MPM 1D1 Summative Review #1 PDF

# MPM 1D1 - Summative Review # 1 ## Units 1-2 **Topics Covered:** BEDMAS, Fractions, Percents, Proportions, Independent/ Dependent Variables, Correlations, Relationships, Discrete/Cont. Data ## 1. Evaluate each of the following. **(a)** 18 + (-6) = 12 **(b)** (-5)(-3) = 15 **(c)** -7+19-12 = 0...

# MPM 1D1 - Summative Review # 1 ## Units 1-2 **Topics Covered:** BEDMAS, Fractions, Percents, Proportions, Independent/ Dependent Variables, Correlations, Relationships, Discrete/Cont. Data ## 1. Evaluate each of the following. **(a)** 18 + (-6) = 12 **(b)** (-5)(-3) = 15 **(c)** -7+19-12 = 0 **(d)** -16/-4 = 4 **(e)** (2/3)³ = 8/27 **(f)** √16/√25 = 4/5 **(g)** -22-11 = -33 **(h)** (-5)² = 25 **(i)** -43/-69 = 1/2 **(j)** (-1)²⁴ = 1 **(k)** -(-2)² = -4 **(l)** -25+17 = -8 ## 2. Complete the following chart. Make sure all fractions are in LOWEST TERMS. | FRACTION | DECIMAL | PERCENT | |---------------|---------|---------| | 38/100 = 19/50 | 0.38 | 38% | | -65/100 = -13/20| -0.65 | -65% | | 4 1/5 = 21/5 | 4.2 | 420% | ## 3. Evaluate the following using BEDMAS. Show all work. **(a)** 5×3- [18- (-6)] ÷ 3 = 7 **(b)** 5-2/3 × (3/4)² = 548/155 ## 4. Determine the value of x in the following proportions. ROUND TO 2 DECIMAL PLACES IF NECESSARY. **(a)** 3/x = 17/35 x = 6.18 **(b)** 4:x = 14:56 x=16 ## 5. Football equipment, which regularly sells for $588, is on sale for 25% off. Determine the total cost of the equipment, including 13% tax. $49.33 ## 6. 25% of a number is 66.25. What is the number? 265 ## 7. Complete the table to the right. **(a)** What type of relationship does this data represent? EXPLAIN HOW YOU KNOW. *The relationship is linear. This is because the first differences are constant.* **(b)** Does the relationship have a positive or negative correlation? EXPLAIN. *The relationship has a negative correlation. This is because the first differences are negative.* **Table:** | x | y | FIRST DIFF. | |---|-----|-------------| | 1 | 70 | | | 3 | 62 | -8 | | 5 | 54 | -8 | | 7 | 44 | -10 | | 9 | 32 | -12 | ## 8. The graph below shows Mike's motion. Describe his motion using sentences. BE CLEAR AND SPECIFIC ABOUT DIRECTIONS, TIMES, ETC. *From 0-3 minutes, Mike walks quickly, then slows down (nonlinearly) away from the sensor.* *From 3-4 minutes, he walks at a constant speed of 400 m/min away from the sensor.* *He stops for 1 minute (4-5 minutes).* *He goes back towards the sensor at a constant speed of 600 m/min.* ## 9. A group of friends collect data to see whether hours watching TV had an effect on their exam scores. The following results were obtained. | HOURS WATCHING TV | EXAM SCORE | |--------------------|-------------| | 8 | 72 | | 7 | 67 | | 4 | 81 | | 3 | 93 | | 9 | 54 | | 10 | 66 | **(a)** Create a scatter plot. Include a line of best fit. **(b)** Fill in the table below regarding this information. | QUESTION | ANSWER | |-------------------------------------------|-------------| | What type of correlation seems to exist? | negative | | Is the relationship linear or non-linear? | linear | | Is the data discrete or continuous? | continuous | **(c)** Describe the relationship that seems to exist with these variables. *Weak negative correlation. As you watch more TV, your exam score goes down.* **(d)** Is the origin (0, 0) a reasonable element of the data? EXPLAIN. *No. The y-intercept is above 100. The line will not go through the origin.