Free Printable OGUN STATE 2022 MATHEMATICS OLYMPIAD COMPETITION 2022 FOR JUNIOR

1.

Participants from China, Japan and Korea will be attending a conference. 96 of them are from China, 72 are from Japan and 48 are from Korea. The organiser wishes to group them into discussion groups such that the participants are distributed equally among the groups. The number of discussion topics that the organiser needs to prepare depends on the number of discussion groups formed. What is the greatest number of discussion topics that the organiser has to prepare for the conference?

a)

23

b)

24

c)

25

d)

26

2.

Canteen A, canteen B and Canteen C repeat their lunch menus every 12 days, 8 days and 10 days respectively. All three canteens serve noodle soup today. How many days later will all the three canteens serving noodle soup again?

a)

100 days

b)

110 days

c)

120 days

d)

130 days

3.

Find the difference between the square of 7 and the sum of the first 7 odd numbers.

a)

0

b)

1

c)

2

d)

3

4.

A rectangular block of metal is 0. 24 m long, 0. 19 m wide and 0. 15 m high. If the metal block is melted to form a cube, find the length of each side of the cube.

a)

0. 19 m

b)

0. 29 m

c)

0. 39 m

d)

0. 49 m

5.

A cuboid, with dimensions 28 cm by b cm by 15 cm, has a volume of 6 720 cm³. Find the breadth, b, of the cuboid.

a)

14 cm

b)

15 cm

c)

16 cm

d)

17 cm

6.

A metal cube has a volume 27 cm³. It is to be painted on all its faces. Find the total area of the faces that will be coated with paint.

a)

51 cm²

b)

52 cm²

c)

53 cm²

d)

54 cm²

7.

What is the y-intercept?

a)

40

b)

10

c)

1

d)

2

8.

What is the y-intercept of this graph?

a)

1

b)

2

c)

3

d)

420

9.

Ranjan was facing south. He took 7/8 turns to his left and then he turned 135 degrees in a clockwise direction. Which direction is he facing now?

a)

North

b)

North-East

c)

East

d)

South-East

10.

Solve using BODMAS:
[{(364 x 8) + 85} - 3474/9] + 3 x 15/5

a)

2620

b)

7833

c)

1620

d)

6833

11.

The age of a son is 5years more than 1/5th the age of his father. If his father's age is 30, what is the age of his son?

a)

11 years

b)

12 years

c)

13 years

d)

7 years

12.

Find the solution of the given simultaneous equations.

y\ =\ 2x-3

3x-2y=4

a)

(2, 1)

b)

$\left(-\frac{7}{3},-\frac{23}{3}\right)$

c)

(-7, -17)

d)

(7, 4)

e)

no solution

13.

Two pencils and a ruler cost 49 cents in total. One pencil and two rulers cost 62 cents in total. Find the cost of each item.

a)

pencil: 13 cents

ruler: 23 cents

b)

pencil: 15 cents

ruler: 23.50 cents

c)

pencil: 12 cents

ruler: 25 cents

d)

pencil: 18 cents

ruler: 26 cents

14.

I have only 2 cent and 5 cent coins. The total number of coins is 25, and their total value is 92 cents. How many of each coin do I have?

a)

number of 2 cent coins: 16

number of 5 cent coins: 9

b)

number of 2 cent coins: 8

number of 5 cent coins: 17

c)

number of 2 cent coins: 13

number of 5 cent coins: 12

d)

number of 2 cent coins: 11

number of 5 cent coins: 14

15.

A baker's basket contains bread rolls and sandwich loaves. The loaves weigh 750 g and rolls 150 g. The total number of loaves and rolls is 16 and their total weight is 6 kg. How many rolls and how many loaves are in the basket?

a)

There are 7 sandwich loaves and 9 bread rolls in the basket.

b)

There are 12 sandwich loaves and 4 bread rolls in the basket.

c)

There are 8 sandwich loaves and 8 bread rolls in the basket.

d)

There are 6 sandwich loaves and 10 bread rolls in the basket.

16.

Find the solution of the simultaneous equations given the graph.

a)

(0, 2)

b)

(2, 2)

c)

(-1, 3)

d)

no solution

17.

