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math exams: August 2011
Pharmacy College Admission Test Evaluate the expression: 1000(2^{-1.5}) 2828,427 2000.00
353.55
3000
Evaluate the expression: \log_{49}7 \frac{1}{4} \frac{1}{2}
\frac{2}{5}
\frac{1}{49}
Place into standard form: (5+i)-(7-7i) -2+8i 2+8i
12+8i
-2+6i
Find the domaine of the function: f(x)=\sqrt{-6x+12} x \geq 3
x \leq -2
x \leq -1 x \leq 2
What is the value of: 3\ln e^{6} 6 18
9
12
What is the value of: \csc (150 deg) 1
-1
-2 2
Solve the equation: x^{2}-10x+50=0 5+5i or 5-5i 2+5i or 2-5i
4+5i or 4-5i
1+5i or 1-5i
What is the value of x : \log_{10}x=-3 0.01 0.001
0.1
1
Factor the expression: x^{2}-3ix-2 (x+i)(x+2i) (x+i)(x-2i)
(x-i)(x-2i)
(-x-i)(x-2i)
Identify the horizontal and vertical asymptotes for: \frac{5x^{2}}{x^{2}-9} y=5 , x=-3 , x=3 y=-5 , x=-3
y=5 , x=3
y=5 , x=-3
Answer Key
1 C
2 B
3 A
4 D
5 B
6 D
7 A
8 B
9 C
10 A
Pharmacy College Admission Test For how many positive integers, n , is true that n^{2} \leq 3n 2 3
4
5 If a^{4}=16 , then 3^{a} 3 9
16 27
\sqrt{20}\sqrt{5}= 2\sqrt{5} 10
4\sqrt{5} 5\sqrt{10}
The sum of three positive consecutive even integers is x. \frac{x}{3}+2 3x \frac{x-2}{3} \frac{x}{3} What is the average of 5^{10} , 5^{20} , 5^{30} , 5^{40} and 5^{50} ?5^{9}+5^{19}+5^{29}+5^{39}+5^{49} 5^{30}
5^{149} 150
Which of the following is equal to (5^{6} \times 5^{9})^{10} ?25^{150} 25^{540}
5^{540} 5^{150}
What is the value of 3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}} ?3 9
27 30
How many integers satisfy the inequality |x| < 2 \pi .
3 4 7 More than 7 What is the average of 5^{a} \times 5^{b}=5^{300} 50 100
150 200
If 5^{a}5^{b}=\frac{5^{c}}{5^{d}} , what is d in terms of a , b and c ?\frac{c}{a+b} c+ab
c-a-b c+a-b
Answer Key
1 B
2 B
3 B
4 D
5 A
6 D
7 B
8 D
9 C
10 C
Pharmacy College Admission Test Which of the following is equivalent to 5^{9} 5^{4}+5^{4}+5^{1} 5^{2} \times 5^{4} \times 5^{3}
\frac{10^{9}}{2^{10}}
(5^{4})^{5} Which of the following is equivalent to \sqrt{289} 14 15
16
17 Which of the following is a perfect square? 120 121
122
123 Which of the following is equivalent to 3\sqrt{10} 3\sqrt{5} \times \sqrt{5} \sqrt{90}
3\sqrt{5} + 3\sqrt{2}
3\sqrt{5}+3\sqrt{5} Which of the following is equivalent to 10^{\frac{2}{5}} \sqrt[5]{5} \sqrt[5]{10} \sqrt[5]{20} \sqrt[5]{100} Which of the following fractions is equivalent to \frac{3}{6} \times \frac{2}{5} ? \frac{6}{30} \frac{5}{30} \frac{5}{11} \frac{15}{12} Which of the following expressions is equivalent to \frac{7}{6} \div \frac{5}{2} ?\frac{9}{6}+\frac{9}{5} \frac{7}{8}+\frac{5}{8} \frac{7}{6}+\frac{2}{5} \frac{1}{7}+\frac{2}{35} If 3^{x}=729 , what is x^{3} ? What is the value of ||4|-|-7|| -11 -3 0 3 What is the value of (\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2} 2\sqrt{15} \sqrt{15} 0 15 Answer Key
1 B
2 D
3 B
4 B
5 D
6 A
7 D
8 125
9 D
10 A
Pharmacy College Admission Test Solve 15x-32=18-10x -14 10
14
2 Solve \frac{x}{8}=\frac{x-2}{4} 12 4
6
-\frac{1}{2} Which of the following are the factors of t^{2}+8t+16 (t-8)(t-2)
(t+8)(t+2)
(t+1)(t+16) (t+4)(t+4) Solve for a in term of b, if 6a+12b=24 24-12b 2-\frac{1}{2}b
4-2b
24-18b If ax+2b=5c-dx , what does x equal in terms of a, b, c, and d? a-d
(5c-2b)(a-d)
\frac{5c-d-2b}{a} \frac{5c-2b}{a-d} If (z-9)(z+3)=0 , what are the two possible values of z? z=-9 abd z=3 z=9 abd z=0 z=0 abd z=-3 z=9 abd z=-3 If z^{2}-6z=16 , which of the following could be a value of z^{2}+6z ?-8 112 110 18 If 3\sqrt{ a}-10=2 , what is the value of a?16 4 32 64 Given \frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10 , find the value of x.18 4 12 9 Solve the equation \frac{5x}{8}-\frac{3x}{5}=2 .40 80 160 -80 Answer Key
