

Category: Complex numbers

$
\text { If } a-2 i+3 b i=4+10 i
$

$
\text { then } a, b \text { are } \ldots
$

$
4,5
$

$ 4, \frac{10}{3} $

$ 4,4 $

$ 1,3 $

Correct

Incorrect

Question 58 of 74

58. Question

Category: Complex numbers

$
\text { If } \frac{26}{2+3 i}=a+b i
$

$
\text { then } a, b \text { are } \ldots
$

$
2,-3
$

$ 4,-6 $

$ 6,-9 $

$ 6,9 $

Correct

Incorrect

Question 59 of 74

59. Question

Category: Percentages and ratios

$
\text { What is } 30 \% \text { of } 42 \text { ? }
$

$ 12 $

$ 12.6 $

$ 14.4 $

$ 24 $

Correct

Incorrect

Question 60 of 74

60. Question

Category: Percentages and ratios

$
\text { If the score of a student in the } 1^{s t}
$

$
\text { exam was } 80 \text {, what is the score in }
$

$
\text { the } 2^{n d} \text { exam if it was }20 \%
$

$
\text { more than the } 1^{\text {st }} \text { one? }
$

$ 88 $

$ 96 $

$ 100 $

$ 120 $

Correct

Incorrect

Question 61 of 74

61. Question

Category: Percentages and ratios

$
\text {If } y=a x \text { and it is known that }
$

$
y \text { is } 20 \% \text { more than } x\text { ,then }
$

$
a=\ldots
$

$ 0.2 $

$ 0.8 $

$ 1.2 $

$ 1.4 $

Correct

Incorrect

Question 62 of 74

62. Question

Category: Percentages and ratios

$
\text { If the price of an item was } 400 \$
$

$
\text { before it decreased by } 10 \% \text { twice, }
$

$
\text { what is the final price after}
$

$
\text { decreasing? }
$

$ 390 $

$ 360 $

$ 324 $

$ 320 $

Correct

Incorrect

Question 63 of 74

63. Question

Category: Probability

A

B

C

D

Correct

Incorrect

Question 64 of 74

64. Question

Category: Probability

A

B

C

D

Correct

Incorrect

Question 65 of 74

65. Question

Category: Data analysis I

$
\text { If } 5 \text { students had a quiz and their }
$

$
\text { scores were } 7,11,12,6,9 \text {, }
$

$
\text { what is their average score? }
$

$ 7 $

$ 8 $

$ 9 $

$ 10 $

Correct

Incorrect

Question 66 of 74

66. Question

Category: Data analysis I

$
\text { The average of } 3,7, x, y \text { is } 6
$

$
\text { what is } x+y ?
$

$ 12 $

$ 13 $

$ 14 $

$ 15 $

Correct

Incorrect

Question 67 of 74

67. Question

Category: Data analysis I

A

B

C

D

Correct

Incorrect

Question 68 of 74

68. Question

Category: Data analysis I

A

B

C

D

Correct

Incorrect

Question 69 of 74

69. Question

Category: Data analysis I

A

B

C

D

Correct

Incorrect

Question 70 of 74

70. Question

Category: Data analysis I

A

B

C

D

Correct

Incorrect

Question 71 of 74

71. Question

Category: Data analysis II

$
\text {Which of the following data has }
$

$
\text {smallest standard diviation? }
$

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Question 72 of 74

72. Question

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Question 73 of 74

73. Question

Category: Log

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Question 74 of 74

74. Question

Category: Log

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\( \frac{3}{x-2}+\frac{4}{2(x-2)}=\ldots \ldots \)

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\(
\frac{3}{x-2}+\frac{4}{2(x-2)}=\ldots \ldots
\)