1 Mathematics Exam: Test A ?

1
Mathematics Exam: Test A
1. What is the last digit of 330 ?
(a) 9
(b) 2
(c) 3
(d) 0
(c) 125%
(d) 8%
(b) 8
(c) 4
(d) 2
(b) 3
(c) 4
(d) 9
2. What percentage of 112 is 14?
(a) 0.125%
(b) 12.5%
3. If 4x + 4y = 16, then what is the value of x + y?
(a) 6
4. If
p
1+
√
x = 2 then x =
(a) 1
5. What is the value of (3x − 2)(4x + 1) − (3x − 2)4x + 1 when x = 4?
(a) 10
(b) 11
(c) 9
(d) 1
6. Suppose that a and b are nonzero real numbers, and that the equation x 2 + ax + b = 0 has solutions
a and b. What is the pair (a, b)?
(a) (2, 1)
(b) (1, −2)
(c) (−1, 2)
(d) (−2, −1)
7. The product of three consecutive integers is 8 times their sum. What is the sum of their squares?
(a) 87
(b) 77
(c) 97
(d) 67
8. What is x if 35−x = 81x+1 ?
(a)
1
5
(b)
1
3
(c)
1
4
(d)
4
5
9. If x + 2 is a factor of x 4 + x 3 + 3x 2 + kx − 10 then k =
(a) 5
10. If f (x) =
(a) 11
(b) 0
(c) −5
(d) 1
x+4
and f −1 is the inverse function of f what is f −1 (5)?
3
(b) 34
Facoltà di Economia Università di Bologna
(c) 43
(d) 51
2
Mathematics Exam: Test A
11. The set {x ∈ R : x|x| = 2x + 1} is
(a)
n
√ o
1; −1 + 2
(b)
n
√ o
−1; 1 + 2
12. Which of the following is the same as
(a)
2
5
(b)
2
9
(c)
n
√ o
−1; 1 − 2
2 − 4 + 6 − 8 + 10 − 12 + 14
3 − 6 + 9 − 12 + 15 − 18 + 21
2
(c)
7
(d)
n
√ o
−1; −1 − 2
(d)
2
3
13. A cubical block of metal weighs 6 pounds. How much will another cube of the same metal weigh if
its sides are twice as long?
(a) 32
(b) 81
(c) 12
(d) 48
14. In a class of 78 students 41 are taking French, 22 are taking German and 9 students are taking both
French and German. How many students are not enrolled in either course?
(a) 6
(b) 15
(c) 33
(d) 24
(c) −25
(d) 25
15. If f (x) = |x 2 − 50|, what is the value of f (−5)?
(a) 75
(b) −5
16. What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?
(a) 100
(b) 90
(c) 95
(d) 105
17. Stacey, Carla, Julia and Rose want to take seats in a cinema. There is only 1 aisle seat and the rest
are in a line next to it. If Rose want to sit in the aisle seat, Julia wants to sit next to Stacey, and Carla
doesn’t want to sit next to Julia, how will they sit (starting at the aisle)?
(a) Rose, Julia, Stacey,
Carla
(b) Rose, Carla, Julia,
Stacey
(c) Stacey, Carla, Julia, Rose
(d) Rose, Stacey, Julia,
Carla
(b) 232
(c) 830
(d) 8120
18. 230 + 230 + 230 + 230 =
(a) 226
19. n and p are integers greater than 1. 5 × n is the square of a number. 75 × n × p is the cube of a
number. The smallest value for n + p is
(a) 20
(b) 18
(c) 14
(d) 30
20. After being dropped a certain ball always bounces back to 2/5 of the height of its previous bounce.
After the first bounce it reaches a height of 125 inches. How high (in inches) will it reach after its
fourth bounce?
(a) 20
21.
√
(b) 15
(c) 10
(d) 8
(b) 0.25
(c) 0.5
(d) 2.5
√
5 percent of 5 5:
(a) 0.05
Facoltà di Economia Università di Bologna
3
Mathematics Exam: Test A
22. −20, −16, −12, −8, . . .: in the sequence above, each term after the first is 4 greater than the preceding
term. Which of the following could not be a term in the sequence?
(a) 0
(b) 200
(c) 762
(d) 668
23. For how many integer values of n will the value of the expression 4n + 7 be an integer greater than
1 and less than 200?
(a) 48
(b) 49
(c) 50
(d) 51
24. Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now
in terms of P ?
(a) − 17
P +6
(b)
P
11
+6
(c)
11
P
+6
(d) − 11
P −6
25. 12 litres of water are poured into an aquarium of dimensions 50 cm length , 30 cm breadth, and 40
cm height. How high (in cm) will the water rise? ( 1 litre = 1000 cubic cm).
(a) 6
(b) 8
(c) 10
(d)
12
5
26. Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If
only one person gets off at stop number 7 , how many people got on at the first stop?
(a) 128
(b) 64
(c) 32
(d) 16
27. I have different shapes. The triangle is smaller than the rectangle. The rectangle is larger than the
circle. The circle is smaller than the square. The octagon is larger than the triangle. The pentagon
is smaller than the octagon. The ellipse is larger than the pentagon. Which of these cannot be the
largest shape?
(a) Rectangle
(b) Circle
(c) Octagon
(d) Square
28. x and y are integers. x + y < 11 , and x > 6 What is the smallest possible value of x − y ?
(a) 4
(b) 1
(c) 2
(d) −2
29. 3x + y = 19 , and x + 3y = 1. Find the value of 2x + 2y.
(a) 10
(b) 20
(c) 18
(d) 5
30. The number 0.127 is how much greater than 1/8 ?
(a)
1
500
(b)
1
2
Facoltà di Economia Università di Bologna
(c)
2
10
(d)
2
500