* ## 10. Solve the following equations. SHOW ALL WORK. **(a)** -4(3x+4)=-28 x = 1 **(b)** 5 (2t-1) + 9 = 2 (t-2) t = -1 ## 11. Solve the following equations. SHOW ALL WORK. **(a)** 3a/2 + 5 = -3 a=-17/3 **(b)** x/3 - 2/4 = x/2 - 1 x=2 ## 12. Solve and check the following equation. 5(2t-1) + 9 = 2(t -2) t=-1 ## 13. Three times a number decreased by eleven is thirty-seven. Determine the number. You must solve this by writing an equation. 16 ## 14. Find two consecutive odd numbers so that the sum of two times the smaller number and five times the larger number is 87. SOLVE FULLY. BY WRITING AN EQUATION 11 & 13 ## 15. A soccer team goes to Starr Burger after a game. The number of drinks ordered is 2 less than the number of burgers. If burgers cost $3.25 and drinks cost $1.50, how many of each were ordered if the coach paid a total of $49.25? SOLVE FULLY. 11 burgers, 9 drinks # MPM 1D1 - Summative Review # 2 ## Units 3-4 **Topics Covered:** Exponent Rules, Polynomials, Like Terms, Distributive Property, Solving Equations, Translating Words to Math, Word Problems ## 1. Write each of the following as a single power. **(a)** 4⁴ × 4³ = 4⁷ **(b)** (-2)⁵x (-2)² = (-2)⁷ **(c)** 6²⁶/6²¹ = 6⁵ **(d)** 5⁵/5³ = 5² **(e)** (5³)^-6 = 5^-18 **(f)** [(-8)⁴]⁵ = (-8)²⁰ ## 2. Simplify the following expressions. **(a)** (7x⁴)(-5x²) = -35x⁶ **(b)** 28a⁹/4a⁵ = 7a⁴ **(c)** (-5ab²c⁵)(4ab³c⁴) = -20a²b⁵c⁹ **(d)** 32x⁶y⁴z⁷/-4x²y²z⁴ = -8x⁴y²z³ ## 3. Simplify this expression. SHOW ALL STEPS! (2g²h³)×(-3g²h²)² / (3gh)(6g²h²) = 9g⁴h⁴ ## 4. Read each statement below carefully. Determine whether each is TRUE or FALSE by writing a T or F in the blank provided. **(a)** The coefficient of 11x²y³z is x²y³z. **F** **(b)** a² - 3a + 3 is a polynomial. **T** **(c)** The coefficient of -8mn⁵ is mn. **F** **(d)** 11xy² and -13x²y are like terms. **F** **(e)** (2d²e)(-5d³e) = -7d⁵e⁷ **T** **(f)** 3t⁵t² + 4tu - v has 4 terms and 4 variables. **F** ## 5. Simplify each of the following to a single power. THEN EVALUATE. **(a)** 7⁸×7⁴ = 117 649 **(b)** (7⁶)⁵ × (7³)^-5 ÷ (7^-2)^-6 = 343 ## 6. Simplify the following expressions. **(a)** 8m² + 5n²-9n² - 6m² = 2m² - 4n² **(b)** 11x² - 2x - 7 + 2x – 17 + 2x² = 13x² – 24 ## 7. Simplify the following. **(a)** (2x – 3) – (3x + 1) = -x - 4 **(b)** 2x(4x – 8) – 3x(3x + 2) = -x² - 22x ## 8. Write an algebraic expression or equation for each of the following statements. **(a)** Double a number decreased by three. **2x-3** **(b)** The value of n dimes (in cents). **10n** **(c)** A number tripled gives 24. **3n = 24** **(d)** 10 more than quadruple a number. **4x + 10** **(e)** Martin's age in six years will be thirteen. **x+6 = 13** ## 9. Solve the following equations. **(a)** n + 18 = 25 n =7 **(b)** m - 13 = 18 m = 31 **(c)** 7x = 63 x = 9 **(d)** -13/5 = r r = -65 **(e)** x/2 = 20 x = 40 **(f)** -30 = 6n n=-5 ## 10. Solve the following equations. SHOW ALL WORK. **(a)** -4(3x+4) = -28 x = 1 **(b)** 5 (2t-1) + 9 = 2 (t-2) t = -1 ## 11. Solve the following equations. SHOW ALL WORK. **(a)** 3a/2 + 5 = -3 a = -17/3 **(b)** x/3 - 2/4 = x/2 - 1 x = 2 ## 12. Solve and check the following equation. 5(2t-1) + 9 = 2(t -2) t=-1 ## 13. Three times a number decreased by eleven is thirty-seven. Determine the number. You must solve this by writing an equation. 