SPS Math Diagnostic – Post Grade 7 Answer Key Contents Place Value .................................................................................................................................................... 2 Decimals ........................................................................................................................................................ 3 Fractions........................................................................................................................................................ 3 Percent ........................................................................................................... Error! Bookmark not defined. Parts of a Whole............................................................................................. Error! Bookmark not defined. Integers ......................................................................................................................................................... 4 Finding Numbers on a Number Line .............................................................. Error! Bookmark not defined. Addition......................................................................................................................................................... 5 Subtraction.................................................................................................................................................... 6 Multiplication ................................................................................................................................................ 7 Division.......................................................................................................................................................... 8 Factors and Multiples..................................................................................... Error! Bookmark not defined. Order of Operations ....................................................................................... Error! Bookmark not defined. Cartesian Plane ........................................................................................................................................... 10 Patterns .......................................................................................................... Error! Bookmark not defined. Solving Equations ........................................................................................................................................ 11 1 SPS Math Diagnostic – Post Grade 7 Answer Key Place Value 1. What is the value of the underlined digit? a) 1986 900 b) 8721986 2. Fill in the empty spaces on the table Standard Form Expanded Form 20000 2000 + 400 + 50 + 7 In Words Two thousand four hundred fifty seven 167 089 100000+60000+7000+80+9 One hundred sixty seven thousand eighty nine 3 206 951 3000000 + 200000 + 6000 + 900 + 50 + 1 Three million two hundred six thousand nine hundred fifty-one 2457 3. Round the following numbers: a) 384.58 to the nearest tenth 384.6 b) 6562.41 to the nearest thousand 7000 2 SPS Math Diagnostic – Post Grade 7 Answer Key Decimals 1. Colour the blocks to show the indicated decimal numbers: a) 0.75 2. What decimal would describe the shaded part of the diagram? 0.5 3. Use <, >, or = to make the statements true: a) 0.6 _ >___ 0.006 b) 42.18 __<__ 42.7 Fractions 1. What fraction would describe the shaded part of the diagram? 3 2. Show in at least 3 different ways. 5 varied 5 10 3. Order the following fractions from smallest to largest. a) 7 4 3 8 10 10 10 10 3/10, 4/10, 7/10, 8/10 b) 5 1 1 2 6 3 2 3 1/3, 1/2, 2/3, 5/6 4. Are the shaded fractions of the following diagrams equivalent? YES or NO 5. Give an equivalent fraction for each of the following: a) 6 12 varied b) 60 90 varied 3 SPS Math Diagnostic – Post Grade 7 Answer Key 6. Circle the bigger fraction. If both fractions are equal, circle both. a) 3 5 𝑜𝑟 4 b) 5 1 2 𝑜𝑟 1 3 7. Write a mixed number and an improper fraction to describe the shaded portion of the following diagram. 