1 D
2 B
3 D
4 C
5 D
6 D
7 B
8 A
9 D
10 B
Pharmacy College Admission Test 2(5x-5)+5(2x+2)= 0 20x
20x-10
20x+10 If x=a+2 , and y=-8-a then x+y= 10
2a-6
-10 -6 If x \ne -5 , then \frac{x^{2}+3x-10}{x+5}-(x-2)= If (a-\frac{1}{a})^{2}=8 , then a^{2}+\frac{1}{a^{2}}= 8 6
10
12 (x+y)^{2}=16 , and x^{2}+y^{2}=6 then xy= 5 10
6
4 (x+y)=2 , and x^{2}-y^{2}=6 then x-y= 12 4
6
\frac{1}{3} \frac{15y+3}{3}-5y= 1 0
10y+1
3 if b^{2}-a^{2}=9 then 5(a-b)(a+b)= \frac{9}{5}
4
50 -45 When c \ne 3 , then \frac{c^{2}-9}{c-3}= c-3 1
c+3
3-c If b>0 , and b^{2}-1=10 \times 12 , then b= 1
12
10 11 Answer Key
1 B
2 D
3 0
4 C
5 A
6 D
7 A
8 D
9 C
10 D
Pharmacy College Admission Test If 3x+7=5x+1 2.5 3.5 4 3 What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?15 6 17 18 The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B?r_{A}=\frac{r_{B}}{8} r_{A}=8r_{B} r_{A}=4r_{B} r_{A}=2\sqrt{2}r_{B} If x^{2}-2xy+y^{2}=121 , x-y= 10 11 12 13 If c is equal to the sum b and twice of a, which of the following is the average of b and c?a b c a+b f(x)=4x+8 , f(c+3)=8 , f(c)= -8 0 3 8 5^{n}.125^{m}=78,125 , n+3m= 5 6 7 8 \frac{3b^{2}}{a^{3}}=27a^{2} 9a^{3} \frac{1}{9a^{3}} \frac{1}{a^{3}} \frac{1}{3a^{3}} Which of the following statements must be true about the x and y coordinates that satisfy the equation ay-ax=0 , a \ne 0 , x \ne 0 ,y \ne 0 xy=1 x=-y y>x x=y What is the length of the side of a cube whose volume is 125 cubic units?4 5 6 7 Answer Key
1 D
2 D
3 D
4 B
5 D
6 D
7 C
8 D
9 D
10 B
Pharmacy College Admission Test If \frac{1}{2} of a number is 3, what is \frac{1}{3} of the number?1 2
3
6 If x=-1 , then x^{5}+x^{4}+x^{3}+x^{2}-5= -10 -6 -5 -3 If f(x)=2^{x}+7x , then f(4)= 24 36
44
54 If x-3=y , then (y-x)^{3}= 27 54 -54 -27 If a>b , and \frac{a}{b}>0 , which of the following is true?a>0 b>0 ab>0 I only
II only
III only
I and II only
Which of the following is equal to (\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2} x^{8}y^{16} \frac{x^{8}}{y^{16}} \frac{y^{16}}{x^{8}} x^{4}y^{8} What is the slope of the line passing through the points (-1,7) and (3,5)?\frac{1}{2} -2 -\frac{1}{2} 1 The symbol \otimes represents a binary operation defined as a \otimes b=3^{a}+2^{b} , what is the value of (-2)\otimes (-3) \frac{72}{17} -72 72 \frac{17}{72} If \sqrt{\frac{49}{x}}=\frac{7}{3} 6 9 25 49 A bike that originally sold for 150 \$ was on sale for 120 \$ . What was the rate of discount?15 \% 21 \% 20 \% 25 \% Answer Key
1 B
2 C
3 C
4 D
5 C
6 A
7 C
8 D
9 B
10 C
Pharmacy College Admission Test
If 0.10 < x < 0.12 , which of the following could be a value of x ?
9 \% 10 \% 11 \% 12 \%
If \frac{xyz}{t}=w and x and t are doubled, what happens to the value of w
The value of w is halved.
The value of w is four times greater.
The value of w is doubled
The value of w remains the same.
What is the tenth term of the pattern below?\frac{3}{2} , \frac{9}{4} , \frac{27}{8} , \frac{81}{16} ,...
\frac{3}{2^{10}} \frac{30}{20} (\frac{3}{2})^{10} \frac{3^{10}}{2}
If a > 0 and b < 0 , which of the following is always negative?
-ab a+b |a|-|b| \frac{a}{b}
Which of the following number pairs is in the ratio 3:7 ?
\frac{1}{3} ,\frac{1}{7} \frac{1}{7} ,\frac{1}{3} \frac{1}{7} ,\frac{3}{7} 7 ,\frac{1}{3}
If x=-\frac{1}{4} , then (-x)^{-3}+(\frac{1}{x})^{2}=
-64 16 64 80
For which of the following values of x is the relationship x < x^{2} < x^{3} true?
-3 -\frac{2}{3} 0 \frac{2}{3}
x^{2}+2xy+y^{2}=169 , -|-(x+y)|= How many distincts factors does 900 have?
