5 SAT Math Practice Tests Paul G. Simpson IV with the staff of www.testprofessors.com
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SAT MATH PRACTICE TEST 1
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Time-25 Minutes 20 Questions
F r o m " 5 S 1. If the median of a set of five consecutive 4. What is the value of the sum of the external A T integers is equal to 13, then what is the value of angles of a triangle subtracted from the sum of the largest of these five integers? the external angles of a pentagon? M a (A) 0 (A) 11 t (B) 30 (B) 13 h (C) 90 (C) 15 (D) 17 (D) 180 P (E) 19 (E) 360 r a c t a rectangle’s length to the length 2. If x 4 x 3 x 1 3 , then what is the value 5. The ratio of i is 3:1. If the area of the of ? of a square’s side c rectangle’s width is 2, square is 36, and the e (A) 1 what is the area of the rectangle? (B) 2 T (C) 3 (A) 24 e s (D) 4 (B) 36 t (E) 5 (C) 72 s (D) 108 " (E) 216
x
3. If the probability of selecting a red marble is
1 ∕ 3 and the probability of selecting a blue marble is 2 ∕ 3, what is the ratio of blue marbles to red marbles? (A) 1:2 (B) 3:2 (C) 2:1 (D) 2:3 (E) 3:1
6. Given that | m − 2 | = 7 and | n − 3 | = 6, where m < 0 and n < 0, what is the value of mn?
(A) 6 (B) 15 (C) 21 (D) 42 (E) 81
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7. The average of a, b, and c is 27. If the value of d is 19, what is the average of a, b, c, and d ?
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(A) 7 (B) 11 (C) 25 (D) 28 (E) 46
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10. A store determines the retail price of a DVD
player by marking up its wholesale price by 60 percent. After a 25 percent discount off the DVD player’s retail price, the DVD player costs $162. What is the wholesale price of the DVD player? (A) 54 (B) 81 (C) 135 (D) 216 (E) 324
S A a 8. If value 4 and b 15, then what is theT b M of 5ab ? a 11. If | -3 x | + 4 y = 6 z + 4 x, what is the value t of x in terms of y and z ? (A) 30 h (B) 60 (C) 300 (A)P ( y/ 4 ) – 6 z (D) 900 y) – 6 z (B) (4/ r (E) 4500 z / y) (C) 4 – (6 a (D) (4/7 y) +c ( 6 z /7) t (E) (7/4 y) + 6 z i 9. Nancy can make 5 bags per hour. Sue can c make 6 bags per hour, and Ned can make 12 e bags per hour. If Nancy and Sue make bags 12. If a segment with a slope of two passes together for one hour, and then Ned joins them, T through points (2, 6) and (-2, - y), what is the how many minutes will it take them to make e value of y ? 126 bags? s t (A) 0 s (A) 60 (B) 2 " (B) 115 (C) 4
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(C) 227 (D) 300 (E) 360
(D) 8 (E) 16
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(A) 30 (B) 90 (C) 195 (D) 221 (E) 224
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(B)
(C)
(D)
(E)
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5 1 2 3 5 3
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14. Bob buys s socks from the store each week. If each sock costs c cents, and he buys the same
16. If a
2b
and b = 24, then what is the M 3c a value of c in terms of a? t h (A) 4/a (B) a P (C) ± (√a) / 4 r (D) ± (√4a) /a (E) ±a (4√a) / a c t i c proportional to y and x = s 17. If x is inversely e when y = 4t , then what is the value of y in terms of t when x = 4 s?T e (A) t ∕ 16 s t (B) t ∕ 4 s (C) 1 ∕ t " (D) t
In the figure above, ray s begins at the origin and passes through point (-3, 2). Which of the following is not a possible value of the slope of line t ?
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15. m, n, and p are three consecutive positive odd integers such that m < n < p. If their sum is 45, what is the value of mp?
13.
(A)
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2/16
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-1
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(E) 16t
number of socks each day, what equation shows how many cents Bob spends on socks per day in terms of s and c?
18. Jordan is now four times older than Grace.
(A) sc (B) sc( s – 7) (C) sc – 7 (D) ( sc)/7 (E) 7/( sc)
(A) 10 (B) 12 (C) 20 (D) 24 (E) 48
In 30 years, he will be 18 years older than Grace. What is Jordan’s age now?
