Free Printable Olympic

1.

40 cookies fit in a box. 30 boxes fit in a package. 10 packages fit on a pallet. 10 pallets fit in a truck. How many cookies are in the truck?

a)

1900

b)

90

c)

120,000

d)

700

2.

A watch shows the time as 8:42am. How much time must elapse for it to be 10:02pm?

a)

1 hour 20 min

b)

13 hours 20 min

c)

1 hour 22 min

d)

14 hours 20 min

3.

A gallon of water weighs 8.34 pounds. How much do 8 gallons weigh?

a)

66.72

b)

88.12

c)

64.29

d)

72.96

4.

Which of the following is not a rate?

a)

miles per gallon

b)

rotations/min

c)

foot-pounds

d)

words per min

5.

Which of the following shapes does not have angles that add up to 360˚?

a)

Square

b)

Circle

c)

Rhombus

d)

Triangle

6.

A sandwich weighs 250g. The bread weighs 100g, the meat weighs 75g and the cheese weighs 75g. What percentage of the weight of the sandwich is meat?

a)

75%

b)

25%

c)

30%

d)

45%

7.

A log is split in half and then split in half again, and split in half a third time. How much of the whole log is each piece worth?

a)

1/6

b)

1/4

c)

1/8

d)

1/16

8.

A beaver builds a dam to stop some water. He used 600 sticks and 12lbs of mud to build the dam. 1 stick weighs 0.1 lbs. How much does his whole dam weigh?

a)

60lbs

b)

72lbs

c)

600lbs

d)

612lbs

9.

Round the following to the nearest ten thousandth place

3.14159265359

a)

3.142

b)

3.14

c)

3.1416

d)

3.141593

10.

A tree is 78 feet tall. A frog can jump 1.3 feet into the air and hang on the tree. How many jumps would it take for the frog to reach the top of the tree?

a)

50 jumps

b)

60 jumps

c)

70 jumps

d)

49 jumps

11.

A dragonfly can beat its wings 30 times per second. Write an equation in slope-intercept form that shows the relationship between flying time in seconds and the number of times the dragonfly beats its wings.

(a)

12.

A balloon is released from the top of a platform that is 50 meters tall. The balloon rises at the rate of 40 meters per second. Write an equation in slope-intercept form that tells the height of the balloon above the ground after a given number of seconds.

(a)

13.

The cost of renting a sailboat at lake is $20 per hour plus $12 for life jackets. Write an equation in slope-intercept form that can be used to calculate the total amount you would pay for using this sailboat.

(a)

14.

The cash register subtracts $2.50 from a $25 coffee cafe gift card for ever medium coffee the customer buys. Write an equation in slope-intercept form to represent this situation.

(a)

15.

What is the factored form of $x^2+7x-30$

a)

$\left(x+10\right)\left(x-7\right)$

b)

$\left(x+10\right)\left(x+3\right)$

c)

$\left(x-10\right)\left(x+3\right)$

d)

$\left(x+10\right)\left(x-3\right)$

16.

What is the remainder of $\left(3x^3-5x^2-4x+1\right)\left(x+3\right)$

a)

-25

b)

113

c)

25

d)

-113

17.

The number, 512115273999132, is NOT divisible by which of the following factors?

a)

2

b)

3

c)

4

d)

8

18.

Ms. Hernandez began her math class by saying:
I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?

What is the 5th number Ms. Hernandez is thinking of?

a)

15

b)

16

c)

17

d)

18

19.

If h(x) = x ³ + x and g(x) = 2x + 3, then g(h(2)) = ?

a)

10

b)

17

c)

19

d)

23

20.

Each side of the smaller square in the figure is x inches long, and each side of the larger square is c inches longer than a side of the smaller square. The area of the larger square is how many square inches greater than the area of the smaller square?

a)

x²

b)

(x + c)²

c)

2xc + c²

d)

c²

21.

A cube with edges ½ inch long is shown. What is the length, in inches, of a diagonal that runs from one corner of the cube to the opposite corner?

a)

3/4

b)

√3/2

c)

√2/2

d)

1/2

22.

Each of the variables t, w, x, y, and z represents a different positive real number. Given the equations below, which of the 4 variables w, x, y, and z necessarily has the greatest value?