Over the last five games, what is the average difference between the Laker's final score and the other teams?

a)

11

b)

14

c)

26

d)

2

18.

The number of pages that Mikayla wrote in her journal each day from Monday to Friday is shown below:

9, 8, 12, 6, 10

What is the mean number of pages she wrote per day?

a)

5

b)

6

c)

9

d)

11

19.

The Variance of a data is 2.5. Find the new variance if each data is multiplied by 3.

a)

22.5

b)

7.5

c)

13.5

20.

if each number in a set of data is added or substracted with a constant, the range, interquartile range, variance and standard deviation also will change.

a)

True

b)

False

21.

Pat needs 14 sticks of pepperoni to make 28 pizzas. How many sticks of pepperoni are needed to make 36 pizzas?

a)

15 pizzas

b)

252 sticks

c)

18 sticks

d)

18 pizzas

22.

A car travels 420 miles in 8 hours. If the car continues at the same rate, how far will it travel in 12 hours?

a)

630 miles

b)

630 hours

c)

600 miles

d)

540 hours

23.

12 ounce shampoo bottle lasts Mike 16 weeks. How long would you expect an 18-ounce bottle of the same brand to last him?

a)

24 weeks

b)

6 weeks

c)

30 weeks

d)

20 weeks

24.

If I wanted to place a fence around my backyard to keep my dog from running away, I would be looking at?

a)

Perimeter

b)

Area

25.

15 of the students in a history class passed a History test. If these students are 75% of all the students in the class, how many students are in the history class? Round you answer to the nearest whole number if necessary.

a)

20 students

b)

11 students

c)

32 students

d)

24 students

26.

Beeny went to his local zoo where 55% of it's exhibits featured reptiles. If the zoo features 20 exhibits in total, how many of the zoo's exhibits feature reptiles? Round your answer to the nearest whole number if necessary.

a)

20 exhibits

b)

11 exhibits

c)

32 exhibits

d)

24 exhibits

27.

At a construction job for a store, 24 painters were tasked with painting the interior. These painters made up 75% of the painting crew, so how many painters in all worked on this job? Round your answer to the nearest whole number if necessary.

a)

20 painters

b)

32 painters

c)

11 painters

d)

24 painters

28.

For one English test, Mary had to answer 25 questions. Of these 25 questions, Mary answered 5 of them correctly. What percent did Mary get on her English test? Round your answer to the nearest whole number if necessary.

a)

20%

b)

40%

c)

60%

d)

80%

29.

Ms. Kings second period P.E. Class has 56 students. 40 of these students enjoy playing baseball. This holds true for all 77 students in all of Ms. King's classes. How many of the 77 students enjoy playing baseball?

a)

55

b)

48

c)

114

d)

168

30.

Mallory bought pizza and soda for a party. If she spent $12.57 on the sodas and $10.95 for each pizza, how many pizzas did she buy if her total is $89.22?

a)

10.95x + 12.57 = 89.22

b)

12.57x + 10.95 = 89.22

c)

89.22x -10.95 = 12.57

d)

12.57 + 10.95 = 89.22

31.

Kamari completed his math homework in 1/3 of an hour.

He had to complete 4 math problems.

He spent an equal amount of time on each problem.

How much of an hour did Kamari spend on each problem?

a)

1/12

b)

1/7

c)

3/4

d)

12

32.

Keon is planting to rectangular gardens. His rose garden is 6 feet long and 3/8 foot wide. His tulip garden is 6 feet long and 6/8 foot wide.

Which statement is true about the two gardens?

a)

The rose and tulip gardens have the same area

b)

The rose garden has an area that is 3/8 square foot less than the tulip garden.

c)

The tulip garden is smaller than the rose garden.

d)

The area of the tulip garden is double the area of the rose garden.

33.

In Maddie’s garden, 1/3 of her plants are tomatoes. Of those tomatoes, 2/5 of them are ripe. What fraction of the plants are ripe tomatoes?

a)

2/8

b)

3/15

c)

3/8

d)

2/15

34.

You have inherited land that was purchased for $30,000 in 1990. The value of the land increased by approximately 5% per year. What is the approximate value of the land in the year 2011?

a)

$83,579

b)

$10,217

c)

$14,963,655

d)

$28,500

35.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

36.

