Midterm Review 2025 Math 8 PDF

Name_______________________________ Math 8 Midterm Review Units 1 - 4 Unit 1: Exponents and Scientific Notation Rules for Exponents: a b (x )(x ) = xa + b ab (x ) = xab...

Name_______________________________ Math 8 Midterm Review Units 1 - 4 Unit 1: Exponents and Scientific Notation Rules for Exponents: a b (x )(x ) = xa + b ab (x ) = xab x 0 =1 𝐱𝐚 a - b -a 𝟏 =x x = 𝐱𝐛 𝐱𝐚 1) Evaluate: 2 3 a) 5 b) (-3) c) -24 d) 6 0  3 e) 2 x (-3)2 f) -16 -2 -3 g) 3 h) (-2) 2 2 i) (1/2) j) (-3)  -3 k) (-3) l) -40 2) Simplify using the laws of exponents. Leave your answer in exponential notation (positive exponents only). 2 a) 4 x 45 b) 2 4 x8 𝟖𝟔 32 c) d) (5 ) 𝟖𝟒  3 -6 𝟐𝟓 e) (-5) x (-5) f) 𝟓𝟑 2 45 2 -2 g) (4 x3 ) h) (3 ) 3) Perform the indicated operation and simplify with positive exponents only. 2 3 5 2 a) (4x y )(-2x y ) 4 22 b) (-3x y ) 𝟏𝟐𝐱 𝟖 𝐲 𝟑 c) −𝟑𝐱 𝟏𝟎 𝐲  Scientific Notation: b a x 10 where 1 < a < 10 To Multiply Numbers in Scientific Notation: (a x b 10 )(c x d 10 ) = ac x 10b + d To Divide Numbers in Scientific Notation: b -d (a x 10 ) = a/c x 10 b d (c x 10 ) Remember, when adding or subtracting numbers in scientific notation, the powers of 10 must match before adding/subtracting! 4) Write the following numbers in scientific notation: a) 45,000,000 b) 0.00034 c) 870,000 d) 0.0000016 5) Write the following numbers in standard form. a) 5.24 x 104 -5 b) 3.02 x 10 c) 7.3 x 108 6) Perform the indicated operation and leave answer in scientific notation. 6 a) (5.25 x 10 ) x (4 x 103) -8 b) (3.4 x 10 ) x (8 x 105) c) (1.2 x 105) + (5.35 x 106)  d) (8.9 x 105)(6.5 x 106) 𝟑.𝟓 𝐱 𝟏𝟎𝟗 e) 𝟏.𝟒 𝐱 𝟏𝟎−𝟑 12 9 f) (5.1 x 10 ) – (6.3 x 10 ) 7) The world population is around 7 billion. There are 4 2.4 x 10 ants for every human on the planet. About how many ants are there in the world? Express your answer in scientific notation. 8) Mars is approximately 54,000,000 km from the sun, 9 whereas Jupiter is about 6.3 x 10 from the sun. What is the difference between Mars’ and Jupiter’s distances from the sun? Express your answer in scientific notation. Unit 2 Equations and Inequalities Solve for the variable in #1 - 8 1) 3(x – 2) = -18 2) 10x – x + 3 = 39 3) 7(n + 2) + 7 = -28 4) 6x + 4(x + 8) = 52 5) 5y – 4 = 2y + 5 6) 3x + 10 = -2x – 25 7) 4(y – 2) = 2(y + 6) 8) 8x – 3(2x + 5) = 85 – 3x 9) 5(x + 3) = 2x + 6 In #10 - 13 Use an algebraic solution to solve each problem. Show all work. 10) 3 times a number increased by 22 is equal to 14 less than 7 times the number. Find the number. 11) A jacket costs $30 more than a shirt. If the total cost of two shirts and one jacket is $150, find the cost of each item. 12) Allison is twice as old as John. Brian is 4 years older than John. The sum of their ages is 36. Find the age of each person. 13) Find three consecutive odd integers whose sum is 171. 14) Solve and graph the inequality on the number line: a) 3x –4 4 b) y + 2x ≤ 3 Unit 4: Systems Solve each system of equations using either substitution or elimination. Check the solution! 1) 8x – 2y = 10 2) 4x - 6y = 14 y = 2x - 3 2x - y = -3 3) 3x + 2y = 10 4) -3x + y = 7 4x + 3y = 12 8x − 3y = -26 5) Solve each system of equations graphically. Check the solution! y =x+2 4x + 3y = 6 6) Is (2, 1) a solution to the system of equations below? y – 3x =7 2x +y = 5