1.23w = t
1.01x = t
0.99y = t
0.23z = t

a)

w

b)

x

c)

y

d)

z

23.

In the figure, A, B, C, and D are collinear, FC is parallel to ED, BE is perpendicular to ED, and the measures of ∠FAB and ∠EBA are as marked. What is the measure of ∠FCB ?

a)

84⁰

b)

63⁰

c)

57⁰

d)

33⁰

24.

A neighborhood recreation program serves a total of 280 children who are either 11 years old or 12 years old. The sum of the children’s ages is 3,238 years. How many 11-year-old children does the recreation program serve?

a)

122

b)

132

c)

158

d)

208

25.

What is the x-intercept of the graph of y = x² – 4x + 4?

a)

-1

b)

0

c)

1

d)

2

26.

Which one of the following expressions has an even integer value for all integers a and c?

a)

8a + 2ac

b)

ac + a²

c)

3a + 3c

d)

2a + c

27.

Which of the following is an equation of the circle with its center at (0,0) that passes through (3,4) in the standard (x,y) coordinate plane?

a)

x² + y² = 5

b)

x² + y² = 25

c)

x - y = -1

d)

x + y = 7

28.

The large rectangle shown above is made of 4 smaller rectangles. The smaller dimension of the smaller rectangle is 9 cm. Find the area of the large rectangle (in cm^2).

a)

108

b)

972

c)

2015

d)

Not enough given information

e)

None of the above

29.

In mathematics, $x!$ is defined as $\left(x\right)\cdot\left(x-1\right)\cdot\left(x-2\right)...\left(1\right)$ . Find the value of $9+\left(8+7\right)\cdot\left(6!-5-4-3-2-1\right)$ .

a)

955

b)

2019

c)

2034

d)

3216

e)

None of the above

30.

Find the value of 2020 x 20 - 20 x 20 + 2020.

a)

2020

b)

42020

c)

40000

d)

40202

e)

None of the above

31.

The next term of the sequence 3, 2, 5, 9, 44 is ....

a)

86

b)

87

c)

88

d)

395

e)

2015

32.

Which of the following is correct?

a)

$\left(x+y\right)^3=x^3+y^3$

b)

$-10^2=100$

c)

$\sqrt[]{x^2+9y^2}=x+3y$

d)

$\frac{x}{x+y}=\frac{x}{x}+\frac{x}{y}$

e)

None of the above

33.

Simplify $3^1\cdot3^3\cdot3^5\cdot3^7\cdot3^9\cdot3^{11}\cdot3^{13}\cdot3^{15}\cdot3^{17}\cdot\left(\frac{1}{3}\right)^{75}$ .

a)

27

b)

81

c)

243

d)

729

e)

None of the above

34.

An operator $\nabla$ acts on two integers to give:

$3\nabla2=94$

$5\nabla3=259$

$1\nabla6=136$

$4\nabla9=1681$

What does $5\nabla7$ equal to?

a)

2549

b)

3549

c)

4925

d)

4935

e)

None of the above

35.

The HCF of two positive integers is 3.

If the sum of the two integers is 21, which could NOT be their LCM?

a)

18

b)

30

c)

36

d)

7

e)

None of the above

36.

Which of the following is equal to $ax-2by+3c$ , given that:

$x=3a-4b^2$

$y=4b-3c^2$

$z=-2bc$

a)

$3a^2-4ab^2-8b^2$

b)

$3a^2-4ab^2-8b^2+12bc^2$

c)

$3a^2-4ab^2-8b^2-12bc^2$

d)

$3a^2-4ab^2+8b^2+12bc^2$

e)

None of the above

37.

If 4567N is divisible by 12, then what is the value of N?

a)

8

b)

6

c)

4

d)

2

e)

0

38.

If 5D68D is divisible by 36, then what is the value of D?

a)

0

b)

2

c)

4

d)

8

e)

None of the above

39.

Find the value of P, if:

$\frac{1+2+3\cdot\cdot\cdot120}{110}=\frac{2+4+6+P}{2}$ .

a)

232

b)

242

c)

252

d)

262

e)

None of the above

40.

