Do You Measure up to the International Elite?

We can't hear enough about the Germans and the Japanese, can we? But just how well do you measure up to these superior beings and all the other "foreign kids" who are supposed to be such geniuses in algebra?

Here are some problems that will take a few minutes to solve. Try them and find out where you stand compared to the world's 13 year old students.

I1. Brad wanted to find three consecutive whole numbers that add up to 81.
He wrote the equation (n - 1) + n + (n + 1) = 81. What does the n stand
for?
A. The least of the three whole numbers
B. The middle whole number
C. The greatest of the three whole numbers
D. The difference between the least and greatest of the three whole
numbers

I4. The numbers in the sequence 2, 7, 12, 17, 22, … increase by fives. The
numbers in the sequence 3, 10, 17, 24, 31, … increase by sevens. The
number 17 occurs in both sequences. If the two sequences are continued,
what is the next number that will be seen in both sequences?

Answer:___________________________

J18. The table represents a relation between x and y.
What is the missing number in the table?
A. 2
B. 3
C. 4
D. 5
E. 6
x y
1 1
2 ?
4 7
7 13
J-18

K4. x
2 < 7 is equivalent to
A. x < 7
2
B. x < 5
C. x < 14
D. x > 5
E. x > 14
K-4

L11. A rubber ball rebounds to half the height it drops. If the ball is dropped from
a rooftop 18 m above the ground, what is the total distance traveled by the
time it hits the ground the third time?
A. 31.5 m
B. 40.5 m
C. 45 m
D. 63 m
L-11

L13. These shapes are arranged in a pattern.
Which set of shapes is arranged in the same pattern?
A.
B.
C.
D.
L-13

L16. Find x if 10x – 15 = 5x + 20
Answer: ____________________________________
L-16

N13. If x = 2, what is the value of 7x + 4
5x –4 ?
Answer:_____________________________

O7. If 3(x + 5) = 30, then x =
A. 2
B. 5
C. 10
D. 95

P10. If m represents a positive number, which of these is equivalent to
m + m + m + m ?
A. m +4
B. 4m
C. m 4
D. 4(m +1)

P15. Which of these expressions is equivalent to y 3 ?
A. y + y + y
B. y ´ y ´ y
C. 3y
D. y 2 + y

Q1. Juan has 5 fewer hats than Maria, and Clarissa has 3 times as many hats as
Juan. If Maria has n hats, which of these represents the number of hats that
Clarissa has?
A. 5 – 3n
B. 3n
C. n – 5
D. 3n – 5
E. 3(n – 5)

Q2. Subtract: 2x
9 - x
9 =
A. 1
9
B. 2
C. x
D. x
9
E. x
81

Q7. P = LW. If P = 12 and L = 3, then W is equal to
A. 3
4
B. 3
C. 4
D. 12
E. 36

R9. Which one of the following is FALSE when a, b, and c are different real
numbers?
A. (a + b) + c = a + (b + c)
B. ab = ba
C. a + b = b + a
D. (ab)c = a(bc)
E. a – b = b – a

R11. A group of students has a total of 29 pencils and everyone has at least one
pencil. Six students have 1 pencil each, 5 students have 3, and the rest have 2.
How many students have only 2 pencils?
A. 4
B. 6
C. 8
D. 9

T1. There are 54 kilograms of apples in two boxes. The second box of apples
weighs 12 kilograms more than the first. How many kilograms of apples are
in each box? Show your work.

vii
I09 Color of card drawn from bag.
J13 Number of students per grade.
K07 Number of blue pens in drawer?
L10 Highest temperature on chart.
M03 Chance of picking red marble.
N18 Probability of even numbered chip.
O01 Speed of car from graph.
O05 Number of red faces.
P17 Temperature on table and thermometers.
Q04 Heights of four girls on graph.
R08 Distance car will travel.
V02 Price of renting office space.
Algebra
I01 What does N stand for?
I04 Number sequence.
J18 Number missing from table.
K04 x/2 < 7 is equivalent to…
L11 Total distance traveled by ball.
L13 Shapes in a pattern.
L16 Solve for x.
N13 Substitute for x.
O07 Solve for x.
P10 Equivalent algebraic expressions.
P15 Equivalent algebraic expression.
Q01 Expression representing number of hats.
Q02 Substraction of algebraic expressions.
Q07 Solve for W.
R09 False algebraic expression.
R11 Number of students with two pencils.
S01A Sequence of triangles (a).
S01B Sequence of triangle (b).
T01A Weight of apples (a).
T01B Weight of apples (b).