Meet 5 – Event A
2015-2016
Questions are worth 2-2-2-4-4 points respectively.
NO CALCULATORS ALLOWED
_______________1.
Simplify. Write your answer in descending order.
(x – 7)2 – (5x + 1)
_______________2.
Write the expression in completely factored form.
3x2 – 6x – 72
__________3.
%
There are 7 almonds, 12 cashews, 27 peanuts, 11 pecans, and 15 pistachios in a
jar of mixed nuts. Donald reaches in and takes a nut at random. What is the
probability that Donald takes either an almond or a pistachio? Write your
answer as a percentage rounded to the nearest tenth.
__________4.
in3
A birdfeeder is shown. Inside the birdfeeder, there is one layer of
seed and one layer of corn. The amount of seed in the feeder is
1.5 times the amount of corn. How many cubic inches of corn are
in the feeder? Write your answer in terms of .
Step 1:
__________5.
Triangle QRS undergoes a sequence of 3 transformations to form triangle Q’R’S’
as shown. The 2nd transformation (Step 2) is given.
Step
2: a
__________
__________
Step 3:
Choose 2 transformations from the list below
which, when performed as Step 1 and Step 3,
transform triangle QRS into triangle Q’R’S’. Write
the letters representing each transformation on the
appropriate line.
Name_________________________________School___________________________________
©2015 by the Minnesota Junior High School Mathematics League
Meet 5 – Event A
2015-2016
ANSWERS
Questions are worth 2-2-2-4-4 points respectively.
x2 – 19x + 48
_______________1.
(x – 7)2 – (5x + 1) = x2 – 14x + 49 – 5x – 1 =
x2 – 19x + 48
3(x – 6)(x + 4)
_______________2.
3x2 – 6x – 72 = 3(x2 – 2 – 24) = 3(x – 6)(x + 4)
or) 3(x + 4)(x – 6), or any combination
of the factors 3, (x – 6), and (x + 4)
30.6%
__________3.
__________4.
40 in3
7+15
7+12+27+11+15
=
22
72
=
11
36
= 0.3055555 = 30.6%
x: height of corn, V: volume of corn
15 150
=
; 1500 = 150𝑥; 𝑥 = 10
𝑥
100
𝑉 = 𝜋(4)(10) = 𝟒𝟎𝝅
Step 1: f
__________5*.
Step
2: a
__________
__________
Step
3: d
*No partial credit; student must list
letter f for Step 1 and letter d for Step 3
for 4 points.
©2015 by the Minnesota Junior High School Mathematics League
Meet 5 – Event B
2015-2016
Questions are worth 2-2-2-4-4 points respectively.
NO CALCULATORS ALLOWED
_______________1.
Simplify.
2 – 4x(x – 3) + 5x2
Write your answer in descending order.
c=
m
_______________2.
A right triangle is shown. Solve for c.
Write your answer as a simplified
radical expression.
_______________3A.
cm2
A rectangular prism is shown.
A) Find the surface area of the prism in
square centimeters.
B) Find the volume of the prism in cubic
centimeters.
Write your answers as simplified
expressions in terms of x.
cm3
_______________3B.
Consider the graph of y = x2 for Question 4.
__________4.
__________
2
units
_______________5.
The system of equations has two solutions of (x, y).
y = x2
y = 2x + 3
Find both solutions. Write each solution as an
ordered pair.
In the figure, r represents the radius of the circle.
Find the area of the shaded region in square units.
Write your answer in terms of .
Name_________________________________School___________________________________
©2015 by the Minnesota Junior High School Mathematics League
Meet 5 – Event B
2015-2016
ANSWERS
Questions are worth 2-2-2-4-4 points respectively.
x2 + 12x + 2
_______________1.
2 – 4x(x – 3) + 5x2 = 2 – 4x2 + 12x + 5x2 =
x2 + 12x + 2
_______________2.
c = 6√34 m
182 + 302 = c2; 324 + 900 = c2; 1224 = c2;
𝑐 = √1224 = √36(34) = 𝟔√𝟑𝟒
_______________3A*.
6x2 + 64x cm2
SA: 2(3x)(x) + 2(3x)(8) + 2(x)(8) = 6x2 + 48x + 16x = 6x2 + 64x
24x2 cm3
_______________3B*.
V: 3x(x)(8) = 24x2
*1 point each
(3, 9)
__________4*.
(-1, 1)
__________
*2 points each
40.5 ‒ 81 units2
_______________5.
r2 + r2 = 182; 2r2 = 324; r2 = 162; r = √162
162𝜋
Area of circle = 162; Area of ¼ circle = 4 = 40.5𝜋
Area of triangle =
162
2
= 81; Area of shaded region = 40.5 ‒ 81
©2015 by the Minnesota Junior High School Mathematics League
Meet 5 – Team Event 2015-2016
Questions are worth 4 points each.
