Math 150 Practice Test 3 Solutions

LEVEL 1 ALGEBRA READINESS TEST TYPICAL QUESTIONS FROM COMPETENCY AREAS Integers Jim wrote a check for $318.00. If his balance was then $2126.00, what was his balance before he wrote this check? (A) $808 (B) $1808 (C) $2444 (D) $5306 What number multiplied by 6 gives –18 as a result? (A) –12 (B) –3 Decimals 7.20 = 2.4 (A) 0.03 (C) 3 (B) 0.30 (D) –54 (C) 3.00 (D) 30.0 Which of the following best approximates 1.147 – 114.7? (A) –100 (B) –10 (C) 10 (D) 100 Fractions The ratio of “winning” tickets to tickets sold in the California Lottery is 2 to 5. If 3,500,000 tickets are sold, how many are “winners”? (A) 700,000 (B) 750,000 (C) 1,400,000 (D) 1,500,000 1 + 12 = 1 − 34 (A) –6 (B) –2 (C) 2 Exponents If in the formula p = kt , k = 36 and p = 144 , then t = (A) 14 (B) 4 4 (b + 2) = (A) 4b + 2 (D) 6 (C) 12 (B) b + 6 (D) 108 (C) b + 8 (D) 4b + 8 y Geometry In the figure shown, what is the length of segment AB? (A) –5 (C) 13 A (0, 5 ) (B) 5 (D) 19 B(12, 0) If C is the midpoint of segment AB in the figure shown, then the coordinates of C are (A) ( 72 , 72 ) (B) ( 6, 72 ) (C) ( 19 2 , 7 2 ) (D) y A (0, 2. B 3. C 7 )
C (19, ) 7 2 B(12, 0)
What is the diameter of the circle whose area is 36π ? (A) 12 (B) 18 Answers: 1. C 4. A x 5. C 6. D (C) 6π 7. B (D) 18π 8. D 9. C 10. B 11. A LEVEL 2 ELEMENTARY ALGEBRA TEST TYPICAL QUESTIONS FROM COMPETENCY AREAS Arithmetic 2 ( 0.12 ) = (A) 0.00144 (B) 0.0144 (C) 0.144 (D) 0.24 (E) 1.44 Polynomials One of the factors of x 2 − x − 6 is (A) x + 3 (B) x + 2 (C) x − 1 (D) x − 2 (E) x − 6 Linear Equations and Inequalities If 6 x − 3 = 8 x − 9 , then x = (A) –6 (B) –3 (C) 3 (D) − 67 (E) Quadratic Equations What are the possible values of x such that 3 x 2 − 2 x = 0 ? (A) − 23 only (B) 0 only (C) 23 only (D) 0 and 6 7 2 3 (E) − 23 and 6 7 7 7 Graphing 5 ? 9 On the number line below, which letter best locates 0 (A) P 1 7 P Q R S T • • • • • 3 7 2 7 (B) Q 5 7 4 7 (C) R Rational Expressions 2 1 1 − = (A) w +1 w −1 w+2 (B) 1 w −1 (D) S (C) 2 w−3 w2 − 1 (E) T w+3 w2 − 1 (D) (E) 3w − 1 w2 − 1 Exponents and Square Root If x > 0 , then 64 x16 = (A) 8 x 4 Geometry and Measurement In the right triangle shown to the right, what is the length of AC? (A) 8 (B) (C) 18 (D) (E) (B) 8 x8 (C) 16 x 4 12 18 13 5 A C Word Problems If x is to 5 as y is to 8, what is the value of x when y = 2 ? 5 4 5 (A) (B) (C) 16 5 4 2. B 3. C 4. D (E) 32 x8 B 194 Answers: 1. B (D) 32 x 4 5. B 6. C 7. B (D) 16 5 8. B (E) 5 9. C 2 3 LEVEL 3 INTERMEDIATE ALGEBRA TEST TYPICAL QUESTIONS FROM COMPETENCY AREAS Elementary Numeric and Algebraic Operations c +2= d c + 2d c+2 c+2 (A) (B) (C) d d +2 d Rational Expressions c−d = 1 1 d − c c−d (A) dc (B) dc c−d Exponents and Radicals 3 + 27 = (A) 6 (B) 3 3 (D) c + 2d (E) c (C) dc (D) – dc (E) (C) 4 3 (D) 10 3 (E) Linear Equations; Inequalities; Absolute Value If 3 x + 2 y = 8 and y = x − 1, then x = 6 7 (A) –6 (B) (C) 5 5 1 dc 30 (D) 9 5 (E) 2 (D) 3 4 (E) Polynomials; Quadratic Equations One of the roots of ( x − 2 )( 3 x + 4 ) = 0 is (B) − (A) –2 4 3 (C) − 3 4 4 3 The Coordinate Plane and Graphing Which of the following is an equation of a line with slope 3 and y-intercept –4 ? 1 (A) y = x − 4 (B) y = 3 x − 4 (C) y = 3 x + 4 3 (D) y = 4 x − 3 (E) y = 4 x + 3 Functions and Logarithms If log10 x + log10 y = 3 , then xy = (A) 0.001 (B) 1.0 (C) 10 (D) 100 (E) 1000 Word Problems A student who correctly answered 72 questions on a test received a score of 75%. How many questions were on the test? (A) 54 (B) 72 (C) 75 (D) 96 (E) 104 Answers: 1. A 2. C 3. C 4. E 5. B 6. B 7. E 8. D LEVEL 4 PRECALCULS TEST TYPICAL QUESTIONS FROM COMPETENCY AREAS Elementary Operations with Numerical and Algebraic Fractions 3x − 2 2 − = x+2 x−2 3 3x − 4 3x (A) (B) (C) (D) 2 2 x+2 x −4 x −4 Operations with Exponents and Radicals x3a + 2 = x 2 a −1 (B) x a −3 (C) x5 a −1 (A) x a +3 x ( 3 x − 10 ) x −4 2 (D) x a +1 Linear Equations and Inequalities 2t − 1 For what value of t does = 2? 3t + 4 9 3 (A) – 6 (B) − (C) 4 2 (E) There is no value of t satisfying this equation (D) (E) 3x ( x − 4 ) x2 − 4x + 4 (E) x3 9 4 Polynomials and Polynomial Equations If ( x − 1) ( x 2 − 4 ) + 2 ( x − 1)( x + 2 ) = ( x − 1) P , then P = (A) x 2 − 2 (C) x ( x + 2 ) (B) x 2 ( x + 2) (D) x 2 + 2 (E) (D) 2 (E) 9 Functions If f ( x ) = 2 x + 5 and g ( x ) = 1 − x 2 , then f ( g ( 2 ) ) = (A) –3 (B) –1 (C) 1 Trigonometry 3 π If sin θ = and 0 ≤ θ ≤ , then tan θ = 5 2 3 4 5 (A) (B) (C) 2 3 4 (D) 4 5 (E) 3 4 (D) 1 3 (E) 1 9 (D) 5 12 (E) 4 15 Logarithmic and Exponential Functions log 3 27 = (A) 81 (B) 9 (C) 3 Word Problems 2 1 4 If is of of a certain number, then that number is 3 2 5 15 5 5 (A) (B) (C) 4 3 6 Answers: 1. D 2. A 3. B 4. C 5. B 6. E 7. C 8. B 2