$\frac{3}{x-4}+\frac{x}{2x+7}$

a)

$\frac{x^2+2x+21}{\left(x-4\right)\left(2x+7\right)}$

b)

$\frac{x^2+6x+21}{\left(x-4\right)\left(2x+7\right)}$

c)

$\frac{x^2+6x+7}{\left(x-4\right)\left(2x+7\right)}$

d)

$\frac{x^2+2x+7}{\left(x-4\right)\left(2x+7\right)}$

37.

$\frac{3}{x-4}+\frac{x}{2x+7}$

a)

$\frac{x^2+2x+21}{\left(x-4\right)\left(2x+7\right)}$

b)

$\frac{x^2+6x+21}{\left(x-4\right)\left(2x+7\right)}$

c)

$\frac{x^2+6x+7}{\left(x-4\right)\left(2x+7\right)}$

d)

$\frac{x^2+2x+7}{\left(x-4\right)\left(2x+7\right)}$

38.

$\frac{1}{x^2-13x+42}+\frac{x+1}{x-6}-\frac{x}{x-7}$

a)

$-\frac{6}{\left(x-6\right)\left(x-7\right)}$

b)

$\frac{2\left(x^2+6x-3\right)}{\left(x-6\right)\left(x-7\right)}$

c)

$\frac{-x^2+8x-6}{\left(x-6\right)\left(x-7\right)}$

d)

$\frac{x^2-4x-6}{\left(x-6\right)\left(x-7\right)}$

39.

$\frac{2}{x-1}-\frac{1}{x-2}+\frac{3\left(x+2\right)}{\left(x-1\right)\left(x-2\right)}$

a)

$\frac{4x+3}{\left(x-1\right)\left(x-2\right)}$

b)

$\frac{6x+1}{\left(x-1\right)\left(x-2\right)}$

c)

$\frac{4x+1}{\left(x-1\right)\left(x-2\right)}$

d)

$\frac{6x-1}{\left(x-1\right)\left(x-2\right)}$

40.

a)

18/30

b)

24/30

c)

18/24

d)

24/18

41.

a)

A

b)

B

c)

C

d)

D

42.

If y = 2 satisfies the equation 1.3 – ky = 0.2y + 0.3, find the value of k.

a)

0.1

b)

0.2

c)

0.3

d)

0.4

43.

If P = { prime factors of 24}and Q = {prime factors of 35}

List the members of PUQ

a)

{2, 3, 5}

b)

{3, 5, 7}

c)

{2, 3, 5, 7}

d)

{2, 3, 5, 7, 11}

44.

Factorise 2m – 2n + mx – nx

a)

(2 + x)(m - n)

b)

(2 + m)(n -x)

c)

2x(m - n)(m + n)

d)

(2 + n)(m + x)

45.

Simplify $(4/5\times21/4)+(21/2\div5/6)$

a)

$\frac{73}{4}$

b)

$\frac{84}{5}$

c)

3

d)

9

46.

Express the number 0.0063075 correct to three significant figures

a)

0.006

b)

0.0060

c)

0.0063

d)

0.00631

47.

In a class of 28 pupils, 13 have pencils, 9 have erasers and 9 have neither pencils nor erasers. How many pupils have both pencils and erasers?

a)

3

b)

5

c)

6

d)

9

48.

Atta is n years old. His sister’s age is 5 years more than half of his age. How old id his sister

a)

$\frac{n}{2}$ + $\frac{5}{2}$

b)

$\frac{n}{2}$ – 5

c)

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

d)

$\frac{n}{2}$ + 5

e)

$\frac{2}{n}$ + $\frac{2}{5}$

49.

Prashant booked a cab to visit Lingaraj Temple from Patia. The cab fare included a fixed charge of Rs x and a variable charge of Rs y per km for first one hour of journey and then Rs z per km for rest of the time of journey. Distance between Patia and Lingaraj Temple is 20km. (z>y)

What amount Prashant will pay if he completed his journey in one hour?

a)

20x + y

b)

x+ 20y

c)

xy +20

d)

20xyz

50.