2 3 4 5
If x=-\frac{1}{7} , then which of the following is always positive for n > 0 ?
x^{n} n^{x} nx n-x
Answer Key
1 C
2 D
3 C
4 D
5 B
6 D
7 3
8 -13
9 B
10 B
Factor 3a^{2}+3ab-6b^{2}
Factor x^{3}-4x^{2}+2x-8
Factor 25a^{2}-36b^{2}
Resolve into factors x^{2}-ax+bx-ab
Resolve into factors 6x^{2}-9ax+4bx-6ab
Resolve into factors x^{2}+11x+24
Resolve into factors x^{2}-10x+24
Resolve into factors x^{2}-10ax+10a^{2}
Which of the following is equivalent to 5^{9} 5^{4}+5^{4}+5^{1} 5^{2} \times 5^{4} \times 5^{3}
\frac{10^{9}}{2^{10}}
(5^{4})^{5} \frac{5^{5}}{5^{4}} Which of the following is equivalent to \sqrt{289} 14 15
16
17 18 Which of the following is a perfect square? 120 121
122
123 124 Which of the following is equivalent to 3\sqrt{10} 3\sqrt{5} \times \sqrt{5} \sqrt{90}
3\sqrt{5} + 3\sqrt{2}
3\sqrt{5}+3\sqrt{5} \frac{3\sqrt{2}}{\sqrt{5}} Which of the following is equivalent to 10^{\frac{2}{5}} \sqrt[5]{5} \sqrt[5]{10} \sqrt[5]{20} \sqrt[5]{100} \sqrt[5]{1000} Which of the following fractions is equivalent to \frac{3}{6} \times \frac{2}{5} ? \frac{6}{30} \frac{5}{30} \frac{5}{11} \frac{15}{12} \frac{9}{30} Which of the following expressions is equivalent to \frac{7}{6} \div \frac{5}{2} ?\frac{7}{30}+\frac{2}{30} \frac{9}{6}+\frac{9}{5} \frac{7}{8}+\frac{5}{8} \frac{7}{6}+\frac{2}{5} \frac{1}{7}+\frac{2}{35} If 3^{x}=729 , what is x^{3} ? What is the value of ||4|-|-7|| -11 -3 0 3 11 What is the value of (\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2} 2\sqrt{15} \sqrt{15} 0 15 30 Answer Key
1 B
2 D
3 B
4 B
5 D
6 A
7 E
8 125
9 D
10 A
Solve 15x-32=18-10x -14 10
14
2 50 Solve \frac{x}{8}=\frac{x-2}{4} 12 4
6
-\frac{1}{2} -6 Which of the following are the factors of t^{2}+8t+16 (t-4)(t-4) (t-8)(t-2)
(t+8)(t+2)
(t+1)(t+16) (t+4)(t+4) Solve for a in term of b, if 6a+12b=24 24-12b 2-\frac{1}{2}b
4-2b
24-18b 2b-4 If ax+2b=5c-dx , what does x equal in terms of a, b, c, and d?5c-d-2b-a a-d
(5c-2b)(a-d)
\frac{5c-d-2b}{a} \frac{5c-2b}{a-d} If (z-9)(z+3)=0 , what are the two possible values of z? z=-9 abd z=3 z=9 abd z=0 z=0 abd z=-3 z=9 abd z=-3 z=-12 abd z=12 If z^{2}-6z=16 , which of the following could be a value of z^{2}+6z ?-8 112 110 18 108 If 3\sqrt{ a}-10=2 , what is the value of a?16 4 32 64 12 Given \frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10 , find the value of x.18 4 12 9 12 Solve the equation \frac{5x}{8}-\frac{3x}{5}=2 .40 80 160 -80 20 Answer Key
1 D
2 B
3 E
4 C
5 E
6 D
7 B
8 A
9 D
10 B
2(5x-5)+5(2x+2)= 0 20x
20x-10
20x+10 10x^{2}+20+x+20 If x=a+2 , and y=-8-a then x+y= 6 10
2a-6
-10 -6 If x \ne -5 , then \frac{x^{2}+3x-10}{x+5}-(x-2)= If (a-\frac{1}{a})^{2}=8 , then a^{2}+\frac{1}{a^{2}}= 8 6
10
12 100 (x+y)^{2}=16 , and x^{2}+y^{2}=6 then xy= 5 10
6
4 16 (x+y)=2 , and x^{2}-y^{2}=6 then x-y= 12 4
6
\frac{1}{3} 3 \frac{15y+3}{3}-5y= 1 0
10y+1
3 3y+1 if b^{2}-a^{2}=9 then 5(a-b)(a+b)= 45 \frac{9}{5}
4
50 -45 When c \ne 3 , then \frac{c^{2}-9}{c-3}= c-3 1
c+3
3-c o If b>0 , and b^{2}-1=10 \times 12 , then b= 9 1
12
10 11 Answer Key
1 B
2 E
3 0
4 C
5 A
6 D
7 A
8 E
9 C
10 E
