ZBIS Math Competition 2022

GEOMETRY

100

What is the perimeter of a square that has an area of 25?

20

200

the angles of pentagon are y, (y+10), (y+20), (y+30), and (y+40). work out the value of y. 

what is 5y + 100 = 540.  440 divided by 5 is 88. y = 88.

300

At a certain time of day, a 25-foot telephone pole casts a 10-foot shadow. At that same time, how high would a tree have to be in order to cast a 25-food shadow?

62.5 feet. Proportional reasoning with similar triangles.

400

If the integer lengths of the three sides of a right triangle are 12, x, and 13, what is the possible perimeter of the triangle?

30.   12 + 13 + 5 = 30.    12² + 5² = 13² 

500

What is the number of sides of a polygon in which the sum of the degree measures of the interior angles is 4 times the sum of the degree measures of the exterior angles?

10. Sum of the degree measures of exterior angles is 360. S = (n-2)180 = 4 x 360, where n=number of sides. Solving for (n-2) = 8 or n=10.

ALGEBRA 2

100

If x^-2 = 1/64, what is the value of x³ + x⁰?

x³ = 8.    8³ + 8⁰ = 512 +1 = 513

200

Let the function f be defined by f(x) = 3x-1 and let the function g be defined by g(x) = x².   fg(2).

g(2) = 2² = 4.   f(4)=3(4) - 1 = 11

300

3(x + 5) > 2(x - 6)

3x +15 > 2x - 12   

then x > -27

400

What is the equation of the graph obtained by shifting the graph of y=x² horizontally to the left 4 units and vertically down 3 units?

y = (x+4)² - 3

500

A culture of 5000 bacteria triples every 15 minutes. What is the size of the bacteria population after 30 minutes have elapsed?

45000

Fraction and Decimal

100

find the largest fraction: 11/4,  28/11,  or 23/9

answer is 11/4.

200

Susan weighs p pounds. If Susan gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs x pounds, then Susan's weight, p, in terms of x is

x-25

300

work out (36 x 0.5)/(0.2 x 4.5)

20

400

simplify: (4x²(3x⁴)) divided by 6x⁴

2x²

500

Fruit for a dessert costs $1.20 a pound. If 5 pounds of fruit are needed to make a dessert that serves 18 people, what is the cost of the fruit needed to make enough of the same dessert to serve 24 people?

$8.00. If 5 pounds of fruit serve 18 people, then 5/18 pound serves one person, so 24 x 5/18 = 20/3 pounds. Since the fruit costs $1.20 a pound, the cost of the fruit needed to serve 24 people is 20/3 x $1.20 = $8.00.

ALGEBRA 1

100

If (2^3)^2 = 4^p, then 3^p =

27

200

When the number of people who contribute equally to a gift decreases from four to three, each person must pay an additional $10. What is the cost of the gift?

$120.

300

Simplify (x + 2)^2 - x^2

4(x+1) Note: x^2 + 4x + 4 - x^2

400

For the simultaneous equations: 

4x - y = 16 and

6x - y = 26, what is x?

x = 5

500

For how many integer values of b is possible if b+3>0 and 1>2b-9?

Seven. b>-3, and b<5. Since b is an integer, b may be equal to any of the following: -2, -1, 0, 1, 2, 3, or 4.

total of 7 possible integer values.

MIXED

100

What is the order from smallest to largest?

1.75kg, 1975g, 0.9kg, 1800g

0.9kg, 1.75kg, 1800g, 1975g, 

200

what is the value of x.

3x - 1 divided by 2 is 7

x = 5

300

what is equal to x when y = 6+(x/7k)

x = 7k(y - 6)

400

2 workers will take 20 minutes to wash a car. how long will it take for 4 workers to wash a car? 

2 workers = 20 minutes so 4 workers take 10 minutes.

500

x, y, 22, 14, 10... In this sequence, each term after the first term x is obtained by halving the term that comes before it and then adding 3 to that number. What is the value of x-y?

32. x=70, y=38. 70-38=32.