Free Printable VIOLYMPIC MATH IN ENGLISH – GRADE 9: TEST 1

1.

Solve the equation: $2x+7=15$

(a)

2.

Find the value of: $\sqrt{81}$

(a)

3.

Find the domain of the expression: $\sqrt{x-4}$ Answer in form: x≥…

(a)

4.

Simplify: $\sqrt{50}=\,\dots\,\sqrt{2}$

(a)

5.

Solve the equation: $x^2=16$ Answer: x=…; …

4 lines

6.

In a right triangle, the legs are 6 cm and 8 cm. Find the length of the hypotenuse.

(a)

7.

Which formula is correct in a right triangle?

a)

$a^2+b^2=c^2$

b)

$a=b+c$

c)

$a^2=b+c$

d)

$a^2+b^2+c^2=0$

8.

A circle has radius 5 cm. Find its circumference. Answer in form: …π (cm)

(a)

9.

Solve the equation: $3x-5=10$

(a)

10.

Simplify: $\sqrt{72}=\,\dots\,\sqrt{2}$

(a)

11.

Solve the inequality: $x-3>4$ Answer in form: x>…

(a)

12.

Let $A=\sqrt{x^2}$ . If $x=-6$ , find the value of A.

(a)

13.

Solve the system of equations: $\begin{cases}x+y=7\ x-y=1\end{cases}$ Answer: ¿

4 lines

14.

In a right triangle, the hypotenuse is 13 cm and one leg is 5 cm. Find the other leg.

(a)

15.

A circle has diameter 10 cm. Find its area. Answer in form: …π (cm²)

(a)

16.

Which statement is true?

a)

A tangent is perpendicular to the radius at the point of tangency

b)

A tangent is parallel to the radius

c)

Every chord is a diameter

d)

The radius is longer than the diameter

17.

Solve the equation: $\sqrt{x}=7$

(a)

18.

Simplify: $\sqrt{18}-\sqrt{8}$ Answer in form: $a\sqrt{2}$

(a)

19.

From a point outside a circle, two tangents are drawn to the circle. Compare their lengths.

(a)

20.

Solve the equation: $x^2-9x=0$ Answer: x=…; …

4 lines

21.

Solve the equation: $3x+4=19$

(a)

22.

Find the value of: $\sqrt{100}$

(a)

23.

Find the domain of the expression: $\sqrt{2x-6}$ . Answer in form: x ≥ …

(a)

24.

Simplify: $\sqrt{32}=\,\dots\,\sqrt{2}$

(a)

25.

Solve the equation: $x^{2}=25$

4 lines

26.

In a right triangle, the legs are 9 cm and 12 cm. Find the length of the hypotenuse.

(a)

27.

Which formula is correct in a right triangle? A. $a^{2}+b^{2}=c^{2}$ B. $a=b+c$ C. $a^{2}=b+c$ D. $a^{2}+b^{2}+c^{2}=0$

a)

$a^{2}+b^{2}=c^{2}$

b)

$a=b+c$

c)

$a^{2}=b+c$

d)

$a^{2}+b^{2}+c^{2}=0$

28.

A circle has radius 6 cm. Find its circumference. Answer in form: …π (cm)

(a)

29.

Solve the equation: $5x-7=13$

(a)

30.

Simplify: $\sqrt{98}=\,\dots\,\sqrt{2}$

(a)

31.

Solve the inequality: $2x+1>9$ . Answer in form: x > …

(a)

32.

Let $A=\sqrt{x^{2}}$ . If $x=-8$ , find the value of A.

(a)

33.

Solve the system of equations: $\begin{cases}x+y=9\ x-y=3\end{cases}$

4 lines

34.

In a right triangle, the hypotenuse is 10 cm and one leg is 6 cm. Find the other leg.

(a)

35.

A circle has diameter 12 cm. Find its area. Answer in form: …π (cm²)

(a)

36.