3 c) 8. Change 1 3 4 Percent 1. Circle which test score is highest in percent. a) 7 out of 10 b) 15 out of 25 c) 40 out of 50 23 6 4 8 𝑜𝑟 1 2 to a mixed number. 5 6 2. What percent is shaded in the following diagram? 52% Parts of a Whole 3. Fill in the other ways to represent each number: Decimal 0.04 0.62 0.03 Fraction 4 100 62 100 3 100 Percent 4% Decimal 0.30 62% 0.09 3% 0.40 Fraction Percent 6 20 9 100 40 100 30% 9% 40% 4. Give an example of a fraction larger than 0.5. 4 SPS Math Diagnostic – Post Grade 7 Answer Key Integers 1. Order the following sets of integers from smallest to largest -5, +9, 0, -1, -8, -6 __-8___, __-6___, __-5___, __-1___, __0___, __+9___ Finding Numbers on a Number Line 5 Place the numbers where they belong on the number line: 2, -1, , 40%, 0.9 2 -3 -1 Addition 1. 12 + 9 = 21 2. 52 +78 130 3. 63 + 295 = 358 4. 2453 + 729 + 144 = 3326 0 40% 0.9 9. 𝟓 2 𝟐 32.6 +0.4 33.0 10.4.301 + 2.89 = 7.191 4 3 7 7 7 7 11. + = 1 𝑜𝑟 1 5 6 6 12.4 + 5 3 1 17 5 4 20 5. 3.0 + 2.0 = 5.0 13. + = 6. 3.1 + 2.6 = 5.7 14. (-8) + (+12) = +4 7. 7.1 + 2 = 9.1 15.(+5) + (-10) = -5 8. $17.88 + $2.90 = $20.78 3 16.(-6) + (-9)= -15 5 SPS Math Diagnostic – Post Grade 7 Answer Key Subtraction 1. 27 - 3 = 24 2. 64 – 7 = 57 3. 607 – 32 = 575 10.76.3 – 14.209 = 62.091 11.5000 − 122.4= 4877.6 1 2 7 4 3 12 12.4 − 1 = 2 13.0 − 15 = -15 4. 1465 – 348 = 1117 14.3 – 10 = -7 5. 6.0 – 5.0 = 1.0 15.(+8) – (+6)= +14 6. 8.5 – 2.4 = 6.1 16. (+2) – (-6)= +8 7. 32.6 −0.4 32.2 8. 7.1 – 3 = 4.1 9. 17.(-8) – 9 = -17 18. (-4) – (-4) = 0 $47.78 −$31.65 16.13 6 SPS Math Diagnostic – Post Grade 7 Answer Key Multiplication 1. 5 x 9 = 45 6. 7.6 × 5.8 44.08 2. 3 x 16 = 48 3. 1000 x 81 = 81000 4. 3826 x 6 = 22956 5. 25 x 48 = 1200 7. 86.9 x 7 = 608.3 8. 6 x 0.1 = 0.6 9. 0.01 x 5.88 = 0.0588 10.5 x 0.02= 0.1 7 SPS Math Diagnostic – Post Grade 7 Answer Key Division 1. 28 ÷ 7 = 4 2. 10 40 6. 383 6 = 63 𝑅5 =4 7. 3 5.4 = 1.8 3. 9 81 = 9 8. 241.08 6 = 40.18 4. 8 400 = 50 5. 3 402 = 134 8 SPS Math Diagnostic – Post Grade 7 Answer Key Factors and Multiples 1. What are the prime factors of 80? You may use a factor tree if you choose. 2X2X2X2X5 2. What are the factors of 12? 1, 2, 3, 4, 6, 12 5. Using the number grid below, use a to mark the factors of 6 and a to mark the multiples of 6. 3. What is the greatest common factor of 12, 15? 3 4. What is the lowest common multiple of 12, 15? 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Order of Operations 1. 3 + 7 x 4 = 31 4. 2 – 3 (4) 6 – 2 = -2 2. 24 – 8 x 3 = 0 5. 5 + 7 (9 – 4 + 3) = 61 3. 4 x 8 + 8 4 – 3 = 31 6. 5 + 2 (8 – 4) 4 + 4 = 11 9 SPS Math Diagnostic – Post Grade 7 Answer Key Cartesian Plane 1. Write the (x,y) coordinates for each point: A (-5, 6) B (6,5) 2. Which point is described by the coordinates: (3, -1) G (-6, -1) D Patterns 1. How many kilometers will Cindy jog in 5 hours? Hours 1 2 3 4 5 Kilometers 4 8 12 16 20 2. What is the pattern rule? Input Output 23 46 25 50 9 18 47 94 2𝑥 10 SPS Math Diagnostic – Post Grade 7 Answer Key 3. Fill in the table for y = 2x + 1 x y 1 3 2 5 3 7 4 9 4. Which of the following is an example of an expression? a. 2x + 4 b. 5x + 4 = 29 c. A = L x W d. 12 + 6 = 36 𝑥 6. What is the equation for the following statement: one more than double a number is 11? 2𝑡 + 1 = 11 7. Ray earns money cleaning windows. For each house he charges $5 plus $2 for every window cleaned. What is an expression that represents his total earnings? 2𝑤 + 5 5. What is the expression for three times a number minus five? 𝟑𝒕 − 𝟓 Solving Equations 1. 34 = + 9 2. 𝑥 + 5 = 11 25 𝑋=6 3. 3𝑥 = 12 𝑋=4 4. 2𝑥 + 3 = 15 𝑋=6 11