New Spark Olympiad

1.If 𝑥 2 − 5 𝑥 + 6 = 0 x 2 −5x+6=0, what are the values of 𝑥 x?

2, 3

3, 4

1, 6

5, 6

2.What is the value of ( 𝑎 + 𝑏 ) 2 − ( 𝑎 − 𝑏 ) 2 (a+b) 2 −(a−b) 2 ?

4ab

2a 2

4a 2 b 2

2ab

3. Solve for 𝑥 x in the equation 3 𝑥 − 4 = 2 𝑥 + 5 3x−4=2x+5.

9

-1

1

-9

4. If sin ⁡ 𝜃 = 3 5 sinθ= 5 3 , find cos ⁡ 𝜃 cosθ.

4/5

3/5

5/4

2/3

5. Calculate the area of a circle with radius 7 cm.

154 cm²

44 cm²

98 cm²

49 cm²

6. If 5 𝑥 = 125 5 x =125, find 𝑥 x.

2

3

4

5

7. What is the solution to the inequality 3 𝑥 − 7 < 2 𝑥 + 5 3x−7 < 2x+5?

x < 12

x>12

x < −12

𝑥 > − 12 x>−12

8. Find the value of ( 3 + 4 𝑖 ) + ( 5 − 6 𝑖 ) (3+4i)+(5−6i).

8 - 2i

8 + 2i

-8 + 10i

2 - 10i

9. What is the value of 1 2 + 1 3 2 1 + 3 1 ?

5/6

1/6

2/5

5/3

10. If 𝑎 : 𝑏 = 3 : 4 a:b=3:4 and 𝑏 : 𝑐 = 5 : 6 b:c=5:6, find 𝑎 : 𝑐 a:c.

3:6

5:8

9:8

15:24

11. Solve for 𝑥 x: 𝑥 2 + 6 𝑥 + 9 = 0 x 2 +6x+9=0.

-3

3

6

-6

12. What is the sum of the first 10 natural numbers?

50

55

45

60

13. If a sequence is defined by 𝑎 𝑛 = 3 𝑛 + 2 a n =3n+2, find 𝑎 5 a 5 .

17

18

15

14

14.What is the probability of rolling a 4 on a fair 6-sided die?

1/6

1/4

1/3

1/2

15. What is the formula for the area of a trapezium with bases 𝑎 a and 𝑏 b and height ℎ h?

1 2 ℎ ( 𝑎 + 𝑏 ) 2 1 h(a+b)

h(a+b)

2 1 (a+b)

a+b

16.If 𝑎 = 5 a=5 and 𝑏 = 12 b=12, find the value of 𝑎 2 + 𝑏 2 a 2 +b 2 .

13

10

15

17

17. Simplify the expression 2 ( 𝑥 + 3 ) − 4 ( 𝑥 − 1 ) 2(x+3)−4(x−1).

−2x+10

2x+10

−2x−10

2x−10

18. If the perimeter of a rectangle is 20 cm and its length is 6 cm, find its width.

5 cm

4 cm

3 cm

2 cm

19.What is the value of 1 2 + 1 3 2 1 + 3 1 ?

5/6

1/6

2/6

5/3

20. If 𝑦 = 2 𝑥 + 5 y=2x+5, what is the value of 𝑦 y when 𝑥 = − 1 x=−1?

3

-3

7

-7

Nine Class Exam

1.If 𝑥 2 − 5 𝑥 + 6 = 0 x 2 −5x+6=0, what are the values of 𝑥 x?

2.What is the value of ( 𝑎 + 𝑏 ) 2 − ( 𝑎 − 𝑏 ) 2 (a+b) 2 −(a−b) 2 ?

3. Solve for 𝑥 x in the equation 3 𝑥 − 4 = 2 𝑥 + 5 3x−4=2x+5.

4. If sin ⁡ 𝜃 = 3 5 sinθ= 5 3 , find cos ⁡ 𝜃 cosθ.

5. Calculate the area of a circle with radius 7 cm.

6. If 5 𝑥 = 125 5 x =125, find 𝑥 x.

7. What is the solution to the inequality 3 𝑥 − 7 < 2 𝑥 + 5 3x−7 < 2x+5?

8. Find the value of ( 3 + 4 𝑖 ) + ( 5 − 6 𝑖 ) (3+4i)+(5−6i).

9. What is the value of 1 2 + 1 3 2 1 + 3 1 ?

10. If 𝑎 : 𝑏 = 3 : 4 a:b=3:4 and 𝑏 : 𝑐 = 5 : 6 b:c=5:6, find 𝑎 : 𝑐 a:c.

11. Solve for 𝑥 x: 𝑥 2 + 6 𝑥 + 9 = 0 x 2 +6x+9=0.

12. What is the sum of the first 10 natural numbers?

13. If a sequence is defined by 𝑎 𝑛 = 3 𝑛 + 2 a n =3n+2, find 𝑎 5 a 5 .

14.What is the probability of rolling a 4 on a fair 6-sided die?