Which statement is true? A. A tangent is perpendicular to the radius at the point of tangency B. A tangent is parallel to the radius C. Every chord is a diameter D. The diameter is shorter than the radius

a)

A tangent is perpendicular to the radius at the point of tangency

b)

A tangent is parallel to the radius

c)

Every chord is a diameter

d)

The diameter is shorter than the radius

37.

Solve the equation: $\sqrt{x}=8$

(a)

38.

Simplify: $\sqrt{50}-\sqrt{18}$ . Answer in form: a $\sqrt{2}$

(a)

39.

From a point outside a circle, two tangents are drawn to the circle. Compare their lengths.

(a)

40.

Solve the equation: $x^{2}-16x=0$

4 lines

41.

Solve the equation: $4x-9=19$

(a)

42.

Find the value of: $\sqrt{121}$

(a)

43.

Find the domain of the expression: $\sqrt{3x-12}$ . Answer in form: x ≥ …

(a)

44.

Simplify: $\sqrt{72}=\, …\, \sqrt{2}$

(a)

45.

Solve the equation: $x^2=49$ . Answer: x = … ; …

4 lines

46.

In a right triangle, the legs are 5 cm and 12 cm. Find the length of the hypotenuse.

(a)

47.

Which formula is correct in a right triangle? A. $a^2+b^2=c^2$ B. $a=b+c$ C. $a^2=b+c$ D. $a^2+b^2+c^2=0$

a)

$a^2+b^2=c^2$

b)

$a=b+c$

c)

$a^2=b+c$

d)

$a^2+b^2+c^2=0$

48.

A circle has radius 7 cm. Find its circumference. Answer in form: …π (cm)

(a)

49.

Solve the equation: $6x-11=13$

(a)

50.

Simplify: $\sqrt{162}=\, …\, \sqrt{2}$

(a)

51.

Solve the inequality: $3x-5\ge10$ . Answer in form: x ≥ …

(a)

52.

Let $A=\sqrt{x^2}$ . If $x=-15$ , find the value of A.

(a)

53.

Solve the system of equations: $x+y=11$ ; $x-y=5$ . Answer: ?

4 lines

54.

In a right triangle, the hypotenuse is 17 cm and one leg is 8 cm. Find the other leg.

(a)

55.

A circle has diameter 14 cm. Find its area. Answer in form: …π (cm²)

(a)

56.

Which statement is true? A. The radius is perpendicular to the tangent at the point of tangency B. A tangent passes through the center C. Every chord is a radius D. The diameter is shorter than the radius

a)

The radius is perpendicular to the tangent at the point of tangency

b)

A tangent passes through the center

c)

Every chord is a radius

d)

The diameter is shorter than the radius

57.

Solve the equation: $\sqrt{x}=9$

(a)

58.

Simplify: $\sqrt{98}-\sqrt{50}$ . Answer in form: $a\sqrt{2}$

(a)

59.

From a point outside a circle, two tangents are drawn to the circle. Compare their lengths.

4 lines

60.

Solve the equation: $x(x-25)=0$ . Answer: x = … ; …

4 lines

61.

Solve the equation: $5x-14=21$

(a)

62.

Find the value of: $\sqrt{144}$

(a)

63.

Find the domain of the expression: $\sqrt{4x-20}$ . Answer in form: x ≥ …

(a)

64.

Simplify: $\sqrt{200}=\dots\sqrt{2}$

(a)

65.

Solve the equation: $x^2=81$

4 lines

66.

In a right triangle, the legs are 7 cm and 24 cm. Find the length of the hypotenuse.

(a)

67.

Which formula is correct in a right triangle?

a)

$a^2+b^2=c^2$

b)

$a=b+c$

c)

$a^2=b+c$

d)

$a^2+b^2+c^2=0$

68.

A circle has radius 9 cm. Find its circumference. Answer in form: $\dots\pi$ (cm)

(a)

69.

Solve the equation: $7x-18=31$

(a)

70.

Simplify: $\sqrt{288}=\dots\sqrt{2}$

(a)

71.

Solve the inequality: $4x-9>15$ . Answer in form: $x>\dots$

(a)

72.

Let $A=\sqrt{x^2}$ . If $x=-20$ , find the value of A.