If 3x+7=5x+1 2.5 3.5 4 3 4.5 What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?19 15 6 17 18 The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B?r_{A}=\frac{r_{B}}{8} r_{A}=8r_{B} r_{A}=4r_{B} r_{A}=2\sqrt{2}r_{B} r_{A}=\frac{r_{B}}{4} If x^{2}-2xy+y^{2}=121 , x-y= 10 11 12 13 14 If c is equal to the sum b and twice of a, which of the following is the average of b and c?a b c a+b b+c f(x)=4x+8 , f(c+3)=8 , f(c)= -8 0 3 8 -3 5^{n}.125^{m}=78,125 , n+3m= 5 6 7 8 9 \frac{3b^{2}}{a^{3}}=27a^{2} 3a^{3} 9a^{3} \frac{1}{9a^{3}} \frac{1}{a^{3}} \frac{1}{3a^{3}} Which of the following statements must be true about the x and y coordinates that satisfy the equation ay-ax=0 , a \ne 0 , x \ne 0 ,y \ne 0 x>y xy=1 x=-y y>x x=y What is the length of the side of a cube whose volume is 125 cubic units?4 5 6 7 4.5 Answer Key
1 D
2 E
3 D
4 B
5 D
6 D
7 C
8 E
9 E
10 B
If \frac{1}{2} of a number is 3, what is \frac{1}{3} of the number?1 2
3
6 8 If x=-1 , then x^{5}+x^{4}+x^{3}+x^{2}-5= -10 -6 -5 -3 -1 If f(x)=2^{x}+7x , then f(4)= 24 36
44
54 64 If x-3=y , then (y-x)^{3}= 27 54 -54 -27 81 If a>b , and \frac{a}{b}>0 , which of the following is true?a>0 b>0 ab>0 I only
II only
III only
I and II only
I and III only
Which of the following is equal to (\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2} x^{8}y^{16} \frac{x^{8}}{y^{16}} \frac{y^{16}}{x^{8}} x^{4}y^{8} x^{8}y^{8} What is the slope of the line passing through the points (-1,7) and (3,5)?\frac{1}{2} -2 -\frac{1}{2} 1 2 The symbol \otimes represents a binary operation defined as a \otimes b=3^{a}+2^{b} , what is the value of (-2)\otimes (-3) -\frac{17}{72} \frac{72}{17} -72 72 \frac{17}{72} If \sqrt{\frac{49}{x}}=\frac{7}{3} 6 9 25 49 147 A bike that originally sold for 150 \$ was on sale for 120 \$ . What was the rate of discount?15 \% 21 \% 20 \% 25 \% 30 \% Answer Key
1 B
2 C
3 C
4 D
5 C
6 A
7 C
8 E
9 B
10 C
If 0.10 < x < 0.12 , which of the following could be a value of x ? 9 \% 10 \% 11 \% 12 \% 13 \% If \frac{xyz}{t}=w and x and t are doubled, what happens to the value of w The value of w is two times smaller.
The value of w is halved.
The value of w is four times greater.
The value of w is doubled
The value of w remains the same.
What is the tenth term of the pattern below?\frac{3}{2} , \frac{9}{4} , \frac{27}{8} , \frac{81}{16} ,...\frac{3}{2^{10}} \frac{30}{20} (\frac{3}{2})^{10} \frac{3^{10}}{2}
\frac{300}{200} If a > 0 and b < 0 , which of the following is always negative? -ab a+b |a|-|b| \frac{a}{b}
b^{a} Which of the following number pairs is in the ratio 3:7 ?\frac{1}{3} ,\frac{1}{7} \frac{1}{7} ,\frac{1}{3} \frac{1}{7} ,\frac{3}{7} 7 ,\frac{1}{3} 1 ,\frac{1}{7} If x=-\frac{1}{4} , then (-x)^{-3}+(\frac{1}{x})^{2}= -80 -64 16 64 80 For which of the following values of x is the relationship x < x^{2} < x^{3} true? -3 -\frac{2}{3} 0 \frac{2}{3} 3 x^{2}+2xy+y^{2}=169 , -|-(x+y)|= How many distincts factors does 900 have?2 3 4 5 more than 5
If x=-\frac{1}{7} , then which of the following is always positive for n > 0 ?x^{n} n^{x} nx n-x \frac{x}{n} Answer Key
1 C
2 E
3 C
4 D
5 B
6 E
7 3
8 -13
9 A
10 B
For how many positive integers, n , is true that n^{2} \leq 3n 2 3
4
5 more than 5
If a^{4}=16 , then 3^{a} 3 9
16 27
81 \sqrt{20}\sqrt{5}= 2\sqrt{5} 10
4\sqrt{5} 5\sqrt{10}
10\sqrt{5} The sum of three positive consecutive even integers is x. \frac{x}{3}-1 \frac{x}{3}+2 3x \frac{x-2}{3} \frac{x}{3} What is the average of 5^{10} , 5^{20} , 5^{30} , 5^{40} and 5^{50} ?5^{9}+5^{19}+5^{29}+5^{39}+5^{49} 5^{30}
5^{149} 150
5^{29} Which of the following is equal to (5^{6} \times 5^{9})^{10} ?25^{150} 25^{540}
5^{540} 5^{150}
5^{15} What is the value of 3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}} ?3 9