A a square and a hexagon is shown with the parts of a larger polygon.

How many sides does the polygon have?

a)

10

b)

12

c)

20

d)

24

e)

30

41.

Which of the following operations yield the largest result, given that:

X = 0.0000125

Y = 0.00008

a)

$X+Y$

b)

$X-Y$

c)

$X\cdot Y$

d)

$\frac{X}{Y}$

e)

None of the above

42.

Five areas of a large rectangle split into nine pieces are given above.

What's the sum of the areas of the other four?

a)

$\frac{10}{3}$

b)

2

c)

3

d)

$\frac{5}{2}$

e)

None of the above

43.

A palindrome is a number that has the same value when written backwards (ex. 1221).

How many 6-digit palindromes are there?

a)

190

b)

900

c)

1000

d)

90000

e)

None of the above

44.

A one-price snacks store increased their price for snacks by 20%.

Previously, $x can net 60 packets of snacks. How many packets can $x buy now?

a)

50

b)

48

c)

40

d)

56

e)

None of the above

45.

An operator acts between two integers with the function $x\Delta y=\left(x-1\right)\left(x-2\right)\cdot\cdot\cdot\left(x-y\right)$ .

Assuming $8\Delta x=840$ , what is the value of $x\Delta\left(x-3\right)$ ?

a)

6

b)

12

c)

24

d)

36

e)

None of the above

46.

A farmer buys 36 metres of fence to build an enclosure to keep his livestock.

He decides to erect a 4-sided enclosure in such a way that it has the largest possible area.

What is the area of such enclosure (in m^2)?

a)

63

b)

72

c)

81

d)

90

e)

None of the above

47.

The following is a false proof stating that $\pi\ge2019$ .

$x=\pi,\ y=3,\ z=2019$ (1)

$-x\le-y,\ z-y>0$ (2)

$x\ge y,\ z>y$ (3)

$x\ge z$ (4)

$\pi\ge2019$ (5)

Where did the mistake occur?

a)

(1)→(2)

b)

(2)→(3)

c)

(3)→(4)

d)

(4)→(5)

e)

None of the above

48.

The value of $\frac{2022^3-2\cdot2022^2-2020}{2021^3+2\cdot2021^2-2023}$ can be expressed as a fraction $\frac{m}{n}$ where both variables do not have a common factor other than 1. What is the value of m + n?

a)

4039

b)

4041

c)

4043

d)

4045

e)

None of the above

49.

The modulo function $y\ mod\ x$ determines the remainder when y is divided by x.

Given that $a\ mod\ 10=5$ and $b\ mod\ 10=4$ , a new variable, c, is created.

What is $c\ mod\ 10$ ?

a)

4

b)

5

c)

7

d)

9

e)

None of the above

50.

Considering all positive integers from 1 to 200, which is not true?

a)

Sum of even numbers > sum of odd numbers

b)

0 is the least occurring digit

c)

Mean of even numbers > mean of odd numbers

d)

Sum of even numbers - sum of odd numbers = 200

e)

Average of all 200 numbers is not an integer

51.

Simplify $\left|1-\sqrt[]{\left(x+3\right)^2}\right|$ , given that x < -4.

a)

x + 2

b)

-x - 2

c)

x + 4

d)

-x - 4

e)

None of the above

52.

A cube is made of 64 smaller cubes.

If the larger cube has all its sides painted, how many smaller cubes have exactly 1 painted face?

a)

6

b)

12

c)

24

d)

72

e)

None of the above

53.

If the net of this cube is folded, which of the cubes can be formed?

a)

b)

c)

d)

e)

54.

Given the following polygon, HE // DB, GE ⊥ BG, DF ⊥ HF;

H = 138 deg, B = D + 4 deg. Find E (in deg).

a)

134

b)

44

c)

46

d)

138

e)

None of the above

55.

Assume n and $\frac{108}{n^3}$ are both positive integers. How many values of n are there?

a)

1

b)

2

c)

3

d)

4

e)

None of the above

56.

How many consecutive 0's are there in $2^{11}\cdot3^7\cdot5^5\cdot7^3\cdot11^2$ ?

a)

11

b)

16

c)

6

d)

5

e)

None of the above

57.