Prashant booked a cab to visit Lingaraj Temple from Patia. The cab fare included a fixed charge of Rs x and a variable charge of Rs y per km for first one hour of journey and then Rs z per km for rest of the time of journey. Distance between Patia and Lingaraj Temple is 20km. (z>y)

What amount Prashant will pay if returns to Patia in the same cab and travels only 5 km in the second hour of journey?

a)

x + 35y + 5z

b)

35xy + 5z

c)

xyz + 5

d)

5

51.

Prashant booked a cab to visit Lingaraj Temple from Patia. The cab fare included a fixed charge of Rs x and a variable charge of Rs y per km for first one hour of journey and then Rs z per km for rest of the time of journey. Distance between Patia and Lingaraj Temple is 20km. (z>y)

Abhishant called Prashant and asked to pick him, which added 12km to his journey. How much more Prashant has to pay if they completed the journey in one hour?

a)

12y

b)

x + 12y

c)

12x

d)

Prashant paid the same amount.

52.

Two circles are drawn inside a big circle with diameters 2/3rd and 1/3rd of the diameter of the big circle as shown in the figure. The length of the diameter of the circle is 18 cm.

The radius of both circles enclosed inside the big circle are______ and _______.

a)

6cm, 3cm

b)

12cm, 6cm

c)

8cm, 4cm

d)

18cm, 9cm

53.

Ramu put a square fence around his vegetable garden to keep the deer away from eating his corn. One side was 10 m in length. If the posts were placed 2 m apart, how many posts did he use?

a)

16

b)

20

c)

10

d)

5

54.

Anil can do a piece of work in 5 days and Ankur in 4 days. How long will they take do the same work, if they work together?

a)

12/9

b)

9/20

c)

30/9

d)

20/9

55.

Which 3-D shape can you make with 4 triangles and a square?

a)

cone

b)

cube

c)

square pyramid

d)

rectangular prism

56.

It takes 20 workers 6 hours to build a wall. How much time would 30 workers need to complete the job?

a)

4 hours

b)

16 hours

c)

40 hours

d)

2 hours

57.

It takes 10 waitresses 3 hours to serve food. How much food would be served if 5 more waitresses were hired?

a)

2 hours

b)

1 hour

c)

8 hours

d)

3 hours

58.

It takes 20 workers 6 hours to build a wall. How much time would 30 workers need to complete the job?

a)

4 hours

b)

16 hours

c)

40 hours

d)

2 hours

59.

981 + 5327 + 3692 =

a)

4078

b)

10,000

c)

9437

d)

3018

60.

What is the coordinate of so that point Q is $\frac{2}{5}$ the distance from B to A.

a)

-17

b)

-14

c)

-11

d)

-8

61.

Find the coordinates of Point R so that it is $\frac{3}{7}$ The distance from D to C.

a)

4

b)

8

c)

12

d)

16

62.

Point Q is _______ (what fraction?) the distance from C to D.

a)

5/7

b)

2/3

c)

1/3

d)

2/7

63.

A group of 3 friends each have video games at their home. Then each friend buys 5 more video games. Now the three friends have a total of 30 video games. How many video games did each friend start with?

a)

3(x+5) = 30

b)

x(3+5) = 30

c)

5(x+3) = 30

d)

30(3+5) = x

64.

You decide to rent a bike for $25 plus $3.00 per hour. If you spent a total of $40.00, how many hours did you rent the bike?

a)

1 hour

b)

4 hours

c)

2 hours

d)

5 hours

65.

For a field trip, 13 students rode in cars and the rest filled seven buses. How many students were in each bus if 251 students were on the trip?

a)

231

b)

5

c)

65

d)

34

66.

Half of your baseball card collection got wet and was ruined. Bought 11 cards to replace some that were lost. How many did you begin with if you now have 31?

a)

40

b)

51

c)

73

d)

62

67.

Paul bought a notebook for $2.50 and 3 pencils. He spent a total of $5.47. How much did each pencil cost?

a)

$.99

b)

$2.97

c)

$7.97

d)

$1.17

OGUN STATE 2022 MATHEMATICS OLYMPIAD COMPETITION 2022 FOR JUNIOR

Total questions: 67

Worksheet time: 2hrs 31mins

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