27 30
81 How many integers satisfy the inequality |x| < 2 \pi .
0 3 4 7 More than 7 What is the average of 5^{a} \times 5^{b}=5^{300} 50 100
150 200
250 If 5^{a}5^{b}=\frac{5^{c}}{5^{d}} , what is d in terms of a , b and c ?\frac{c}{a+b} c+ab
c-a-b c+a-b
\frac{b}{ac} Answer Key
1 B
2 B
3 B
4 E
5 A
6 D
7 B
8 E
9 C
10 C
2(5x-5)+5(2x+2)= 0 20x
20x-10
20x+10 10x^{2}+20+x+20 If x=a+2 , and y=-8-a then x+y= 6 10
2a-6
-10 -6 If x \ne -5 , then \frac{x^{2}+3x-10}{x+5}-(x-2)= If (a-\frac{1}{a})^{2}=8 , then a^{2}+\frac{1}{a^{2}}= 8 6
10
12 100 (x+y)^{2}=16 , and x^{2}+y^{2}=6 then xy= 5 10
6
4 16 (x+y)=2 , and x^{2}-y^{2}=6 then x-y= 12 4
6
\frac{1}{3} 3 \frac{15y+3}{3}-5y= 1 0
10y+1
3 3y+1 if b^{2}-a^{2}=9 then 5(a-b)(a+b)= 45 \frac{9}{5}
4
50 -45 When c \ne 3 , then \frac{c^{2}-9}{c-3}= c-3 1
c+3
3-c o If b>0 , and b^{2}-1=10 \times 12 , then b= 9 1
12
10 11 Answer Key
1 B
2 E
3 0
4 C
5 A
6 D
7 A
8 E
9 C
10 E
Solve 15x-32=18-10x -14 10
14
2 50 Solve \frac{x}{8}=\frac{x-2}{4} 12 4
6
-\frac{1}{2} -6 Which of the following are the factors of t^{2}+8t+16 (t-4)(t-4) (t-8)(t-2)
(t+8)(t+2)
(t+1)(t+16) (t+4)(t+4) Solve for a in term of b, if 6a+12b=24 24-12b 2-\frac{1}{2}b
4-2b
24-18b 2b-4 If ax+2b=5c-dx , what does x equal in terms of a, b, c, and d?5c-d-2b-a a-d
(5c-2b)(a-d)
\frac{5c-d-2b}{a} \frac{5c-2b}{a-d} If (z-9)(z+3)=0 , what are the two possible values of z? z=-9 abd z=3 z=9 abd z=0 z=0 abd z=-3 z=9 abd z=-3 z=-12 abd z=12 If z^{2}-6z=16 , which of the following could be a value of z^{2}+6z ?-8 112 110 18 108 If 3\sqrt{ a}-10=2 , what is the value of a?16 4 32 64 12 Given \frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10 , find the value of x.18 4 12 9 12 Solve the equation \frac{5x}{8}-\frac{3x}{5}=2 .40 80 160 -80 20 Answer Key
1 D
2 B
3 E
4 C
5 E
6 D
7 B
8 A
9 D
10 B
Which of the following is equivalent to 5^{9} 5^{4}+5^{4}+5^{1} 5^{2} \times 5^{4} \times 5^{3}
\frac{10^{9}}{2^{10}}
(5^{4})^{5} \frac{5^{5}}{5^{4}} Which of the following is equivalent to \sqrt{289} 14 15
16
17 18 Which of the following is a perfect square? 120 121
122
123 124 Which of the following is equivalent to 3\sqrt{10} 3\sqrt{5} \times \sqrt{5} \sqrt{90}
3\sqrt{5} + 3\sqrt{2}
3\sqrt{5}+3\sqrt{5} \frac{3\sqrt{2}}{\sqrt{5}} Which of the following is equivalent to 10^{\frac{2}{5}} \sqrt[5]{5} \sqrt[5]{10} \sqrt[5]{20} \sqrt[5]{100} \sqrt[5]{1000} Which of the following fractions is equivalent to \frac{3}{6} \times \frac{2}{5} ? \frac{6}{30} \frac{5}{30} \frac{5}{11} \frac{15}{12} \frac{9}{30} Which of the following expressions is equivalent to \frac{7}{6} \div \frac{5}{2} ?\frac{7}{30}+\frac{2}{30} \frac{9}{6}+\frac{9}{5} \frac{7}{8}+\frac{5}{8} \frac{7}{6}+\frac{2}{5} \frac{1}{7}+\frac{2}{35} If 3^{x}=729 , what is x^{3} ? What is the value of ||4|-|-7|| -11 -3 0 3 11 What is the value of (\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2} 2\sqrt{15} \sqrt{15} 0 15 30 Answer Key
1 B
2 D
3 B
4 B
5 D
6 A
7 E
8 125
9 D
10 A
For how many positive integers, n , is true that n^{2} \leq 3n 2 3
4
5 more than 5
If a^{4}=16 , then 3^{a} 3 9
16 27
81 \sqrt{20}\sqrt{5}= 2\sqrt{5} 10
4\sqrt{5} 5\sqrt{10}
10\sqrt{5} The sum of three positive consecutive even integers is x. \frac{x}{3}-1 \frac{x}{3}+2 3x \frac{x-2}{3} \frac{x}{3} What is the average of 5^{10} , 5^{20} , 5^{30} , 5^{40} and 5^{50} ?5^{9}+5^{19}+5^{29}+5^{39}+5^{49} 5^{30}
5^{149} 150
5^{29} Which of the following is equal to (5^{6} \times 5^{9})^{10} ?25^{150} 25^{540}
5^{540} 5^{150}
5^{15} What is the value of 3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}} ?3 9