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19. If u is inversely proportional to v and u = -5 when v1/2 = 3-1, then what is the value of v when u = -1?
(A) 1/12 (B) 1/25 (C) 5/6 (D) 5/3 (E) 25/9
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20. Max decides to carve out a cylinder in a
wooden cube. The cube has a side length of 6 cm, and the cylinder has a radius of 2 cm. What is the surface area of the cube after the cylinder has been carved out? (A) 21 6 24 (B) 21 6 16 (C) 144 24 (D) 21 6 16 (E) 18 36
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SECTION END
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Time: 20 Minutes 16 Questions
F r o m " 5 S 4. A pump to 24 feet. At this rate, how high is the T pump after the lever is pulled for 2 seconds? M a (A) 3 t (B) 4 h (C) 8 (D) 12 P (E) 18 Ifr the area of rectangle ABCD is 24, and ED =a 4 3 , then what is the length of AB? c t (A) 2 2. What is the value of ( 3 ) ( 4) ? i (B) 3 c (C) 4 e (A) -25 (D) 6 (B) -11 (E) 8 T (C) 0 e (D) 7 s (E) 11 t 5. If a is an odd integer and b is ans even integer, " which of the following must be an odd integer? 1. It takes 6 seconds of pulling a lever to raise a
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3. In the xy-plane, segment DE passes through
points (2, 4) and (-4, 8). What is the midpoint of segment DE? (A) (-6, 4) (B) (-2, 12) (C) (-1, 6) (D) (5, 5) (E) (6, 4)
I. ab + 1 II. 2a + 2b III. 3(a – b) (A) I only (B) II only (C) I and III (D) II and III (E) None of the Above
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6. If f ( x) = -4 x – (3 x − 8), what is the value of f (2)?
(A) - 14 (B) - 12 (C) - 10 (D)-8 (E)-6
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F r o m " 5 S A T
7. If a, b, and c are positive consecutive even integers and c > b > a, what is the value of b2 in terms of a?
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9. Trent walked from John’s house three miles
due north then four miles due east, while John walked six miles due south and eight miles due west. If John were to walk directly to Trent’s location, how many hours would it take him if John walks at a rate of three miles per hour? (A) 4 (B) 5 (C) 10 (D) 14 (E) 15
M 10. a t h P r a c t 8. If 3 x + 2, 2 x − 10, and x − 1 are integers, and i x + 3 is the average of these numbers, then which of the following is a possible value of x? In the figure above,c if segment BD bisects segment CA, what is e the area of triangle CED? (A) 2 T (B) 5 (A) 6 e (C) 6 (B) 9 s (D) 8 (C) 12 t (E) 9 (D) 18 s (E) 36 " (A) a2 + 1 (B) (a − 1)2 (C) (a + 2)2 (D) a2 + 4 (E) (a + 1)2
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11. If k = m n , k is not 0, and the values of m and n are doubled, then the value of k increases
by which of the following factors? (A) 0 (B) 2 (C) 4 (D) 8 (E) 16
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12.
15.
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18, 42,…
In the sequence above, each term after the first term, 18, is thirty less than four times the preceding term. What is the sum of the units digits of the first 12 terms?
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The graph above represents y = f ( x). If f ( x) = 0, what is the sum of all the values of x?
(A) 2 (B) 8 (C) 9 (D) 60 (E) 77
M a t h 16. P r a c 13. If 4c − 16e = | (-8d ) |, then what is the t value of c in terms of d and e? i c (A) 16d + 4e e (B) 2(2d +e) (A) -3 (B) -2 (C) -1 (D) 1 (E) 2
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(C) 4(d +e) (D) 64d 2 + 16e2 (E) 16d 2e2
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14. If exactly three triangles are used to
construct a rectangle, what is the minimum number of right triangles that can be used in the rectangle’s construction? (A) 0 (B) 1 (C) 2 (D) 4 (E) 6
The graph above has a function of b. Which of the following has the approximate value of b(2)? (A) 0.5 (B) 0.9 (C) 1 (D) 1.5 (E) 1.9
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Time-25 Minutes 18 Questions
F r o m " 5 S 4. A integers is -13. If the sum of the integersT is 14, what is the total number of integers in the set? M a (A) 24 t (B) 25 h (C) 26 1. The smallest integer of a set of consecutive
In the number line above, which point best approximates the value of ( k m)2?