__________1.
NO CALCULATORS ALLOWED
Solve the system of equations for x and y.
2x – 5y = 70
7x + 10y = 14
Write your answer as an ordered pair.
Use the following information for Questions 2 and 3.
The figure shows a person and 4 locations: A, B, C, and D. The person in the figure must visit
each location exactly once, but the order of the visits is unimportant.
__________2.
In how many different orders can the person visit each store exactly once?
__________3.
What is the probability that the person visits location C first and
location B last? Write your answer as a reduced fraction.
_______________4.
Write the prime factorization of 345.
__________5.
A rectangular prism is shown. The dashed line represents a
diagonal drawn from the upper right vertex to the lower left vertex.
What is the length, in units, of this diagonal? Write your answer
as a simplified radical expression.
x=
__________6.
Solve the equation for x.
2
3(𝑥−1)
=
5
8𝑥
Use the following information to answer Questions 7 and 8.
Dylan writes each letter of his first and last name on a card, and then
places all the cards in a bucket. The diagram shows the amount of cards
containing each letter in the bucket, where X represents 1 card.
__________7.
Dylan chooses 1 card at random. What is the probability that he chooses the letter D? Write your
answer as a reduced fraction.
__________8.
Dylan puts the card from Question 7 back into the bucket. Then he randomly selects a new card.
What is the probability that Dylan selects a letter that ONLY appears in his last name? Write your
answer as a reduced fraction.
$
__________9.
A bakery sells 6-inch cakes and 8-inch
cakes. The table shows the bakery’s cake
sales for two days last week.
Day
Monday
Tuesday
6” Cakes
Sold
20
45
8” Cakes
Sold
10
30
Total
Earnings
$390.00
$1,012.50
How much more does an 8-inch cake cost than a 6-inch cake?
__________10.
Triangle ABC is graphed on a coordinate plane. Vertex A is located at (-5, -7). Triangle ABC is
reflected across the line y = x to form triangle A’B’C’. What is the location of A’? Write your
answer as an ordered pair.
Name_________________________________School___________________________________
©2015 by the Minnesota Junior High School Mathematics League
Meet 5 – Team Event 2015-2016
Questions are worth 4 points each.
(14, -8.4)
__________1.
2
or) (14, −8 )
5
ANSWERS
2(2x – 5y = 70) = 4x – 10y = 140
4x – 10y = 140
+7x + 10y = 14
11x
= 154; x = 14
2(14) – 5y = 70; 28 – 5y = 70; -5y = 42; y = -8.4
ABCD
ABDC
ACBD
ACDB
ADBC
ADCB
24
__________2.
1
12
__________3.
BACD
BADC
BCAD
BCDA
BDAC
BDCA
CABD
CADB
CBAD
CBDA
CDAB
CDBA
DABC
DACB
DBAC
DBCA
DCAB
DCBA
3  5  23
_______________4.
10√5
__________5.
202 + 62 = x2; 𝑥 = √436
2
(√436) + 82 =?2 ; ? = √500 = 𝟏𝟎√𝟓
x = -15
__________6.
2
3(𝑥−1)
=
5
8𝑥
; 2(8x) = 15(x – 1); 16x = 15x – 15; x = -15
1
6
__________7.
2 + 1 + 3 + 4 + 1 + 2 + 2 + 1 + 1 + 1 + 1 + 1 = 18; 3/18 = 1/6
4
9
__________8.
1C + 2E + 1H + 1R + 1S + 1T + 1U = 8 letters only in last name; 8/18 = 4/9
$7.50
__________9.
3(20x + 10y = 390)
45x + 30y = 1012.5
60x + 30y = 1170
- 45x + 30y = 1012.5
15x
= 157.5; x = 10.5
20(10.5) + 10y = 390; 210 + 10y = 390; 10y = 180; y = 18
18 – 10.5 = 7.5
(-7, -5)
__________10.
©2015 by the Minnesota Junior High School Mathematics League