(a)

73.

Solve the system of equations:

4 lines

74.

In a right triangle, the hypotenuse is 26 cm and one leg is 10 cm. Find the other leg.

(a)

75.

A circle has diameter 18 cm. Find its area. Answer in form: $\dots\pi$ (cm $^2$ )

(a)

76.

Which statement is true?

a)

The radius is perpendicular to the tangent at the point of tangency

b)

A tangent passes through the center

c)

Every chord is a radius

d)

The diameter is shorter than the radius

77.

Solve the equation: $\sqrt{x}=11$

(a)

78.

Simplify: $\sqrt{200}-\sqrt{72}$ . Answer in form: $a\sqrt{2}$

(a)

79.

From a point outside a circle, two tangents are drawn to the circle. Compare their lengths.

(a)

80.

Solve the equation: $x^2-36=0$

4 lines

81.

Solve the equation: $6x-11=25$

(a)

82.

Find the value of: $\sqrt{169}$

(a)

83.

Find the domain of the expression: $\sqrt{5x-15}$ . Answer in form: $x\ge\dots$

(a)

84.

Simplify: $\sqrt{450}=\dots\sqrt{2}$

(a)

85.

Solve the equation: $x^2=121$

4 lines

86.

In a right triangle, the legs are 9 cm and 40 cm. Find the length of the hypotenuse.

(a)

87.

Which formula is correct in a right triangle?

a)

$a^2+b^2=c^2$

b)

$a=b+c$

c)

$a^2=b+c$

d)

$a^2+b^2+c^2=0$

88.

A circle has radius 10 cm. Find its circumference. Answer in form: …π (cm)

(a)

89.

Solve the equation: $8x-21=19$ Answer: x = …

(a)

90.

Simplify: $\sqrt{392}=\,\ldots\sqrt{2}$ Answer: …

(a)

91.

Solve the inequality: $5x+4\ge 24$ Answer in form: x ≥ …

(a)

92.

Let $A=\sqrt{x^2}$ . If $x=-30$ , find the value of A. Answer: …

(a)

93.

Solve the system of equations: $\begin{cases}x+y=19\ x-y=9\end{cases}$ Choose the correct ordered pair $(x,y)$ .

a)

(12,7)

b)

(14,5)

c)

(10,9)

d)

(16,3)

94.

In a right triangle, the hypotenuse is 41 cm and one leg is 9 cm. Find the other leg. Answer: …

(a)

95.

A circle has diameter 20 cm. Find its area. Answer in form: …π (cm²)

(a)

96.

Which statement is true? A. The radius is perpendicular to the tangent at the point of tangency B. A tangent passes through the center C. Every chord is a radius D. The diameter is shorter than the radius Answer: …

a)

The radius is perpendicular to the tangent at the point of tangency

b)

A tangent passes through the center

c)

Every chord is a radius

d)

The diameter is shorter than the radius

97.

Solve the equation: $\sqrt{x}=13$ Answer: …

(a)

98.

Simplify: $\sqrt{450}-\sqrt{200}$ Answer in form: a√2

(a)

99.

From a point outside a circle, two tangents are drawn to the circle. Compare their lengths. Answer: …

a)

Equal

b)

One is longer than the other

c)

Both shorter than the radius

d)

Cannot be compared without measurements

100.

Solve the equation: $x^2-49=0$ Choose the correct solution set for x.

a)

x = −7 only

b)

x = 7 only

c)

x = −7 or 7

d)

x = −49 or 49

101.

Solve the equation: $7x-19=30$ Answer: x = …

(a)

102.

Find the value of $\sqrt{196}$ . Answer: …

(a)

103.

Find the domain of the expression $\sqrt{6x-24}$ . Answer in form: x ≥ …

(a)

104.

Simplify: $\sqrt{648}=\,\ldots\sqrt{2}$ Answer: …

(a)

105.

Solve the equation: $x^2=169$ Choose the correct solution set for x.

a)

x = −13 or 13

b)

x = 169 only

c)

x = −169 or 169

d)

x = 13 only

106.