27 30
81 How many integers satisfy the inequality |x| < 2 \pi .
0 3 4 7 More than 7 What is the average of 5^{a} \times 5^{b}=5^{300} 50 100
150 200
250 If 5^{a}5^{b}=\frac{5^{c}}{5^{d}} , what is d in terms of a , b and c ?\frac{c}{a+b} c+ab
c-a-b c+a-b
\frac{b}{ac} Answer Key
1 B
2 B
3 B
4 E
5 A
6 D
7 B
8 E
9 C
10 C
If 0.10 < x < 0.12 , which of the following could be a value of x ? 9 \% 10 \% 11 \% 12 \% 13 \% If \frac{xyz}{t}=w and x and t are doubled, what happens to the value of w The value of w is two times smaller.
The value of w is halved.
The value of w is four times greater.
The value of w is doubled
The value of w remains the same.
What is the tenth term of the pattern below?\frac{3}{2} , \frac{9}{4} , \frac{27}{8} , \frac{81}{16} ,...\frac{3}{2^{10}} \frac{30}{20} (\frac{3}{2})^{10} \frac{3^{10}}{2}
\frac{300}{200} If a > 0 and b < 0 , which of the following is always negative? -ab a+b |a|-|b| \frac{a}{b}
b^{a} Which of the following number pairs is in the ratio 3:7 ?\frac{1}{3} ,\frac{1}{7} \frac{1}{7} ,\frac{1}{3} \frac{1}{7} ,\frac{3}{7} 7 ,\frac{1}{3} 1 ,\frac{1}{7} If x=-\frac{1}{4} , then (-x)^{-3}+(\frac{1}{x})^{2}= -80 -64 16 64 80 For which of the following values of x is the relationship x < x^{2} < x^{3} true? -3 -\frac{2}{3} 0 \frac{2}{3} 3 x^{2}+2xy+y^{2}=169 , -|-(x+y)|= How many distincts factors does 900 have?2 3 4 5 more than 5
If x=-\frac{1}{7} , then which of the following is always positive for n > 0 ?x^{n} n^{x} nx n-x \frac{x}{n} Answer Key
1 C
2 E
3 C
4 D
5 B
6 E
7 3
8 -13
9 A
10 B
If \frac{1}{2} of a number is 3, what is \frac{1}{3} of the number?1 2
3
6 8 If x=-1 , then x^{5}+x^{4}+x^{3}+x^{2}-5= -10 -6 -5 -3 -1 If f(x)=2^{x}+7x , then f(4)= 24 36
44
54 64 If x-3=y , then (y-x)^{3}= 27 54 -54 -27 81 If a>b , and \frac{a}{b}>0 , which of the following is true?a>0 b>0 ab>0 I only
II only
III only
I and II only
I and III only
Which of the following is equal to (\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2} x^{8}y^{16} \frac{x^{8}}{y^{16}} \frac{y^{16}}{x^{8}} x^{4}y^{8} x^{8}y^{8} What is the slope of the line passing through the points (-1,7) and (3,5)?\frac{1}{2} -2 -\frac{1}{2} 1 2 The symbol \otimes represents a binary operation defined as a \otimes b=3^{a}+2^{b} , what is the value of (-2)\otimes (-3) -\frac{17}{72} \frac{72}{17} -72 72 \frac{17}{72} If \sqrt{\frac{49}{x}}=\frac{7}{3} 6 9 25 49 147 A bike that originally sold for 150 \$ was on sale for 120 \$ . What was the rate of discount?15 \% 21 \% 20 \% 25 \% 30 \% Answer Key
1 B
2 C
3 C
4 D
5 C
6 A
7 C
8 E
9 B
10 C
If 3x+7=5x+1 2.5 3.5 4 3 4.5 What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?19 15 6 17 18 The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B?r_{A}=\frac{r_{B}}{8} r_{A}=8r_{B} r_{A}=4r_{B} r_{A}=2\sqrt{2}r_{B} r_{A}=\frac{r_{B}}{4} If x^{2}-2xy+y^{2}=121 , x-y= 10 11 12 13 14 If c is equal to the sum b and twice of a, which of the following is the average of b and c?a b c a+b b+c f(x)=4x+8 , f(c+3)=8 , f(c)= -8 0 3 -3 8 5^{n}.125^{m}=78,125 , n+3m= 5 6 7 8 9 \frac{3b^{2}}{a^{3}}=27a^{2} 3a^{3} 9a^{3} \frac{1}{9a^{3}} \frac{1}{a^{3}} \frac{1}{3a^{3}} Which of the following statements must be true about the x and y coordinates that satisfy the equation ay-ax=0 , a \ne 0 , x \ne 0 ,y \ne 0 x>y xy=1 x=-y y>x x=y What is the length of the side of a cube whose volume is 125 cubic units?4 5 6 7 4.5 Answer Key
1 D
2 E
3 D
4 B
5 D
6 D
7 C
8 E
9 E
10 B
If 3x+7=5x+1 2.5 3.5 4 3 4.5 What is the next term in the sequence: 6, 3, 10, 7, 14, 11, ...?19 15 6 17 18 The area of the basis of Cylinder A is 8 times the area of the basis of Cylinder B. What is the radius of Cylinder A in terms of the radius of Cylinder B?r_{A}=\frac{r_{B}}{8} r_{A}=8r_{B} r_{A}=4r_{B} r_{A}=2\sqrt{2}r_{B} r_{A}=\frac{r_{B}}{4} If x^{2}-2xy+y^{2}=121 , x-y= 10 11 12 13 14 If c is equal to the sum b and twice of a, which of the following is the average of b and c?a b c a+b b+c f(x)=4x+8 , f(c+3)=8 , f(c)= -8 0 3 8 -3 5^{n}.125^{m}=78,125 , n+3m= 5 6 7 8 9 \frac{3b^{2}}{a^{3}}=27a^{2} 3a^{3} 9a^{3} \frac{1}{9a^{3}} \frac{1}{a^{3}} \frac{1}{3a^{3}} Which of the following statements must be true about the x and y coordinates that satisfy the equation ay-ax=0 , a \ne 0 , x \ne 0 ,y \ne 0 x>y xy=1 x=-y y>x x=y What is the length of the side of a cube whose volume is 125 cubic units?4 5 6 7 4.5 Answer Key
1 D
2 E
3 D
4 B
5 D
6 D
7 C
8 E
9 E
10 B
If \frac{1}{2} of a number is 3, what is \frac{1}{3} of the number?1 2
3
6 8 If x=-1 , then x^{5}+x^{4}+x^{3}+x^{2}-5= -10 -6 -5 -3 -1 If f(x)=2^{x}+7x , then f(4)= 24 36
44
54 64 If x-3=y , then (y-x)^{3}= 27 54 -54 -27 81 If a>b , and \frac{a}{b}>0 , which of the following is true?a>0 b>0 ab>0 I only
II only
III only
I and II only
I and III only
Which of the following is equal to (\frac{x^{-7}y^{-5}}{x^{-3}y^{3}})^{-2} x^{8}y^{16} \frac{x^{8}}{y^{16}} \frac{y^{16}}{x^{8}} x^{4}y^{8} x^{8}y^{8} What is the slope of the line passing through the points (-1,7) and (3,5)?\frac{1}{2} -2 -\frac{1}{2} 1 2 The symbol \otimes represents a binary operation defined as a \otimes b=3^{a}+2^{b} , what is the value of (-2)\otimes (-3) -\frac{17}{72} \frac{72}{17} -72 72 \frac{17}{72} If \sqrt{\frac{49}{x}}=\frac{7}{3} 6 9 25 49 147 A bike that originally sold for 150 \$ was on sale for 120 \$ . What was the rate of discount?15 \% 21 \% 20 \% 25 \% 30 \% Answer Key
1 B
2 C
3 C
4 D
5 C
6 A
7 C
8 E
9 B
10 C
If 0.10 < x < 0.12 , which of the following could be a value of x ? 9 \% 10 \% 11 \% 12 \% 13 \% If \frac{xyz}{t}=w and x and t are doubled, what happens to the value of w The value of w is two times smaller.
The value of w is halved.
The value of w is four times greater.
The value of w is doubled
The value of w remains the same.
What is the tenth term of the pattern below?\frac{3}{2} , \frac{9}{4} , \frac{27}{8} , \frac{81}{16} ,...\frac{3}{2^{10}} \frac{30}{20} (\frac{3}{2})^{10} \frac{3^{10}}{2}
\frac{300}{200} If a > 0 and b < 0 , which of the following is always negative? -ab a+b |a|-|b| \frac{a}{b}
b^{a} Which of the following number pairs is in the ratio 3:7 ?\frac{1}{3} ,\frac{1}{7} \frac{1}{7} ,\frac{1}{3} \frac{1}{7} ,\frac{3}{7} 7 ,\frac{1}{3} 1 ,\frac{1}{7} If x=-\frac{1}{4} , then (-x)^{-3}+(\frac{1}{x})^{2}= -80 -64 16 64 80 For which of the following values of x is the relationship x < x^{2} < x^{3} true? -3 -\frac{2}{3} 0 \frac{2}{3} 3 x^{2}+2xy+y^{2}=169 , -|-(x+y)|= How many distincts factors does 900 have?2 3 4 5 more than 5
If x=-\frac{1}{7} , then which of the following is always positive for n > 0 ?x^{n} n^{x} nx n-x \frac{x}{n} Answer Key
1 C
2 E
3 C
4 D
5 B
6 E
7 3
8 -13
9 A
10 B
For how many positive integers, n , is true that n^{2} \leq 3n 2 3
4
5 more than 5
If a^{4}=16 , then 3^{a} 3 9
16 27
81 \sqrt{20}\sqrt{5}= 2\sqrt{5} 10
4\sqrt{5} 5\sqrt{10}
10\sqrt{5} The sum of three positive consecutive even integers is x. \frac{x}{3}-1 \frac{x}{3}+2 3x \frac{x-2}{3} \frac{x}{3} What is the average of 5^{10} , 5^{20} , 5^{30} , 5^{40} and 5^{50} ?5^{9}+5^{19}+5^{29}+5^{39}+5^{49} 5^{30}
5^{149} 150
5^{29} Which of the following is equal to (5^{6} \times 5^{9})^{10} ?25^{150} 25^{540}
5^{540} 5^{150}
5^{15} What is the value of 3^{\frac{1}{3}} \times 3^{\frac{2}{3}} \times 3^{\frac{3}{3}} ?3 9
