Quarterly # 3 Algebra 1A Review: Multiple Choice, Select All That Apply, Open-Ended
infinitely many solutions 1. infinitely many solutions one solution no solution cannot be determined
infinitely many solutions 1. Graph the first line. Graph the second line. The equations are of the same line. infinitely many solutions Answer:
infinitely many solutions 2. infinitely many solutions one solution no solution cannot be determined
2. The graphs intersect at one point. Answer: Graph the first line. Graph the second line. The graphs intersect at one point. one solution Answer:
infinitely many solutions 3. infinitely many solutions one solution no solution cannot be determined
3. The graphs do not intersect. Answer: Graph the first line. Graph the second line. The graphs do not intersect. no solution Answer:
4. (2, 2) (2, 2) (4, 2) (2, 4)
4. The graphs intersect at the point (2, 4). Answer: Graph the first line. Graph the second line. The graphs intersect at the point (2, 4). (2, 4) Answer:
5. 1 1 7 7
5. Substitute 5 into the equation: 2x + y = 3 2(5) + y = 3 10 + y = 3 10 10 y = 7 7 Answer:
6. (2, 5) (2, 5) (5, 2) (4, 7)
6. 1 x + y = 3 x y = 7 If you add the equations, y cancels out. 2 2 x = 2 x + y = 3 Use either equation to find y: (2, 5) Answer: 2 + y = 3 –2 –2 y = 5
7. 2 2 5 5
7. 6x + 5y = 27 +5y cancels with 5y 5y 5( ) +5y cancels with 5y 6x + 5y = 27 5y In order to get 5y, multiply the bottom row by 5. 5 Answer:
8. (2, 4) (2, 4) (4, 2) (4, 2)
8. Answer: Cancel x by making 20x and 20x. 4 ( ) 5 ( ) 4 ( ) 5 ( ) Get either variable to cancel. 20x + 28y = 136 20x 15y = 110 Substitute into any equation to find x: 13y = 26 13 13 4x + 3y = 22 y = 2 4x + 3(2) = 22 4x + 6 = 22 6 6 4x = 16 4 4 (4, 2) Answer: x = 4
9. (1, 6) (3, 2) (2, 3) (4, 1)
9. Answer: See which point is NOT shaded in the graph. Plot each point: (1, 6), (3, 2), (2, 3), (4, 1) The point (1, 6) is outside of the shaded region. (1, 6) Answer:
10. (3, 1) (0, 0) (1, 0) (2, 4)
10. Answer: See which point is shaded in the graph. Plot each point: (3, 1), (0, 0), (1, 0), (2, 4) The point (2, 4) is inside of the shaded region. (2, 4) Answer:
11. y ≥ x + 4 1 3 y ≤ x + 4 1 3 y ≥ 3x + 4 y ≤ 3x + 4
11. Answer: The shading is above the line: use ≥. The y-intercept is 4. The inequality is in the form y ≥ mx + 4. Find the slope, m. Use (0, 4) and (1, 1). Answer: y ≥ 3x + 4 m = 1 – 4 1 – 0 = – 3 1 = – 3
12. 7x 8 7x 6 8x 8 8x 6
12. (7x )(x ) 4 2 = 7x x 4 2 When multiplying powers, add the exponents and keep the base. = 7x 4+2 = 7x 6 7x 6 Answer:
13. y 20 4y 5 y 9 4y 9
13. Answer: (y ) When raising powers, multiply the exponents 5 4 When raising powers, multiply the exponents and keep the base. = y 54 = y 20 y 20 Answer:
14. a 8 a 3 a 12 a 4
14. Answer: a When dividing powers, subtract the exponents 6 2 When dividing powers, subtract the exponents and keep the base. = a 6 – 2 There are 4 more factors of “a” in the numerator. = a 4 a 4 Answer:
15. 3x 4 y 5 14 x 4 y 5 3x 6 y 5 14x 4 y 5
15. = = Answer: Divide the coefficients. 21x y 21 ÷ 7 = 3 7x y 5 3 7x y 1 8 Divide the coefficients. 21 ÷ 7 = 3 Place the x as x in the numerator. 1 1 3x x y 5 1 3 y 8 = 3x 5+1 y 8 – 3 = Mult. add exponents. Div. subtract exponents 3x 6 y 5 Answer:
16. 4x + 5x y + 3xy + 6y 5x y 4x + 3xy + 6y 6y + 3xy + 5x y 4x 6 4 3 2 4 3 6 2 5x y 4x + 3xy + 6y 6y + 3xy + 5x y 4x 2 4 3 6 4 3 2 6 6y + 5x y + 3xy 4x
16. Answer: Descending Order: greatest power of x to least power of x. 5x y + 6y 4x + 3x y 4 3 6 1 2 4x + 5x y + 3xy + 6y 6 4 3 2 Answer: Separate the terms and determine their signs.
17. 7m – 3 2 2 7m + 11 7m – 18m – 3 2 2 6m – 18m – 3
17. Answer: 6m – 9m + 4 Line up the like terms. Add the coefficients. 2 Line up the like terms. Add the coefficients. + 1m – 9m – 7 2 7m – 18m – 3 2 Answer:
18. 3 4 73 a = the cost of an adult c = the cost of a child 3 4 73 3 7 94 a = the cost of an adult c = the cost of a child 3a + 4c = 73 3 adults & 4 children 3a + 7c = 94 3 adults & 7 children Highlight the important information in order to answer the question. The group number is not important for writing the system.
18. 3a + 4c = 73 3a + 7c = 94 3a + 4c = 73 3a 7c = 94 3a + 4c = 73 1( ) 3a + 4(7) = 73 3a + 28 = 73 3c = 21 28 28 3 3 Adult ticket = $15 Child’s ticket = $7 3a = 45 c = 7 3 3 a = 15 Take the opposite of one row (multiply by 1) for “a” to cancel. Solve for c. Substitute into any of the equation to find “a”. Explain what the solution means.
19. 7x x When dividing powers, subtract the exponents. 2 x 10 When dividing powers, subtract the exponents. The “7” is a coefficient and cannot change location. = 7x 210 = 7x 8 A negative exponent in the numerator = a positive exponent in the denominator. 7 x 8 =
20. 4y3 + 8x3 6xy y3 – 4x3 + 12xy Line up the like terms. 18xy Combine the like terms. 4y3 + 8x3 6xy
20. 4y3 + 8x3 6xy Find the degree of each polynomial. 1+1 = 2 The highest degree of the polynomials = 3
20. 4y3 + 8x3 6xy The polynomial has 3 terms: 4y3, 8x3, 6xy
20. 8x3 – 6xy – 4y3 terms and look at the exponents of x. Separate the terms and look at the exponents of x. 4y3 + 8x3 6xy 4y3 + 8x3 6x1y1 The exponents of x are decreasing (getting lower). 8x3 – 6xy – 4y3
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