In a right triangle, the legs are 11 cm and 60 cm. Find the length of the hypotenuse. Answer: …

(a)

107.

Which formula is correct in a right triangle? A. $a^2+b^2=c^2$ B. $a=b+c$ C. $a^2=b+c$ D. $a^2+b^2+c^2=0$ Answer: …

a)

$a^2+b^2=c^2$

b)

$a=b+c$

c)

$a^2=b+c$

d)

$a^2+b^2+c^2=0$

108.

A circle has radius 12 cm. Find its circumference. Answer in form: …π (cm)

(a)

109.

Solve the equation: $9x-28=17$ Answer: x = …

(a)

110.

Simplify: $\sqrt{800}=\,\ldots\sqrt{2}$ Answer: …

(a)

111.

Solve the inequality: $6x-5>31$ Answer in form: x > …

(a)

112.

Let A = $\sqrt{x^2}$ . If $x=-45$ , find the value of A. Answer: ………

(a)

113.

Solve the system of equations: $x+y=23$ , $x-y=11$ . Answer: ¿

(a)

114.

In a right triangle, the hypotenuse is 61 cm and one leg is 11 cm. Find the other leg. Answer: ………

(a)

115.

A circle has diameter 24 cm. Find its area. Answer in form: …π (cm²)

(a)

116.

Which statement is true? A. The radius is perpendicular to the tangent at the point of tangency B. A tangent passes through the center C. Every chord is a diameter D. The diameter is shorter than the radius Answer: ………

a)

The radius is perpendicular to the tangent at the point of tangency

b)

A tangent passes through the center

c)

Every chord is a diameter

d)

The diameter is shorter than the radius

117.

Solve the equation: $\sqrt{x}=14$ . Answer: ………

(a)

118.

Simplify: $\sqrt{648}-\sqrt{200}$ . Answer in form: $a\sqrt{2}$

(a)

119.

From a point outside a circle, two tangents are drawn to the circle. Compare their lengths. Answer: ………

(a)

120.

Solve the equation: $x^2-64=0$ . Answer: x=…; …

(a)

121.

Solve the equation: $8x-23=41$ . Answer: ………

(a)

122.

Find the value of: $\sqrt{225}$ . Answer: ………

(a)

123.

Find the domain of the expression: $\sqrt{7x-28}$ . Answer in form: x ≥ …

(a)

124.

Simplify: $\sqrt{882}=…\sqrt{2}$ . Answer: ………

(a)

125.

Solve the equation: $x^2=196$ . Answer: x=…; …

(a)

126.

In a right triangle, the legs are 16 cm and 30 cm. Find the length of the hypotenuse. Answer: ………

(a)

127.

Which formula is correct in a right triangle? A. $a^2+b^2=c^2$ B. $a=b+c$ C. $a^2=b+c$ D. $a^2+b^2+c^2=0$ Answer: ………

a)

$a^2+b^2=c^2$

b)

$a=b+c$

c)

$a^2=b+c$

d)

$a^2+b^2+c^2=0$

128.

A circle has radius 13 cm. Find its circumference. Answer in form: …π (cm)

(a)

129.

Solve the equation: $10x-37=23$ . Answer: ………

(a)

130.

Simplify: $\sqrt{968}=…\sqrt{2}$ . Answer: ………

(a)

131.

Solve the inequality: $7x-9>40$ . Answer in form: x > …

(a)

132.

Let A = $\sqrt{x^2}$ . If $x=-56$ , find the value of A. Answer: ………

(a)

133.

Solve the system of equations: $x+y=27$ , $x-y=13$ . Answer: ¿

(a)

134.

In a right triangle, the hypotenuse is 65 cm and one leg is 16 cm. Find the other leg. Answer: ………

(a)

135.

A circle has diameter 26 cm. Find its area. Answer in form: …π (cm²)

(a)

VIOLYMPIC MATH IN ENGLISH – GRADE 9: TEST 1 – CLUSTER LEVEL

Total questions: 135

Worksheet time: 2hrs 43mins

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