16 ## 14. Find two consecutive odd numbers so that the sum of two times the smaller number and five times the larger number is 87. SOLVE FULLY. BY WRITING AN EQUATION 11 & 13 ## 15. A soccer team goes to Starr Burger after a game. The number of drinks ordered is 2 less than the number of burgers. If burgers cost $3.25 and drinks cost $1.50, how many of each were ordered if the coach paid a total of $49.25? SOLVE FULLY. 11 burgers, 9 drinks # MPM 1D1 - Summative Review # 2 ## Units 3-4 **Topics Covered:** Exponent Rules, Polynomials, Like Terms, Distributive Property, Solving Equations, Translating Words to Math, Word Problems ## 1. Write each of the following as a single power. **(a)** 4⁴ × 4³ = 4⁷ **(b)** (-2)⁵x (-2)² = (-2)⁷ **(c)** 6²⁶/6²¹ = 6⁵ **(d)** 5⁵/5³ = 5² **(e)** (5³)^-6 = 5^-18 **(f)** [(-8)⁴]⁵ = (-8)²⁰ ## 2. Simplify the following expressions. **(a)** (7x⁴)(-5x²) = -35x⁶ **(b)** 28a⁹/4a⁵ = 7a⁴ **(c)** (-5ab²c⁵)(4ab³c⁴) = -20a²b⁵c⁹ **(d)** 32x⁶y⁴z⁷/-4x²y²z⁴ = -8x⁴y²z³ ## 3. Simplify this expression. SHOW ALL STEPS! (2g²h³)×(-3g²h²)² / (3gh)(6g²h²) = 9g⁴h⁴ ## 4. Read each statement below carefully. Determine whether each is TRUE or FALSE by writing a T or F in the blank provided. **(a)** The coefficient of 11x²y³z is x²y³z. **F** **(b)** a² - 3a + 3 is a polynomial. **T** **(c)** The coefficient of -8mn⁵ is mn. **F** **(d)** 11xy² and -13x²y are like terms. **F** **(e)** (2d²e)(-5d³e) = -7d⁵e⁷ **T** **(f)** 3t⁵t² + 4tu - v has 4 terms and 4 variables. **F** ## 5. Simplify each of the following to a single power. THEN EVALUATE. **(a)** 7⁸×7⁴ = 117 649 **(b)** (7⁶)⁵ × (7³)^-5 ÷ (7^-2)^-6 = 343 ## 6. Simplify the following expressions. **(a)** 8m² + 5n²-9n² - 6m² = 2m² - 4n² **(b)** 11x² - 2x - 7 + 2x – 17 + 2x² = 13x² – 24 ## 7. Simplify the following. **(a)** (2x – 3) – (3x + 1) = -x - 4 **(b)** 2x(4x – 8) – 3x(3x + 2) = -x² - 22x ## 8. Write an algebraic expression or equation for each of the following statements. **(a)** Double a number decreased by three. **2x-3** **(b)** The value of n dimes (in cents). **10n** **(c)** A number tripled gives 24. **3n = 24** **(d)** 10 more than quadruple a number. **4x + 10** **(e)** Martin's age in six years will be thirteen. **x+6 = 13** ## 9. Solve the following equations. **(a)** n + 18 = 25 n =7 **(b)** m - 13 = 18 m = 31 **(c)** 7x = 63 x = 9 **(d)** -13/5 = r r = -65 **(e)** x/2 = 20 x = 40 **(f)** -30 = 6n n=-5 ## 10. Solve the following equations. SHOW ALL WORK. **(a)** -4(3x+4) = -28 x = 1 **(b)** 5 (2t-1) + 9 = 2 (t-2) t = -1 ## 11. Solve the following equations. SHOW ALL WORK. **(a)** 3a/2 + 5 = -3 a = -17/3 **(b)** x/3 - 2/4 = x/2 - 1 x = 2 ## 12. Solve and check the following equation. 5(2t-1) + 9 = 2(t -2) t=-1 ## 13. Three times a number decreased by eleven is thirty-seven. Determine the number. You must solve this by writing an equation. 16 ## 14. Find two consecutive odd numbers so that the sum of two times the smaller number and five times the larger number is 87. SOLVE FULLY. BY WRITING AN EQUATION 11 & 13 ## 15. A soccer team goes to Starr Burger after a game. The number of drinks ordered is 2 less than the number of burgers. If burgers cost $3.25 and drinks cost $1.50, how many of each were ordered if the coach paid a total of $49.25? SOLVE FULLY. 11 burgers, 9 drinks # MPM 1D1 - Summative Review # 3 ## Units 5-6 **Topics Covered:** Slope, 1st Differences, Linear vs. Non-Linear, Equations of Lines (Slope-Int., Standard), Parallel/Perp. Lines, Direct/Partial Variations, Intercepts ## 1. Calculate the slope of the line segments through the points shown. DO NOT CONVERT ANSWERS TO DECIMALS. **(a)** A(-6, -4), B(-2, 0) m = 4/4 = 1 **(b)** Q(1, -5), R(6, 2) m = 7/5 ## 2. Each table below represents a linear relation. Determine the slope of each. **(a)** x | y ---|---| -2 | 16 -1 | 12 0 | 8 1 | 4 2 | 0 m = -4 **(b)** x | y ---|---| -2 | -5 1 | -3 4 | -1 7 | 1 10 | 3 m = 2/3 ## 3. Identify the following relations as linear (L) or non-linear (N). **(a)** y = 2 - 5x **L** **(b)** 6x + y = 7 **L** **(c)** y = 2x² + 4 **N** **(d)** 2x³ - y = 4 **N** **(e)** x = -3 **L** **(f)** y = -2√x **N** ## 4. Write the equation that would represent each table of values below. **(a)** x | y ---|---| 0 | 3 1 | 4 2 | 5 3 | 6 4 | 7 y = x + 3 **(b)** x | y ---|---| -4 | 0 -2 | 1 0 | 2 2 | 3 4 | 4 y = 1/2x + 2 **(c)** x | y ---|---| 8 | -3 6 | -1 4 | 1 2 | 3 0 | 5 y = -x + 5 ## 5. Graph these equations USING THE METHOD INDICATED. LABEL AND SCALE YOUR AXES! **(a)** y = 1/2x - 3 (use slope and y-intercept) **(b)** 4x + y - 4 = 0 (calculate x- and y-intercepts) ## 6. Write the equation of the line that passes through the points (-3, -5) and (1, 7). y = 3x + 4 ## 7. Consider each equation below. **(a)** Identify the form that the equation is in. **(b)** Convert the equation to the other form. **(i)** 4x-6y+15=0 **Standard Form** (ii) y = 2/3x + 5/2 **Slope Y-Intercept Form** ## 8. Point A lies on the line shown. Determine the equation of ANOTHER line that is perpendicular to the one shown, going through Point A. y = -2/3x - 10/3 ## 9. A used car purchased for $9,500 decreases in value by approximately $1,200 per year. Let V represent the value of the car and let n represent the number of years that pass after purchase. **(a)** Write an equation for the relation between V and n. V = -1200n + 9500 **(b)** What is the slope? -1200 **(c)** What does the slope represent? The decrease in the value of the car per year **(d)** Does this relationship represent a direct or partial variation? EXPLAIN. Partial variation. The initial value of the car is $9500. ## 10. Solve the following equations. SHOW ALL WORK. **(a)** 2x - 3y = 12 y = 2/3x - 4 **(b)** 2x + 5y – 1 = 0 y = -2/5x + 1/5 ## 11. Solve for x and y: 2x + y = 8 and x - 2y = 10 x = 4, y = 0 # MPM 1D1 - Summative Review # 4 ## Units 7-8 **Topics Covered:** Pythagorean Theorem, Perimeter, Area, Surface Area, Volume, Angle Theorems, Triangle Properties, Quadrilateral Properties ## 1. Calculate the area of the shaded region shown. 95.4 m² ## 2. A Norman window has the shape of a rectangle and a semicircle. Its dimensions are given in the diagram to the right. Determine the amount of glass required for the window. 18.2032 m² ## 3. Determine the distance around the circle shown. 26.376 cm ## 4. A hiker walks 5 km due west from a cabin. She then walks 4 km due south. For the hiker to walk back to the cabin, what distance must she travel? INCLUDE A DIAGRAM WITH YOUR SOLUTION. 