27 30
81 How many integers satisfy the inequality |x| < 2 \pi .
0 3 4 7 More than 7 What is the average of 5^{a} \times 5^{b}=5^{300} 50 100
150 200
250 If 5^{a}5^{b}=\frac{5^{c}}{5^{d}} , what is d in terms of a , b and c ?\frac{c}{a+b} c+ab
c-a-b c+a-b
\frac{b}{ac} Answer Key
1 B
2 B
3 B
4 E
5 A
6 D
7 B
8 E
9 C
10 C
Which of the following is equivalent to 5^{9} 5^{4}+5^{4}+5^{1} 5^{2} \times 5^{4} \times 5^{3}
\frac{10^{9}}{2^{10}}
(5^{4})^{5} \frac{5^{5}}{5^{4}} Which of the following is equivalent to \sqrt{289} 14 15
16
17 18 Which of the following is a perfect square? 120 121
122
123 124 Which of the following is equivalent to 3\sqrt{10} 3\sqrt{5} \times \sqrt{5} \sqrt{90}
3\sqrt{5} + 3\sqrt{2}
3\sqrt{5}+3\sqrt{5} \frac{3\sqrt{2}}{\sqrt{5}} Which of the following is equivalent to 10^{\frac{2}{5}} \sqrt[5]{5} \sqrt[5]{10} \sqrt[5]{20} \sqrt[5]{100} \sqrt[5]{1000} Which of the following fractions is equivalent to \frac{3}{6} \times \frac{2}{5} ? \frac{6}{30} \frac{5}{30} \frac{5}{11} \frac{15}{12} \frac{9}{30} Which of the following expressions is equivalent to \frac{7}{6} \div \frac{5}{2} ?\frac{7}{30}+\frac{2}{30} \frac{9}{6}+\frac{9}{5} \frac{7}{8}+\frac{5}{8} \frac{7}{6}+\frac{2}{5} \frac{1}{7}+\frac{2}{35} If 3^{x}=729 , what is x^{3} ? What is the value of ||4|-|-7|| -11 -3 0 3 11 What is the value of (\sqrt{3}+\sqrt{5})^{2}-(\sqrt{8})^{2} 2\sqrt{15} \sqrt{15} 0 15 30 Answer Key
1 B
2 D
3 B
4 B
5 D
6 A
7 E
8 125
9 D
10 A
Solve 15x-32=18-10x -14 10
14
2 50 Solve \frac{x}{8}=\frac{x-2}{4} 12 4
6
-\frac{1}{2} -6 Which of the following are the factors of t^{2}+8t+16 (t-4)(t-4) (t-8)(t-2)
(t+8)(t+2)
(t+1)(t+16) (t+4)(t+4) Solve for a in term of b, if 6a+12b=24 24-12b 2-\frac{1}{2}b
4-2b
24-18b 2b-4 If ax+2b=5c-dx , what does x equal in terms of a, b, c, and d?5c-d-2b-a a-d
(5c-2b)(a-d)
\frac{5c-d-2b}{a} \frac{5c-2b}{a-d} If (z-9)(z+3)=0 , what are the two possible values of z? z=-9 abd z=3 z=9 abd z=0 z=0 abd z=-3 z=9 abd z=-3 z=-12 abd z=12 If z^{2}-6z=16 , which of the following could be a value of z^{2}+6z ?-8 112 110 18 108 If 3\sqrt{ a}-10=2 , what is the value of a?16 4 32 64 12 Given \frac{(x+6)(x^{2}-2x-3)}{x^{2}+3x-18}=10 , find the value of x.18 4 12 9 12 Solve the equation \frac{5x}{8}-\frac{3x}{5}=2 .40 80 160 -80 20 Answer Key
1 D
2 B
3 E
4 C
5 E
6 D
7 B
8 A
9 D
10 B
2(5x-5)+5(2x+2)= 0 20x
20x-10
20x+10 10x^{2}+20+x+20 If x=a+2 , and y=-8-a then x+y= 6 10
2a-6
-10 -6 If x \ne -5 , then \frac{x^{2}+3x-10}{x+5}-(x-2)= If (a-\frac{1}{a})^{2}=8 , then a^{2}+\frac{1}{a^{2}}= 8 6
10
12 100 (x+y)^{2}=16 , and x^{2}+y^{2}=6 then xy= 5 10
6
4 16 (x+y)=2 , and x^{2}-y^{2}=6 then x-y= 12 4
6
\frac{1}{3} 3 \frac{15y+3}{3}-5y= 1 0
10y+1
3 3y+1 if b^{2}-a^{2}=9 then 5(a-b)(a+b)= 45 \frac{9}{5}
4
50 -45 When c \ne 3 , then \frac{c^{2}-9}{c-3}= c-3 1
c+3
3-c o If b>0 , and b^{2}-1=10 \times 12 , then b= 9 1
12
10 11 Answer Key
1 B
2 E
3 0
4 C
5 A
6 D
7 A
8 E
9 C
10 E