Among $\frac{1}{2020},\frac{2}{2020},\frac{3}{2020},\cdot\cdot\cdot,\frac{200}{2020}$ , how many fractions are in simplest form?

a)

121

b)

59

c)

79

d)

144

e)

None of the above

58.

Two numbers, x and y, result to 100000 when multiplied and both do not have 10 as a factor.

What is x - y?

a)

465

b)

1170

c)

3093

d)

6234

e)

None of the above

59.

The speed of two cyclists, A and B total to 34 km/h.

If the A cycles for 3 hours and the B cycles for 7 hours,

then the total distance they travel will be 150 km.

What is A - B (in km/h), if both cycle at a constant rate?

a)

12

b)

11

c)

10

d)

9

e)

8

60.

How many 5 digit numbers can be written,

using each digit 1-5 exactly once and have the even digits in increasing order?

a)

45

b)

52

c)

60

d)

64

e)

None of the above

61.

The height of a man is 169 cm, correct to the nearest cm.

What is the upper bound of the man’s height (in cm)?

a)

169.4

b)

169.45

c)

169.49

d)

169.5

e)

169.9

62.

Find the value of $\sqrt[]{1+2+3+\cdot\cdot\cdot+100}$ if rounded down.

a)

69

b)

70

c)

71

d)

72

e)

None of the above

63.

The following quadrilateral is divided into 7 sections.

Which statement is true?

a)

S2 + S4 = S6

b)

S1 + S7 = S4

c)

S2 + S3 = S4

d)

S1 + S6 = S4

e)

None of the above

64.

What is the maximum number of regions that can be formed by a circle and a rhombus?

a)

6

b)

7

c)

8

d)

9

e)

10

65.

Which fraction is the largest?

a)

$\frac{60}{119}$

b)

$\frac{64}{127}$

c)

$\frac{62}{123}$

d)

$\frac{63}{125}$

e)

$\frac{61}{121}$

66.

What day will it be $2^{2020}$ days from a Tuesday?

a)

Wed

b)

Thu

c)

Fri

d)

Sat

e)

Non of the above

67.

Find the smallest value of n if 540n is a multiple of 168.

a)

2

b)

7

c)

14

d)

28

e)

None of the above

68.

Six people are discussing the contents of a bag. Their answers are shown above. Two are truth tellers and are sitting next to each other. Two are liars and are also sitting next to each other. What is inside the bag?

a)

Camera

b)

Laptop

c)

Wallet

d)

Watch

e)

Insufficient data

69.

Ellie, Violet, Audrey, Tom and Chris are Secondary 1 or 3 students. They study in

either Greenwich Secondary School or Westwood Secondary School. It is also given

that:

• Tom and Chris are from different schools.

• Ellie and Audrey go to the same school.

• Three students go to Greenwich Secondary School and the other two are from

Westwood Secondary School.

• Violet and Chris are from the same grade.

• Audrey and Tom study at different levels.

• Three students study in Secondary 1 and the other two students in Secondary 3.

If one of them is Secondary 3 student from Westwood Secondary School, who is that person?

a)

Ellie

b)

Violet

c)

Audrey

d)

Tom

e)

Chris

70.

In a triangle ABC, AB = 10 cm, BC = 6 cm, and AC = 8 cm. Find $\frac{\sin a}{\sin b}$ .

a)

0.6

b)

0.75

c)

0.8

d)

Cannot be found

e)

None of the above

71.

In the diagram, ABCD is a square with AB = 20 cm, AD is the diameter of the semicircle, and AB is the radius of a quadrant. Find the area of the shaded region (in cm^2).

a)

$75\pi$

b)

$50\pi$

c)

$75\pi-100$

d)

$50\pi-100$

e)

None of the above

72.

In mathematics, $x!$ is defined as $\left(x\right)\cdot\left(x-1\right)\cdot\left(x-2\right)...\left(1\right)$ .

How many integers from 1 to 40 cannot be the number of consecutive digit 0's at the end of $x!$ , for some integer x?

a)

0

b)

6

c)

7

d)

10

e)

None of the above

Olympic

Total questions: 72

Worksheet time: 2hrs 33mins

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