YEAR 9 MATHS SEMESTER 1 EXAM REVISION BOOKLET 2018

Size: px

Start display at page:

Download "YEAR 9 MATHS SEMESTER 1 EXAM REVISION BOOKLET 2018"

Clifton Blankenship
5 years ago
Views:

1 YEAR 9 MATHS SEMESTER 1 EXAM REVISION BOOKLET 2018 Topics Examined Chapter 12 Measurement (Exercises ; ) o Unit Conversions o Perimeter, Area, Total Surface Area, Volume and Capacity of squares, cylinders, circles (sectors), composite shapes o Pythagoras Chapter 3 Algebra (Exercises ) o Recognising coefficients, terms, linearity, trinomials o Expanding and simplifying algebraic expressions o Formulating expressions from worded situations Chapter 4 Linear Equations o Substitution in equations o Solving Linear Equations o Rearranging equations to find the unknown pronumeral o Using linear equations to find area, perimeter of various polygons o Using linear equations to solve worded problems Chapter 6 Trigonometry ( ) o Knowing the TRIG RATIOs o Finding unknown side lengths using appropriate trigonometric ratios Reading Time: 10 minutes Writing Time: 90 minutes Exam Structure Section A: Vocabulary Section B: Multiple Choice Section C: Short Answer Section D: Analysis (5 minutes) (25 minutes) (45 minutes) (15 minutes) Exam Preparation The following options are suggestions that you might want to think about using to help you revise and study for your exam: Complete the Exam Revision questions on the following pages. Complete any practice work given by your teacher, including Mathspace and Education Perfect. Look over the topic tests and concentrate on the areas where you went wrong. Carefully read through sections of your textbook and class notes and worksheets. Go through Chapter Review Questions for the four topics listed above. Revise with a friend or in a group (such as Homework Club) revising together may help you to better understand key concepts.

2 TOPIC 1: CHAPTER 12 MEASUREMENT Vocabulary: Definition of perimeter, area, prism, volume, capacity Multiple Choice Questions: Q1. What is m equivalent to? A 4.5 mm B 4.5 cm C 450 mm D 45 cm E 450 cm Q2: What is 5 litres equivalent to? A 50 cm 3 B 500 cm 3 C 5000 cm 3 D cm 3 E cm 3 Q3: The circumference of a circle with a diameter of cm is: A cm B mm C cm D cm Q4: The figure below represents the sector of a circle. Its angle is 45 o. If the radius is 2 cm, then the area (in cm 2 ) is: A B C D E 2 2 4

3 Q5: If the total surface area of a cube is 200 cm 2, then the length of an edge is closest to: A 17 cm B 10 cm C 8 cm D 6 cm E 4 cm Short Answer Questions: Q1: Convert km to m, cm and mm. Q2: Convert the following measurements to the units indicated. (a) 2.05 km to m (b) m to mm Q3: Convert the following measures of volume to the units specified. (a) 5.6 litres = cm 3 (b) 3.1 m 3 = litres (c) m 3 = mm 3 Q4. Convert mm 2 to: (a) cm 2 (b) m 2 (c) ha Q4: A rectangle has a width of 14 cm and a perimeter of 120 cm. Find the length of the rectangle.

4 Q5: Calculate the area of each of the following shapes. (Where appropriate, give your answer correct to 2 decimal places.) Q6: Find the area of the figures drawn below. 5 cm 15 cm 8 cm 11 cm 8 cm 7 cm 14 mm

5 28.3 cm 6.2 cm Q7: A circular garden bed has a perimeter of 54 m. What is the area of the garden bed? Q8: A satellite orbits the Earth at an altitude of km. If the radius of the Earth is 6400 km, find the circumference of the orbit. (Answer in scientific notation to the nearest 100 km.) Q9: Find the perimeter of this shape.

6 Q10: Find the area of a circle with a diameter of 56 cm. Give answer correct to 2 decimal places. Q11: Find the area of the sector of a circle shown in the figure below. The radius of the circle is 2 cm. Give answer correct to 2 decimal places. Q12: A cylinder has a radius of 4.7 cm and a height of 8.9 cm. Find the total surface area. Answer correct to 1 decimal place. Q13: Find the total surface area (TSA) of a cube whose edges are 3.53 cm long. Give the answer correct to 2 decimal places. Q14: Show that a square of perimeter 4x + 20 has an area of x x + 25.

She plans to have her guests sleep on inflatable mattresses with dimensions 60 cm by 170 cm. A plan of Nina s bedroom is shown below.