(D) 28 (E) 32
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= w3, then which of the following is a possible value of w? 2. If w is a positive integer and w
(A) -10 (B) -2 (C) -1 (D) 1 (E) 2
3. If p and q are both even integers and r is an
odd integer, which of the following expressions will not result in an answer that is even? (A) pr + q2 (B) q( p + r ) p (C) (rq)2 − p (D) ( p • r )q (E) r ( p – r ) q
P r k (A) pointa (B) point l c (C) point m t i (D) point n c (E) point o e
T e even 5. If p and q are consecutive negative s p, what is integers whose sum is -120, and q
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6. In a sequence, the first term is -3. Each term
after the first term is four less than two times the preceding term. Which term is the first one that has an absolute value greater than 200? (A) 3 (B) 6 (C) 9 (D) 12 (E) none
7. If
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10. If
p q
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x y
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, then what is the value of
q p
in terms of x and y?
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x
x
is the value of x? (A) 1/2 (B) 0 (C) 1 (D) 1.5 (E) 2
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, and x > 0, what
11. If y + z = 18 and 40 percent of 75 percent of p is the average of y and z , what is the value of p?
P r a c t 12. I f - | - f | = 3h − 12 and h = m , what is i terms of m? the value of f inc e T e s t s " 1/2
8. If s2 = t -1 and t 1/4 = u-1/3, then what is the value of s in terms of u?
(A) u-2/3 (B) u-1/3 (C) u1/6 (D) u1/3 (E) u2/3
9. If the average of w and x is 30, the average of p and q is 30, and the average of m and n is 30, what is the average of w, x, p, q, m, and n?
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13. If 30 percent of 50 percent of x is 60 percent of y minus 75 percent of y, then what is the value of x in terms of y?
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14. a and b are positive consecutive integers
and b > a. When b is seven more than a , what is the greatest possible value of a?
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17. If x and y are directly proportional and 2 -2 x = 6 when y = 8, then what is the value of y when x = 2?
" 5 S A -4 x + p 18. The function f ( x) = x + x – 24 and h(t ) = x . 15. If the graphs of y = 3 x − 15 and y = T If 3h(t ) = f (2 x), what is one possible value of x? intersect at point (3, r ), then what is the value of p M ? a r t h P TEST END r a c t i 16. If x☻ y = 3 y − 2( x + y), what is 2☻4? c e T e s t s " 2
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Practice Test 1
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Practice Test 1 S A T
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Answer Key and Explanations P r a c t i c e T e s t s "
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Practice Test 1 Answer Key
Section 1 1. C 2. A 3. C 4. A 5. B 6. B 7. C 8. E 9. E 10. C 11. B 12. C 13. E 14. D 15. D 16. E 17. C 18. D 19. E 20. B
Section 2 1. C 2. B 3. C 4. D 5. C 6. E 7. C 8. C 9. B 10. D 11. E 12. B 13. A 14. C 15. D 16. A
Section 3
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1. D 2. D 3. E 4. C 5. D 6. B 7. C 8. E 9. 30 10. y / (2 y + x) 11. 30 12. ( 1 2 – 3 ) / m or -3/m + 12 13. -y 14. 9 15. 2 16. 0 17. 3/8 or 0.375 18. -6 or 4
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Practice Test 1 Scoring
Finding Your Score Raw score: Notes:
Total Number Right – [Total Number Wrong ÷ 4] = _____
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1) For #9 - #18 in Section 3, only right answers are counted 2) Omissions are not counted towards your raw score 3) If the total number wrong ÷ 4 ends in .5 or .75, it is rounded up
" 5 Raw Score 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24
Math Scoring Table
S Scaled A Score T 800 800 780M 770 a t 750 h 730 720 710 700 690 680 670 660 660 650 640 630 630 620 610 600 590 590 580 570 560 550 550 540 530 520
Raw Score 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6
P r a c t i c e
and below
Scaled Score
520 510 500 490 490 480 470 460 460 450 440 420 410 400 400 390 380 370 350 330 320 310 290 270 250 240 230 220 210 200 200
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