15. What is the formula for the area of a trapezium with bases 𝑎 a and 𝑏 b and height ℎ h?

16.If 𝑎 = 5 a=5 and 𝑏 = 12 b=12, find the value of 𝑎 2 + 𝑏 2 a 2 +b 2 .

17. Simplify the expression 2 ( 𝑥 + 3 ) − 4 ( 𝑥 − 1 ) 2(x+3)−4(x−1).

18. If the perimeter of a rectangle is 20 cm and its length is 6 cm, find its width.

19.What is the value of 1 2 + 1 3 2 1 + 3 1 ?

20. If 𝑦 = 2 𝑥 + 5 y=2x+5, what is the value of 𝑦 y when 𝑥 = − 1 x=−1?

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Nine Class Exam

1.If 𝑥 2 − 5 𝑥 + 6 = 0 x 2 −5x+6=0, what are the values of 𝑥 x?

2.What is the value of ( 𝑎 + 𝑏 ) 2 − ( 𝑎 − 𝑏 ) 2 (a+b) 2 −(a−b) 2 ?

3. Solve for 𝑥 x in the equation 3 𝑥 − 4 = 2 𝑥 + 5 3x−4=2x+5.

4. If sin ⁡ 𝜃 = 3 5 sinθ= 5 3 ​ , find cos ⁡ 𝜃 cosθ.

5. Calculate the area of a circle with radius 7 cm.

6. If 5 𝑥 = 125 5 x =125, find 𝑥 x.

7. What is the solution to the inequality 3 𝑥 − 7 < 2 𝑥 + 5 3x−7 < 2x+5?

8. Find the value of ( 3 + 4 𝑖 ) + ( 5 − 6 𝑖 ) (3+4i)+(5−6i).

9. What is the value of 1 2 + 1 3 2 1 ​ + 3 1 ​ ?

10. If 𝑎 : 𝑏 = 3 : 4 a:b=3:4 and 𝑏 : 𝑐 = 5 : 6 b:c=5:6, find 𝑎 : 𝑐 a:c.

11. Solve for 𝑥 x: 𝑥 2 + 6 𝑥 + 9 = 0 x 2 +6x+9=0.

12. What is the sum of the first 10 natural numbers?

13. If a sequence is defined by 𝑎 𝑛 = 3 𝑛 + 2 a n ​ =3n+2, find 𝑎 5 a 5 ​ .

14.What is the probability of rolling a 4 on a fair 6-sided die?

15. What is the formula for the area of a trapezium with bases 𝑎 a and 𝑏 b and height ℎ h?

16.If 𝑎 = 5 a=5 and 𝑏 = 12 b=12, find the value of 𝑎 2 + 𝑏 2 a 2 +b 2 ​ .

17. Simplify the expression 2 ( 𝑥 + 3 ) − 4 ( 𝑥 − 1 ) 2(x+3)−4(x−1).

18. If the perimeter of a rectangle is 20 cm and its length is 6 cm, find its width.

19.What is the value of 1 2 + 1 3 2 1 ​ + 3 1 ​ ?

20. If 𝑦 = 2 𝑥 + 5 y=2x+5, what is the value of 𝑦 y when 𝑥 = − 1 x=−1?

4. If sin ⁡ 𝜃 = 3 5 sinθ= 5 3 , find cos ⁡ 𝜃 cosθ.

9. What is the value of 1 2 + 1 3 2 1 + 3 1 ?

13. If a sequence is defined by 𝑎 𝑛 = 3 𝑛 + 2 a n =3n+2, find 𝑎 5 a 5 .

16.If 𝑎 = 5 a=5 and 𝑏 = 12 b=12, find the value of 𝑎 2 + 𝑏 2 a 2 +b 2 .

19.What is the value of 1 2 + 1 3 2 1 + 3 1 ?