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Precalculus Practice Test (F08) P.1 to P.5, A.1 & A.2 Name:__________________ Date:___________ Per:____ Any problems without work will be marked wrong on all tests! No calculator. 1. Write the number in scientific notation: a) The diameter of a red blood corpuscle is about 0.000007 of a meter. 2. a) Find the value of x. x −2 11 b) ( 8 × 10 )( 3.5 × 10 ) ( 2 ×10 ) 5 b) Do sides of 7 , 3, 4 form a right triangle? 9 3 2 3. Solve: − 6 ≤ 2x + 1 ≤6 4 4. Simplify: a) 2t2 · (t n+1)3· tn-3. b) (3p2)(-2pq2) 5. Find an equation of the circle with center (-3, 0) and radius 7 and graph. 6-7. Simplify (simple radical form & rationalize). a) 18 + 3 8 − 50 b) 25m 3 7n 2 c) 50 x 3 y 4 d) 3 16a 4 b 3 8. Convert: 9. Simplify: 2 a) x+ 3 1 3 x to exponential form. 3 b) a 2 b −1c 2 to radical form. 3 ⎛ 34 ⎞ ⎛ 14 ⎞ ⎜ a b ⎟ ⎜ ab ⎟ ⎠ ⎝ ⎠ a) ⎝ 1 1 ⎛ − ⎞ ( ab ) 2 ⎜ bc 4 ⎟ ⎝ ⎠ b) 4 8 x3 4 x3 ⋅4 2 y3 y 10. Express in simplest form, using only positive exponents: a) x 2 y −3 (x y ) 3 −1 11. Solve: a) 3(x + 2) = 5(2x – 3) – 7 12. Solve: 2 − 4y 2y + 7 − < 1− y 3 4 ⎛ − 8m 6 b) ⎜⎜ −3 ⎝ n 2 ⎞3 ⎟⎟ ⎠ b) -3x – 4 < -2 (Answer in interval notation.) 13. Find an equation for the line through (4, 7) with the given relationship to y = 2x -4: b) perpendicular a) Parallel 14. Solve: a) 3 + 5 x = 7 b) 9(3x – 4)2 = 16 15. Solve by completing the square: x2 + 14x = -9 16. Solve using the quadratic formula: 2x2 + 7x – 15 = 0 17-18 Perform the operation: 17. (3x4 – 4x3 + 6x2 – 1) – (2x4 – 8x2 – 6x + 5) 18. (2x + 3)(3x2 – 2x + 4) 19-20. Factor completely: a) 24x2 – 7x – 5 c) z3 + 64 b) 5xy – 3y + 10x – 6 d) 3x4 - 48 21. a) Find the distance between P(-6, 5) & Q(3, 2) in simple radical form. b) Find the distance between − 2 3 and on 3 4 the real number line. 22. a) Find the coordinates of W, for segment WX with X(-5, 6) and midpoint M(3, -4). b) Find the midpoint of the line segment with the given endpoints: (-2, 3 ), (5, 0). 23. Write the equation of the line below in general form (3pts): 24. Write a linear equation for someone’s weekly earnings who gets paid $7 per hour and spends $5 each week to ride the bus to work. (3 pts). 25. Derive the quadratic formula: