1 Interest: Investing Money

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1 1 Interest: Investing Money Relating Units of Time 1. Becky has been working at a flower shop for 2.1 yr. a) How long is this in weeks? Round up. 2.1 yr 3 wk/yr is about wk b) How long is this in days? Round up. 2.1 yr 3 d/yr is about d Use 1 yr (year) 36 d (days) 2 wk (weeks) 12 mo (months) 1 mo 30 d 2. Write each length of time as a fraction of the unit given. a) 6 d 36 yr c) 18 wk yr b) 3 d yr d) 8 d mo Working with Percents Percent means out of % is the same as 1 hundredth, or 1 100, or % is the same as 32 hundredths, or , or % is between 32% and 33%. So, it is between 0.32 and Ones Tenths Hundredths Thousandths Write each percent as a decimal. a) 9% d) 4.8% b) 2% e) 11.9% c) 79% f ) 0.8% 32.% 0.32 The whole number part of the percent ends with the number of hundredths in the decimal. 4. Write each decimal as a percent. a) 0.02 % d) % b) 0.8 % e) 0.00 % c) 0.4 % f ) 0.12 % To write a decimal as a percent, write the number of hundredths % % Chapter 1 Interest: Investing Money 1

2 . Calculate each percent. a) 10% of 280 c) 7.% of 200 b) 6% of 27. d) 0.8% of 620 Multiplying Decimals and Fractions 6. Multiply. a) c) b) d) Solving Equations 7. Solve for each variable. 10% of 280 means the same as 10% 3 280, or Tech Tip Multiplying a Decimal by a Fraction To multiply.2 3 4, enter a) 3s s s s c) 2 t 2 4 b) 1.1d 44 d) n Calculating with Exponents An exponent shows how many times a number is multiplied by itself. (2) (2) (2) ( ) Calculate. a) (3) 2 d) 4() 332 b) 8(2.3) e) 4.2(0.8) c) 2.8(1.8) 4 f ) 7.62( ) Tech Tip Square Key (x 2 ) To calculate (2) 2, enter 3 2 x 2 Tech Tip Exponent Key (y x ) Use the exponent key for exponents other than 2. For (2) 6, enter 3 2 y x 6 Apprenticeship and Workplace 11: Review of Essential Skills 2

3 2 Working with Graphs Graphing Data 1. Shade bars on the bar graph to show the monthly ticket sales. The first bar is done for you. 800 Number of Tickets Sold Number of Tickets Sold Month Number sold Number sold January 70 February 00 March Jan. Feb. Mar. Apr. May Month April 60 May Plot points on the grid to show the total amount of money raised for a school trip. The first point is plotted for you. Join the points. Total amount raised Amount of Money Raised for School Trip Week Amount of Money Raised for a School Trip Week Total amount raised ($) Chapter 2 Working with Graphs 3

4 Reading Graphs 3. Matt counted the number of customers in a store each hour, from opening time until closing time. a) About how many customers were in the store at 10 a.m.? b) About how many customers were in the store at 1 p.m.? c) At what time were there about 4 customers in the store? d) At what time were the most customers in the store? Number of customers a.m. Customers in a Store 12 p.m. 2 p.m. 4 p.m. 6 p.m. 8 p.m. Time 10 p.m. 4. Anna, Ben, Candace, and Dan ran for student-council president. The graph shows the election results. Use the graph to estimate what percent of the students voted for each person. Record your estimates in the chart below. Check to make sure that your total is 100%. Explain how you used a fraction to estimate each percent. Percent of Votes in School Election Candace Dan Anna Ben To estimate percents on a circle graph, compare the parts with benchmark fractions or decimals. Examples of benchmarks are 1 or 0%, or 2%, and 1 3 or about 33%. Anna Ben Candace Dan Estimated percent % % % % How I estimated Apprenticeship and Workplace 11: Review of Essential Skills 4

5 3 Units of Measurement 1. Match each object to the amount of space it could cover. beach towel about 1 sq ft ruler about 2 m 2 tablecloth about 1 cm 2 bathroom scale pen about 12 sq in. about 1 sq yd Working with Polygons 2. The area of a polygon is the number of square units of space that it covers. Name each polygon, and determine its area. a) 6 m Surface Area 3 m c) 2.1 ft 4.7 ft Suppose you cut apart this square and then put the pieces together to make a new shape. The new shape would still cover 1 sq ft. 1 ft 1 ft areas of polygons rectangle A (length)(width) lw w Name of polygon: Area m 3 m m 2 b) 14 in. 7 in. 4.2 ft Name of polygon: Area d) 12 cm cm cm l triangle A 1 2 (base)(height) 1 2 bh h b parallelogram A bh h Name of polygon: Name of polygon: b trapezoid A 1 (b 1 B)h 2 b Area Area h B Chapter 3 Surface Area

6 Working with Circles 3. Use the formulas at the right. If your calculator does not have a key for p, use 3.14 as an estimate for p. a) Determine the circumference, to the nearest whole unit. b) Determine the area, to the nearest whole unit. circle formulas radius diameter 4. m diameter m C 3 m m, or about m 10 in. radius in. A 3 ( in.) 2 sq in., or about sq in. circumference C p 3 (diameter) or C 2p 3 (radius) area A p 3 (radius) 2 Using the Pythagorean Theorem The Pythagorean theorem can be used for right triangles. Pythagorean theorem: Suppose you drew a square on each side of a right triangle. You could exactly cover the square on the longest side by combining the areas of the squares on the two shorter sides. Suppose you knew the lengths of two sides of a right triangle. You could use this formula to calculate the length of the third side. a 2 b 2 c 2 a b c 4. Use the Pythagorean theorem to calculate the unknown side length. Label each length on the diagram, to one decimal place. (6 m) 2 1 (8 m) 2 c 2 m 2 1 m 2 c 2 m 2 c 2 " m 2 "c 2 m c c 6 m 8 m The square root of a number is the side length of a square whose area is the number. For example:!9 3 because a square with an area of 9 square units has sides that are 3 units long ( ). Apprenticeship and Workplace 11: Review of Essential Skills 6

7 4 Volume and Capacity Units of Measurement 1. Draw a line to match each volume to an object. cu ft semi-trailer for a truck 60 m 3 suitcase 12 cu yd softball 30 cu in. full tube of toothpaste 120 cm 3 load of dirt in a dump truck 2. Draw a line to match each capacity to a container. 10 gal soup bowl 80 L hot-water tank 1 ml cooking pot 2 c aquarium 1 qt spoon Volume measures the space that an object occupies. Capacity measures the amount that a container can hold. Calculating Volume 3. Calculate the volume. a) 2 ft b) 7 cm 6.4 cm For prisms and cylinders: Volume (area of base)(height) 6 ft 3 ft V (A base )(h) V (A base )(h) ( ft 3 ft)( ft) pr 2 (h) cu ft p( cm) 2 ( cm) cm 3 Chapter 4 Volume and Capacity 7

8 Multiplying with Fractions 4. Multiply. a) 1 2 (2.8 cm)(3. cm)(2 cm) 1 2 ( cm3 ) b) a 3 4 ydb a2 3 ydb sq yd sq yd sq yd cm 3 Multiplying by 1 2 gives the same result as dividing by 2. To multiply two fractions, multiply the numerators and multiply the denominators c) 7 8 mi mi 3 3 sq mi d) a 2 3 ftb a61 2 ftb 3 3 sq ft sq mi sq ft 2 3 To multiply by a mixed number, write the mixed number as an improper fraction sq ft Working with Capacity. Complete each sentence. a) You can pour pt into a 1 gal container. b) You can pour ml into a 1 L container. c) You can pour c into a 1 qt container. d) You can pour c into a 2 gal container. Use the charts inside the back cover of the Workbook. Apprenticeship and Workplace 11: Review of Essential Skills 8

9 Interest: Borrowing Money Working with Money 1. Use mental math to estimate each amount, to the nearest dollar. of $19.99 is about $. a) 1 2 b) 1 3 c) 2 3 d) 1 4 e) 3 4 of $30.2 is about $. of $30.2 is about $. of $99.0 is about $. of $99.0 is about $. 2. Use mental math to estimate each amount, to the nearest dollar. a) 10% of $69.99 is about $. b) 2% of $79.98 is about $. c) 7% of $79.98 is about $. d) 33% of $2100 is about $. e) 20% of $210 is about $. 3. Evaluate to the nearest cent. Estimate to check that your answers make sense. a) 18.% 3 $2200 b) 17.6% 3 $ c) 12.8% 3 $11 00 d) 9.2% 3 $ e) 24.8% 3 $10 37 f) 32.7% 3 $ Evaluate. a) $ (6% of $1000) $ b) $700 1 (12% of $700) $700 1 To calculate 1 4 of a number, divide by 4. To calculate 3 4 of a number, divide by 4 and multiply by 3. 10% or % or 1 2% or % or about 1 3 0% or 1 2 7% or 3 4 Tech Tip Multiplying with Percents To calculate 18.% of $2200, enter 18. % , or When working with money, round to the nearest cent after you have made the final calculation. Chapter Interest: Borrowing Money 9

10 c) $ (16.2% of $3000) $ Calculating with Exponents. Calculate. Round to the nearest hundredth. a) 3.1 c) ( ) 4 b) ( ) 3 d) 3a b 10 Using Interest Formulas Simple interest: To calculate the amount of simple interest, I, earned on an investment, use I Prt where P is the principal, r is the yearly interest rate, and t is the time in years. Tech Tip Multiplying Expressions in Brackets Use 3 to multiply expressions in brackets. For example, for ( ) 4, enter 3 ( ) y x 4 6. Sophie invested $1000 in a guaranteed investment certificate for 3 yr. The interest rate is 1.8% per year. How much interest will Sophie earn? I Prt $ /yr 3 3 yr $ Sophie will earn $ in interest. Compound interest: To calculate the value of an investment amount, A, earning compound interest, use A P(1 1 i) n where A is the total value of the investment with interest, P is the principal, i is the interest per compounding period, and n is the number of compounding periods. 7. Max invested $1200 in a savings account. The account earns 2.3%/yr, compounded monthly. How much will Max s investment be worth in 3 yr? A $1200a b $1200 ( ) 36 $ Max s investment will be worth $ in 3 yr. Apprenticeship and Workplace 11: Review of Essential Skills 10

11 6 Slope and Rates Relating Decimals, Percents, and Fractions 1. Complete each row in the chart by expressing the same number in different ways. Decimal Percent 0.7 7% Fraction in lowest terms To write a fraction in lowest terms, divide the numerator and the denominator by their greatest common factor % 1 8 Writing Ratios in Lowest Terms A ratio compares two numbers. A ratio is in lowest terms if the numbers have no common factors. 14 : 3 is not in lowest terms because 7 is a factor of both numbers and : 3 2 :, in lowest terms 2. Write each ratio in lowest terms. a) 20 : 1 4 : d) 12 : 36 b) 3 : 18 e) 16 : 40 c) 0 : 40 f ) 42 : 24 Converting Measurements 3. a) 2. h min c) 8 yd ft b) 2.1 km m d) 0.2 L ml Writing a ratio as a fraction can help you write it in lowest terms. 14 : : Use the charts inside the back cover of the Workbook. Chapter 6 Slope and Rates 11

12 Working with Integers Sometimes, it helps to think about what the operation means. 3 3 (24) means 3 groups of (24). 3 3 (24) 212 Sometimes, it helps to think about opposites , so 10 4 (2) must be the opposite (2) 22 Sometimes, it helps to think about the related operation. For (22), think about the related multiplication. 7 3 (22) 214, so (22) 7 4. Multiply or divide. a) 6 3 (23) d) b) e) 30 4 (2) When you multiply or divide two integers with the same sign, the result is positive (24) (24) 3 c) 26 3 (27) f ) (23) Think of a number line to subtract with integers. Move left to subtract a positive number. Move right to subtract a negative number ( 4) Subtract. a) d) 4 2 (23) b) e) (26) c) f ) (21) Calculating Tangents 6. Calculate the tangent for each angle of elevation. a) b) tan A opposite adjacent x 3 ft 20 ft 6 m 8 m t hypotenuse A opposite A tan x tan t adjacent to A Apprenticeship and Workplace 11: Review of Essential Skills 12

13 7 Drawing Objects and Shapes Using Equivalent Ratios A ratio compares two numbers. For example, to 26, or : 26, is the ratio of vowels to total letters in the alphabet. Equivalent ratios describe the same relationship. Suppose that you wrote the alphabet twice. The ratio of vowels to total letters would be 10 : 2. The two ratios, : 26 and 10 : 2, are equivalent ratios You get an equivalent ratio when you multiply or divide both terms in a ratio by the same number Sometimes, one number in a pair of equivalent ratios is missing. 16 : 40?: 10 To calculate the missing number, determine the factor that the numbers in one ratio are multiplied or divided by to get the other ratio or Calculate the missing terms. a) b) 40 8 Use the given numbers to determine the multiplication or division factor. 3 4 Chapter 7 Drawing Objects and Shapes 13

14 2. Calculate the missing term. a) 3 : : 2 c) b) d) 12 : 1 : Comparing Similar Shapes 3. Rectangle ABCD was enlarged to make rectangle EFGH. The angles did not change. All the side lengths of rectangle ABCD were multiplied by 2. a) How long is HE? b) How long is EF? F B 3 m A m C D G c) How long is GH?? m d) The ratio of length : width for rectangle ABCD is : 3. What is the ratio of length : width for rectangle EFGH? : E? m H e) What is the ratio from Part d) in lowest terms? : Multiplying Mixed Numbers by Whole Numbers Method 1: Multiply the whole numbers. Then multiply the fraction parts in. (4 3 3 in.) 1 a in.b 12 in. 1 1 in. 13 in. Method 2: Change the mixed number to a fraction in in in. 2 4 in. 13 in is a mixed number wholes and wholes 12 4, so is the fraction name for Multiply. a) in. b) ft Apprenticeship and Workplace 11: Review of Essential Skills 14

15 8 Managing Money Adding and Subtracting with Money When you add or subtract money amounts on paper, line up the dollars and cents. $ $148.3 If there are no cents, write zeros after the decimal point. This keeps the numbers in line. 1. Farida shares an apartment with a roommate. This chart shows the bills that she pays each month. a) How much does Farida pay for her cellphone plus the Internet? Tech Tip Dollars and Cents When you enter money numbers in a calculator, you do not need to enter.00 if there are no cents. Monthly Expenses rent $48.00 utilities $7.43 cellphone $4.00 Internet $3.26 b) What are Farida s total monthly expenses? food $37.00 bus pass $.00 c) Farida earns $ per month. How much money is left after she pays her monthly expenses? Farida s Spending Plan d) How could Farida use the money she has left after expenses? Estimate the cost for each item. Include an amount for monthly saving. savings Total Chapter 8 Managing Money 1

16 Relating Percents to Decimals 2. Write each percent as a decimal. a) 6% c) 1% b) 90% d) 12.% 3. Write each decimal as a percent. a) 0.01 % c) 0.7 % b) 0.4 % d) 0.12 % Calculating Percents 4. Calculate. a) 22% of $37 c) 2% of $100 b) 63% of $1200 d) 37.% of $92 Tech Tip Percents of Money Amounts Calculate 2% of $30. If your calculator has a % key, enter %, or nd % If your calculator does not have a % key, enter , or To write a percent as a decimal, write the number of hundredths. 9% 9 hundredths, or % 80 hundredths, or 0.80, or % 11 hundredths thousandths, or 0.11 Another way to calculate the percent of a number is to calculate 1% of the number. Then multiply by the percent you are determining. To calculate 11% of $10: 1% of $10 $ $1.0 11% of $ $1.0 $16.0. The sale price of an electric guitar is 8% of $400. What is the sale price? Calculating with Exponents An exponent shows how many times a number is multiplied by itself. 6(4) 2 6(4)(4) 3( ) 2 3(0.3)(0.3) 6(16) 3(0.09) Calculate. a) 2(7) 2 c) (0.8) 4 b) 7.2(1.1) d) 8.3( ) 4 Apprenticeship and Workplace 11: Review of Essential Skills 16

17 9 Solving Right Triangle Problems Using the Pythagorean Theorem If you know the lengths of two sides of a right triangle, you can use the Pythagorean theorem to determine the length of the third side. 1. Use the Pythagorean theorem. Calculate the unknown side length. Label each length, to one decimal place. a) c) 6 in. c a b a 2 1 b 2 c 2 3 in. 9 m (3 in.) 2 1 (6 in.) 2 c 2 m (9 m) 2 1 ( m) 2 c 2 m 2 1 m 2 c 2 m 2 c 2 sq in. 1 sq in. c 2 sq in. c 2 " sq in. "c 2 in. c " m 2 "c 2 m c b) (4 cm) 2 1 b 2 (11 cm) 2 16 cm 2 1 b cm 2 4 cm b cm 2 2 cm 2 b 2 cm 2 "b 2 " cm 2 11 cm Suppose that you know the lengths of a and c, but not the length of b. You can use b 2 c 2 2 a 2. b cm Chapter 9 Solving Right Triangle Problems 17

18 Using Trigonometric Ratios Trigonometric ratios work for right triangles. You can use trigonometric ratios to calculate side lengths and angle measures. A 2 hypotenuse adjacent to A In the triangle above, /A is 2. /B must be 6 since Every right triangle with a 2 angle has the same angles. Triangles with the same angles are similar. Similar triangles have the same side : side ratios. B opposite to A C The three trigonometric ratios for A are sin A opposite hypotenuse cos A adjacent hypotenuse tan A opposite adjacent 2. a) Use side lengths to calculate each ratio in the chart below for the triangle at the right. Answer to four decimal places. b) Calculate each ratio using the trig function keys on a calculator. Do your answers match? Ratio a) Using side lengths b) Using a calculator Y sin 3 opposite hypotenuse ft ft sin ft 12.2 ft cos 3 adjacent hypotenuse X 10.0 ft 3 Z tan 3 opposite adjacent 3. a) Use a calculator. Enter the tangent of 3 that you calculated for Question 2. Then press tan 21. What does your calculator show, to the nearest whole number? b) What does this number tell you about the triangle? Tech Tip Inverse Trig Functions The sin 21, cos 21, and tan 21 keys are called inverse trig functions. Apprenticeship and Workplace 11: Review of Essential Skills 18

19 10 Linear Relations Identifying and Extending Patterns 1. Describe each pattern. a) 1, 18, 21, 24 The pattern starts with. Each number is b) 92, 87, 82, 77 The pattern starts with. Each number is c) 2, 4, 8, 16 The pattern starts with. Each number is the number before it. the number before it. the number before it. 2. Write the next two terms in each pattern. a) 40, 43, 46, 49,, b) 9, 91, 87, 83,, c) 6, 18, 4, 162,, d) 226, 201, 176, 11,, Making a Table of Values A table of values shows how two variables are related. Here, the amount of money earned increases by $1 for each hour worked. The following equation shows this relationship: money earned hours 3 $1 3. Complete the table of values for each relation. a) y x 1 4 c) y 2x 2 3 Hours worked Money earned $0 $1 $30 $4 $60 x y 4 b) y x 2 6 x y 26 x y d) y 4x 1 3 x y Chapter 10 Linear Relations 19

20 Plotting Patterns on a Coordinate Grid An ordered pair is a pair of numbers that describes a point on a coordinate grid. An example is (3, 22). The first number describes the distance along the horizontal axis, or x-axis. The second number describes the distance along the vertical axis, or y-axis. You can plot points on a coordinate grid to show a number pattern. If the pattern increases or decreases by the same amount each time, the points form a straight line. A pattern that makes a straight line is called a linear pattern. 4 4 y 2 x (3, 2) 4 4. Plot each pattern on the coordinate grid below. Join the points to form a line. Use a different colour for each pattern. 4 y x a) The first point is (0, 22). x y b) The first point is (24, 26). x y Which pattern in Question 4 is growing faster? How do you know? Apprenticeship and Workplace 11: Review of Essential Skills 20