7 Q15: Consider the cylinder to the right. In the space below calculate the: a) Surface area of the cylinder. b) The volume of the cylinder. Q16: Nina decides to invite some friends for a sleepover. She plans to have her guests sleep on inflatable mattresses with dimensions 60 cm by 170 cm. A plan of Nina s bedroom is shown below. a) Write an expression for the perimeter of Nina s bedroom. b) Write expressions for the area of Nina s bed, Chest of Drawers and Door. c) Write an expression for the area of the floor space that is available.

8 TOPIC 3: CHAPTER 3 ALGEBRA Vocabulary Definition of pronumeral, variable, expression, term, trinomial Inverse Operations. Multiple Choice Q1: In the following expression, what is the coefficient of x 3 : 3x 2 + x 2x 4 3 A -3 x B C D 2 3 E 3 3? Q2: Which of the following is not a linear equation? A 3 x = 8 B 4x = 3 + 8x 9 C 2x = 5x D E x 5 = y + 3 = 5y Q3: What is 2xy xy 2 simplified? A 25xy 2 B xy 2 C 21xy 2 D 21xy 2 E xy 2 Q4: What is the equivalent of 6 4x(x + 2) + 3x? A 6 4x 2 5x B 6 + 4x 2 + 5x C 6 4x 2 + 5x D 6 + 4x 2 + 5x Q5: The equivalent of (3 a)(3 + a) is: A 9 + a 2 B 9 a 2 C 3 + a 2 D 3 a 2

9 Q6: Expand and simplify the following expression: 5(x + 2y) + 6(x 3y): A 11x 2y B 11x + 8y C 11x 8y D 11x + 18y E 11x + 28y Q7: Expand and simplify the following expression: (2x + 3)(2x 3): A 4x 6 B 4x 2 9 C 4x D 4x E 4x Q8: Expand and simplify the following expression: (x 2) 2 : A x 2 4x + 4 B x 2 2x + 2 C x 2 + 4x 4 D x 2 + 2x 2 E 2x x Q9: Expand and simplify the following expression: (x 3)(x + 4) 2(x + 2) A x 2 + 3x + 8 B x 2 x 16 C x 2 + x + 16 D x 2 + 5x 16 Q10: If y = 5x 2 + 2x 1, find y when x = 5: A 134 B 59 C 56 D 24 E 119 Short Answer Questions Q1: For the expression 8xy 2 + 2x + 8y 2 5: i state the number of terms ii state the coefficient of the first term iii state the constant term iv state the term with the smallest coefficient Q2: Simplify the following expressions by collecting like terms. a) 5y 2 + 2y 4y 2 b) 11c 2 d 2cd + 5dc 2 a) n 2 p 2 q 3p 2 q + 6

10 Q3: Expand and simplify by collecting like terms. a) 3(x 2) + 9 b) 2(5m 1) 3 c) 4m(m 3) + 3m 5 d) 7p 2 (3p + 4) Q4. A rectangular rug has a length of 3x cm and a width of x cm. a) Write an expression for its perimeter. b) Write an expression for its area. c) i) f its side length is increased by y cm, write an expression for its new side length. ii) Write an expression for its new perimeter and expand. iii) Calculate the perimeter when x = 90 cm and y = 30 cm. iv) Write an expression for its new area and expand. v) Calculate the area when x = 90 cm and y = 30 cm. Q5. A rectangular garden bed has a length of 15 m and a width of 8 m. It is surrounded by a path of width p m. a) Write down the total area of the garden bed and path. b) Expand the expression you found in a). c) Find the area of the path in terms of p. d) Write an equation that could be solved to find the width of the path if the area of the path is 200 m 2. Q6. Write expressions for the following, where x and y represent numbers: a) number 8 more than y b) the difference between x and y c) the sum of x and y d) 7 times the product of x and y e) 2 times x is subtracted from 5 times y. Q7: A father is 4 times the age of his son. In 4 years time, the father will be 3 times the age of his son. How old is the father now?