6.403 km ## 5. An oil tank has dimensions as shown. Determine the volume of oil it can hold. 8.177 m³ ## 6. A polygon has an interior angle sum of 1440°. What special name is given to this polygon? SHOW ALL WORK. Decagon. ## 7. A certain regular polygon has each of its exterior angles measuring 24°. How many sides would this polygon have? 15 sides ## 8. In AFUN, point O represents a centroid. The area of AFUN is 38 cm² and the length of line segment GO is 6 cm. **(a)** Determine the area of AFUG. (1 mk.) 12.67 cm² **(b)** Determine the length of line segment GU. (1 mk.) 9 cm # MPM 1D1 - Summative Review # 4 ## Units 7-8 **Topics Covered:** Pythagorean Theorem, Perimeter, Area, Surface Area, Volume, Angle Theorems, Triangle Properties, Quadrilateral Properties ## 1. Calculate the area of the shaded region shown. 95.4 m² ## 2. A Norman window has the shape of a rectangle and a semicircle. Its dimensions are given in the diagram to the right. Determine the amount of glass required for the window. 18.2032 m² ## 3. Determine the distance around the circle shown. 26.376 cm ## 4. A hiker walks 5 km due west from a cabin. She then walks 4 km due south. For the hiker to walk back to the cabin, what distance must she travel? INCLUDE A DIAGRAM WITH YOUR SOLUTION. 6.403 km ## 5. An oil tank has dimensions as shown. Determine the volume of oil it can hold. 8.177 m³ ## 6. A polygon has an interior angle sum of 1440°. What special name is given to this polygon? SHOW ALL WORK. Decagon. ## 7. A certain regular polygon has each of its exterior angles measuring 24°. How many sides would this polygon have? 15 sides ## 8. In AFUN, point O represents a centroid. The area of AFUN is 38 cm² and the length of line segment GO is 6 cm. **(a)** Determine the area of AFUG. (1 mk.) 12.67 cm² **(b)** Determine the length of line segment GU. (1 mk.) 9 cm # MPM 1D1 - Summative Review # 3 ## Units 5-6 **Topics Covered:** Slope, 1st Differences, Linear vs. Non-Linear, Equations of Lines (Slope-Int., Standard), Parallel/Perp. Lines, Direct/Partial Variations, Intercepts ## 1. Calculate the slope of the line segments through the points shown. DO NOT CONVERT ANSWERS TO DECIMALS. **(a)** A(-6, -4), B(-2, 0) m = 4/4 = 1 **(b)** Q(1, -5), R(6, 2) m = 7/5 ## 2. Each table below represents a linear relation. Determine the slope of each. **(a)** x | y ---|---| -2 | 16 -1 | 12 0 | 8 1 | 4 2 | 0 m = -4 **(b)** x | y ---|---| -2 | -5 1 | -3 4 | -1 7 | 1 10 | 3 m = 2/3 ## 3. Identify the following relations as linear (L) or non-linear (N). **(a)** y = 2 - 5x **L** **(b)** 6x + y = 7 **L** **(c)** y = 2x² + 4 **N** **(d)** 2x³ - y = 4 **N** **(e)** x = -3 **L** **(f)** y = -2√x **N** ## 4. Write the equation that would represent each table of values below. **(a)** x | y ---|---| 0 | 3 1 | 4 2 | 5 3 | 6 4 | 7 y = x + 3 **(b)** x | y ---|---| -4 | 0 -2 | 1 0 | 2 2 | 3 4 | 4 y = 1/2x + 2 **(c)** x | y ---|---| 8 | -3 6 | -1 4 | 1 2 | 3 0 | 5 y = -x + 5 ## 5. Graph these equations USING THE METHOD INDICATED. LABEL AND SCALE YOUR AXES! **(a)** y = 1/2x - 3 (use slope and y-intercept) **(b)** 4x + y - 4 = 0 (calculate x- and y-intercepts) ## 6. Write the equation of the line that passes through the points (-3, -5) and (1, 7). y = 3x + 4 ## 7. Consider each equation below. **(a)** Identify the form that the equation is in. **(b)** Convert the equation to the other form. **(i)** 4x-6y+15=0 **Standard Form** (ii) y = 2/3x + 5/2 **Slope Y-Intercept Form** ## 8. Point A lies on the line shown. Determine the equation of ANOTHER line that is perpendicular to the one shown, going through Point A. y = -2/3x - 10/3 ## 9. A used car purchased for $9,500 decreases in value by approximately $1,200 per year. Let V represent the value of the car and let n represent the number of years that pass after purchase. **(a)** Write an equation for the relation between V and n. V = -1200n + 9500 **(b)** What is the slope? -1200 **(c)** What does the slope represent? The decrease in the value of the car per year **(d)** Does this relationship represent a direct or partial variation? EXPLAIN. Partial variation. The initial value of the car is $9500. ## 10. Solve the following equations. SHOW ALL WORK. **(a)** 2x - 3y = 12 y = 2/3x - 4 **(b)** 2x + 5y – 1 = 0 y = -2/5x + 1/5 ## 11. Solve for x and y: 2x + y = 8 and x - 2y = 10 x = 4, y = 0 # MPM 1D1 - Summative Review # 4 ## Units 7-8 **Topics Covered:** Pythagorean Theorem, Perimeter, Area, Surface Area, Volume, Angle Theorems, Triangle Properties, Quadrilateral Properties ## 1. Calculate the area of the shaded region shown. 95.4 m² ## 2. A Norman window has the shape of a rectangle and a semicircle. Its dimensions are given in the diagram to the right. Determine the amount of glass required for the window. 18.2032 m² ## 3. Determine the distance around the circle shown. 26.376 cm ## 4. A hiker walks 5 km due west from a cabin. She then walks 4 km due south. For the hiker to walk back to the cabin, what distance must she travel? INCLUDE A DIAGRAM WITH YOUR SOLUTION. 6.403 km ## 5. An oil tank has dimensions as shown. Determine the volume of oil it can hold. 8.177 m³ ## 6. A polygon has an interior angle sum of 1440°. What special name is given to this polygon? SHOW ALL WORK. Decagon. ## 7. A certain regular polygon has each of its exterior angles measuring 24°. How many sides would this polygon have? 15 sides ## 8. In AFUN, point O represents a centroid. The area of AFUN is 38 cm² and the length of line segment GO is 6 cm. **(a)** Determine the area of AFUG. (1 mk.) 12.67 cm² **(b)** Determine the length of line segment GU. (1 mk.) 9 cm # MPM 1D1 - Summative Review # 3 ## Units 5-6 **Topics Covered:** Slope, 1st Differences, Linear vs. Non-Linear, Equations of Lines (Slope-Int., Standard), Parallel/Perp. Lines, Direct/Partial Variations, Intercepts ## 1. Calculate the slope of the line segments through the points shown. DO NOT CONVERT ANSWERS TO DECIMALS. **(a)** A(-6, -4), B(-2, 0) m = 4/4 = 1 **(b)** Q(1, -5), R(6, 2) m = 7/5 ## 2. Each table below represents a linear relation. Determine the slope of each. **(a)** x | y ---|---| -2 | 16 -1 | 12 0 | 8 1 | 4 2 | 0 m = -4 **(b)** x | y ---|---| -2 | -5 1 | -3 4 | -1 7 | 1 10 | 3 m = 2/3 ## 3. Identify the following relations as linear (L) or non-linear (N). **(a)** y = 2 - 5x **L** **(b)** 6x + y = 7 **L** **(c)** y = 2x² + 4 **N** **(d)** 2x³ - y = 4 **N** **(e)** x = -3 **L** **(f)** y = -2√x **N** ## 4. Write the equation that would represent each table of values below. **(a)** x | y ---|---| 0 | 3 1 | 4 2 | 5 3 | 6 4 | 7 y = x + 3 **(b)** x | y ---|---| -4 | 0 -2 | 1 0 | 2 2 | 3 4 | 4 y = 1/2x + 2 **(c)** x | y ---|---| 8 | -3 6 | -1 4 | 1 2 | 3 0 | 5 y = -x + 5 ## 5. Graph these equations USING THE METHOD INDICATED. LABEL AND SCALE YOUR AXES! **(a)** y = 1/2x - 3 (use slope and y-intercept) **(b)** 4x + y - 4 = 0 (calculate x- and y-intercepts) ## 6. Write the equation of the line that passes through the points (-