topic 9 Numeracy 9. Overview Why learn this? Our lives are interwoven with mathematics. Counting, measuring and pattern-making are all part of everyday life. We use numbers to mark signifi cant events (such as birthdays) and for identifi cation (such as passports and credit cards). We use numbers to describe ourselves (for example our height and weight). Shopping involves understanding numbers, and tallying scores in sports requires a comparison of numbers. You may not realise just how much you rely on numbers. What do you know? think List what you know about. Use a thinking tool such as a concept map to show your list. pair Share what you know with a partner, then with a small group. SHare As a class, create a thinking tool such as a large concept map that shows your class s knowledge of. Learning sequence 9. Overview 9. Set C 9. Set
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9. Set C Calculator allowed The cube root of 64 is between: a and and c and 4 and 4 A javelin is thrown times. The mean distance of the throws is 55 m. The fourth throw reaches 6 m. What is the mean distance after 4 throws? a 5 m 57 m c 55 m 60 m The monthly cost (C) of renting a mobile phone is given by the equation C = 0 + 0.x, where x is the call time in minutes. If February s bill was $0, the call time was: a 00 minutes 00 minutes c 500 minutes 450 minutes 4 A music store has two promotions running at the same time: uy Cs for $6.95 each and get the third free. 0% off all Cs which normally retail at $4.95 each. If Emma wants to buy three Cs, what is the best price she can get? a $5.90 $5.40 c $5.90 $54.50 5 A number is multiplied by, then is subtracted. The final answer is the square of 6. What is the original number? 6 A painter quotes $448 to paint the walls of a bedroom with the following dimensions: length = 4 m width = m height =. m. How much extra will he charge to paint the ceiling as well (at the same original cost per square metre)? y a $00 $0 6 c $0 $50 4 7 Solve the equation for q. 4q = 4 8 What is the equation of the graph shown? a y = x y = x c y = x + y = x + x 4 0 4 4 6 0 Maths Quest 9
9 For the triangle shown, x equals: A 6 7 C 8 9 4x x C 0 The scale 00 cm 4 m simplifies to the ratio: A : : 4 C : 4 50 : A house is bought for $450 000 and sold for $55 000. Express the profit as a percentage of the cost price. (Round to decimal places.) A 4.9% 6.67% C 85.7% 6.7% A 00-g block of chocolate is to be broken into its individual squares. What is the mass of 4 squares of chocolate? A 0 g 6 g C 5 g 0 g The area of the composite shape shown is: A 0 cm 40 cm C 50 cm 45 cm 4 What is the next term in the following pattern?, 4, 9, 6,... A 0 5 C 9 6 5 A cyclist travels 5 km in 0 minutes. The speed (in km/h) she is travelling is: A 40 km/h 60 km/h C 80 km/h 0 km/h 6 The intersection point for y = x + 4 and x + y = is: A (, ) (, ) C (, ) (, ) 7 The factorised form of x y 6xy is: A xy (xy ) xy(x y ) C xy(xy 6) x y(xy ) A 4x + 4 5 cm 0 cm cm Topic 9 Numeracy
8 The graph shows the frequency of the number of bread rolls bought at a bakery. What is the total number of rolls bought? A 00 88 C 50 68 9 What are the mean and median of the data shown in the table? A The mean is and median is 4. The mean is and median is. C The mean is 4 and median is. The mean is 4 and median is 4. 0 Which number is exactly halfway between.5 and 4.75? A.95 4.5 C 4.5 4 Write a fraction equivalent to 0.75. Which diagram is the net of a square-based pyramid? A C The table summarises how much time Lian spent on her Maths project. What was the average amount of time each day Lian worked on her project? A 5 minutes 0 minutes C 4 minutes hour 4 raw a line of symmetry through the diagram. 5 If x =, what is the value of A C 4 x x? Frequency Score (x) 8 6 4 0 4 8 6 0 Number of rolls bought at a bakery Frequency 4 4 Time spent on project ay Time Monday 0 minutes Tuesday 5 minutes Wednesday hours 4 Thursday 50 minutes Friday 45 minutes Maths Quest 9
6 A map of Fern Island is shown below. Treasure Point Shipwreck What direction is the treasure from Point Shipwreck? 7 The shape at right is to be enlarged by a factor of. The new area will be: a times the original area 6 times the original area c 9 times the original area times the original area 8 Complete the table of values for the rule y = x. x 0 y 9 The population of a city is expected to increase by.5% each year for the next 5 years. If this city s current population is 00 000, what is it expected to be in 5 years time? a 9 4 755 000 c 750 45 55 406 0 Find the area of material (m ) needed to make a circular cushion with a diameter of 0 cm. Note: Two pieces of material are cut out and sewn together to make the cushion. a.5 m.0 m c.9 m.5 m 9. Set Non-calculator What is the equivalent fraction to 5? a 7 The value of a 5 4 5 + 4 5 7 is: c 7 5 c 4 N cm cm Topic 9 Numeracy
0 80 0 80 A large cube, shown at right, is painted blue. How many cubes, inside this large cube, have no painted faces? a 8 6 c 6 64 4 A glass of water (50 ml) is poured from the jug. How much water is left in the jug? a.75 L.5 L c.5 L L 5 Measure the size of the unknown angle, x, using the protractor. 0 0 0 60 70 40 50 40 50 0 60 0 a 5 66 c 54 6 6 4.076 9.5 equals: a 4.86 4.5 c 4.96 0.48 7 Jake recorded his classmates preferred ice-cream flavours in the table below. 70 0 80 00 Ice-cream flavour Number of students Chocolate 4 Vanilla Strawberry 7 Choc-mint 6 What percentage of students prefers choc-mint flavoured ice-cream? a 60% 0% c 6% 5% 8 A car travels at 75 kilometres per hour. How far will it travel in 4 hours? a 00 km 50 km c 00 km 50 km 9 Which of the following diagrams shows the arrow below multiplied by a scale factor of? x 90 90 00 80 0 70 60 0 50 0 40 40 0 0 50 0 60 70 L L 4 Maths Quest 9
A C 0 XZ is cm. XY is a quarter of the distance of XZ. Find YZ. X Y Z A 8 cm 6 cm C 0 cm 4 cm How many sticks would be needed to make the 5th shape in this pattern? A 0 6 C 8 4 To convert from degrees Fahrenheit ( F) to degrees Celsius ( C), the following formula is used: C = 5 (F ). 9 What is the Fahrenheit temperature equivalent to 5 C? A 86 F 95 F C 70 F 00 F y The two points A and are on which line? A y = x A y = x + 0 x C y = x y = x 4 Solve the equation 4m 5 + 7 =. A m = 5 m = 4 C m = 5 m = 5 A football team played games during a season. The team won 4 more games than it lost. How many games did the team win? A 9 C 4 6 A and C are supplementary angles. AC is 0. Find the size of AC. C 75 A Topic 9 Numeracy 5
7 raw the reflection of the shape shown at right. 8 If p = and q = 5, evaluate q p. A 9 C 9 9 The area of a circle is A = πr. Which value best estimates the area of a circle with a radius of 5 cm? A 75 cm 5 cm C 50 cm 7.5 cm 0 This dot plot shows the ages of people in a choir. What is the most common age of the choir members? A 50 58 C 59 60 What is the probability of getting Tails when a fair coin is tossed? A 0 C 50 5 5 5 54 55 56 57 58 59 60 Ages of people in a choir Insert < or > to make this statement true. 4 5 The following scores were recorded in a test: 8 and 88%. 0 Which is the higher score? 4 The cost of two different books is in the ratio 4 : 5. If the more expensive book costs $5, what does the cheaper book cost? A $5 $0 C $5 $0 5 Calculate the value of m 75 cm + 5 m 6 cm. A 8 m 95 cm 9 m cm C 9 m 0 cm 8 m cm 6 There are 60 squares in a chocolate block. If Stef eats of the block, how many squares are left? A 0 5 C 0 5 6 Maths Quest 9
7 The length of a rectangular sporting field is four times its width. If the perimeter of the field is 00 m, find the length and width. 8 A bag of marbles contains red, 0 yellow, 5 green and 8 blue marbles. arcy chooses one marble without looking. What is the chance it will be green? a c 4 5 9 Which pair of shapes fits together to make a cube? a c 0 What shape is revealed when a triangular prism is cut vertically? Knife Triangular prism a Triangle Square c Rectangle Trapezium 6 the story of mathematics is an exclusive Jacaranda video series that explores the history of mathematics and how it helped shape the world we live in today. NAPLAN: Strategies and tips (eles-688) gives an overview of the NAPLAN tests, as well as providing the best advice on how to prepare for the test beforehand and how to tackle the questions during the test. Topic 9 Numeracy 7
Answers topic 9 Numeracy 9. Set C Calculator allowed C 4 5 6 6 C 7 q = 5 8 A 8 9 C 0 A 4 5 6 C 7 A 8 9 0 4 4 C 5 A 6 North-east 7 C 8 7,,, 0,,, 7 9 A 0 C 9. Set Non-calculator C A 4 5 6 A 7 8 A 9 0 C A 4 A 5 C 6 50 7 8 9 A 0 8 > 0 6 C 4 5 7 l = 80 m w = 0 m 8 C 9 A 0 C 8 Maths Quest 9