11 TOPIC 5: CHAPTER 4 LINEAR EQUATIONS Vocabulary Definition of linear equation. How to find the solution to an equation. Inverse arithmetic operations. Factorisation methods Multiple Choice Q1: The solution to the equation x+2 3 = 6 is: A x = 12 B x = 16 C x = 20 D x = 24 E x = 6 Q2: The solution for x in 2x + 3 = 3x 7 is: A x = 10 B x = 10 C x = 4 5 D x = 2 E x = 2 Q3: The solution for 7(x 5) = 28 is: A x = 1 B x = 9 C x = 7 D x = 7 E x = Q4: The solution for 3(x + 1) = 14 2x is: A x = 17 B x = 17 5 C x = 11 5 D x = 55 E x = 11 Q5: The solution for 2(x + 3) = 3(x + 7) is: A x = 3 B x = 15 C x = 5 D x = 15 E x = 27 5

12 Q6: Which equation matches the following statement? Dividing 7 times a certain number by 4 equals 9: x A = 9 4 4x B = x C = 9 4 7x D = E = 9 7x Q7: Rearrange this formula to make x the subject: y = mx + c A x = ym c B x = y c m C x = y+c m D x = y + c m E x = ym + c Q8: Rearrange this formula to make G the subject: F = GMm r 2 A G = Fr2 Mm B G = Fr2 M m C G = F Mm r 2 D E G = F+Mm r 2 G = FMm r 2 Q9: Rearrange this formula to make b the subject: y = 6b 4a A b = 4a y B b = y+4a 6 C b = y 4a D b = y 4a 6 E b = 6y 4a

13 Short Answer Questions: Q1: The rectangular blocks of land drawn below have the same area. Find the dimensions of each block, and the area. Q2: A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72 m 2, what is the length of the pool? Q3: A rectangular swimming pool is surrounded by a path which is enclosed by a pool fence. All measurements are in metres and are not to scale in the diagram shown. a) Write an expression for the area of the entire fenced-off section. b) Write an expression for the area of the path surrounding the pool. c) If the area of the path surrounding the pool is 34m2, find the dimensions of the swimming pool.

14 TOPIC 6: CHAPTER 6 TRIGONOMETRY Vocabulary Definition of the sides of a right-angle triangle. Multiple Choice Q1: For the triangle below, what trigonometric ratio would be suitable? A B C D E sin α = i h cos α = h g tan α = h i tan α = i g cos α = i g Q2: What is the correct trigonometric ratio for the triangle below? A B C D E tan(γ) = a c sin(γ) = c a cos(γ) = c b sin(γ) = c b tan(γ) = b a

15 Q3: The value of length m, correct to 2 decimal places is: A B C D E m = 18.76cm m = 46.45cm m = 18.77cm m = cm m = cm Q4: What is the appropriate trigonometric ratio to use to solve for y? A y = cos(27) 7.9 B y = tan(27) 7.9 C y = tan(27) 7.9 D y = sin(27) 7.9 E y = sin(7.9) 27 Q5: The value of x to 2 decimal places is? A B C D E 48.65

16 Q6: The value of x correct to 2 decimal places is? A B C D E 99.24mm 92.55mm mm mm mm Q7: If cos(θ) = , the value of θ correct to 2 decimal places is: A B C D E Q8: The value of θ in the triangle shown, correct to 2 decimal places, is: A B C D E Q9: A ladder 4 m long leans against a wall. The foot of the ladder is 130 cm from the wall. The size of the angle the ladder makes with the wall to the nearest degree is: A 19 B 71 C 18 D 70 E 58

17 Q10: Which of the following could be used to find the value of angle a? A sin a = 7 26 B tan a = 7 26 C cos a = 7 13 D tan a = 7 13 E sin a = 7 13 Short Answer Questions Q1: Using Pythagoras theorem, calculate the missing length of the side in the following right-angled triangles. a) b)

18 Q2: A ship that was to travel due north veered off course and travelled N 80 E (or 080 T) for a distance of 280 km, as shown in the diagram. a) How far east has the ship travelled? b) How far north has the ship travelled? Q3: Calculate the unknown values in the figures below. Give your answers correct to 2 decimal places. a) b)

Q4: An ironwoman race involves 3 swim legs and a beach run back to the start as shown in the figure. What is the total distance covered in the race? Q5: Two towers are 30 m apart.

19 Q4: An ironwoman race involves 3 swim legs and a beach run back to the start as shown in the figure. What is the total distance covered in the race? Q5: Two towers are 30 m apart. From the top of tower A, the angle of depression of the base of tower B is 60, and the angle of depression of the top of tower B is 30. What is the height of tower B? Round to the nearest metre. Q5: Calculate the total height of the shape below:

CHAPTER 11 AREAS OF PLANE FIGURES

CHAPTER 11 AREAS OF PLANE FIGURES EXERCISE 45, Page 106 1. Find the angles p and q in diagram (a) below. p = 180-75 = 105 (interior opposite angles of a parallelogram are equal) q = 180-105 - 40 = 35.