Westbourne Grammar School Year 9 Maths Practice Exam - 2024 PDF

NAME: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ TEACHER: =================================================================== Westbourne Grammar School **Year 9** **MATHEMATICS -- Practice Exam** **Reading time:** 10 minutes **Writing time:** 90 minutes +-----------------------------...

NAME: \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ TEACHER: =================================================================== Westbourne Grammar School **Year 9** **MATHEMATICS -- Practice Exam** **Reading time:** 10 minutes **Writing time:** 90 minutes +-----------------------------------+-----------------------------------+ | *Number of Questions* | *Number of Marks* | +===================================+===================================+ | 20 Multiple Choice Questions | 20 | | | | | 10 Short Answer Questions | 57 | | | | | 2 Extended Response Questions | 11 | +-----------------------------------+-----------------------------------+ | Total Score: | / 88 | +-----------------------------------+-----------------------------------+ +-----------------------------------------------------------------------+ | Students are permitted to bring into the examination room: pens, | | pencils, highlighters, erasers, sharpeners, rulers, **one approved | | CAS calculator** (memory DOES NOT need to be cleared), and, if | | desired, one scientific calculator. | | | | Students are **NOT** permitted to bring into the examination room: | | blank sheets of paper and/or white out liquid/tape, **mobile phones | | and/or any other unauthorised electronic or communication devices | | into the examination room.** | | | | **Materials supplied** | | | | Multiple Choice Question Booklet of 7 **pages** | | | | Multiple Choice, Short Answer and Extended Response booklet of **12 | | pages** | | | | **Instructions** | | | | Write your **name and circle your teacher's name on BOTH booklets**. | | | | All written responses must be in English. | | | | **At the end of the examination** | | | | Submit your Multiple-Choice, Short Answer and Extended Response | | Booklet to your teacher. | | | | Submit your Multiple-Choice Question Booklet to your teacher in a | | separate collection. | +-----------------------------------------------------------------------+ Students are NOT permitted to bring mobile phones and/or any other unauthorised electronic devices into the examination room. Section A: Multiple Choice (20 marks) **Circle the correct response on the grid below.** **If you make a mistake completely erase it and make sure only one choice is marked.** 1 A B C D E ---- --- --- --- --- --- 2 A B C D E 3 A B C D E 4 A B C D E 5 A B C D E 6 A B C D E 7 A B C D E 8 A B C D E 9 A B C D E 10 A B C D E 11 A B C D E 12 A B C D E 13 A B C D E 14 A B C D E 15 A B C D E 16 A B C D E 17 A B C D E 18 A B C D E 19 A B C D E 20 A B C D E Section B: Short Answer (57 marks) **Question 1** **A group of 50 students was surveyed about their participation in swimming and running, represented by the table below.**  a. Fill in the missing values in the table. b. What is the probability that a randomly selected student:\ i) Both swims and runs?\ ii) Only swims?\ iii) Does not run? c. What is the probability that a randomly selected student does not run?. (2 + 3 + 1 = 6 marks) **Question 2** Complete the table of values for [--2 ≤ *x* ≤ 2]{.math.inline}, and then plot the graphs on the set of axes provided, labelling each graph with its rule, and intercepts and turning points with coordinates: ---------------------------------------------------------------------------- \ -2 -1 0 1 2 [*x*]{.math.display}\ ------------------------------------------------------ ---- ---- --- --- --- \ [*y* = *x*^2^]{.math.display}\ \ [\$\$y = {- \\frac{x}{2}}\^{2}\$\$]{.math.display}\ \ [*y* = *x*^2^ − 2*x*]{.math.display}\ ---------------------------------------------------------------------------- Chart, line chart, scatter chart Description automatically generated (1+1+1+2+2+2 = 9 marks) **Question 3** Sketch the graph of [*y* = (*x*−2)^2^ + 1]{.math.inline}, labelling the [*x*]{.math.inline} and [*y*]{.math.inline} intercepts with coordinates:  (3 marks) **Question 4** Describe how [*y* =  − 2(*x*−3)^2^ + 5 ]{.math.inline}has been transformed from [*y* = *x*^2^]{.math.inline}. **Question 5** Expand and simplify the following expressions, **showing all steps of working**: a. [(*y*− 2)(*y*+ 1)+ (*y*− 3)(*y*− 2)]{.math.inline} b. [(3*x*+ *y*)² -- 2(*x*+ *y*)(*x*− *y*)]{.math.inline} (2 + 2 = 4 marks) **Question 6** For the parabola [*y* = 2(*x*−4)^2^− 4]{.math.inline}, determine: a. The coordinates of the [*x*]{.math.inline}-intercepts. b. The coordinates of the [*y*]{.math.inline}-intercept. c. The type of turning point. d. The coordinates of the turning point. **Question 7** Simplify these fractions, **showing all steps of working**: The length of a rectangle is [(2*x* + 3)]{.math.inline} cm, and its width is [(*x* + 2)]{.math.inline} cm. a. Write an expression for the area of the rectangle in terms of [*x*]{.math.inline}. b. Write the expression in expanded form. c. If [*x* = 4]{.math.inline} , calculate the area of the rectangle. (1+ 2 + 2 = 5 marks) **Question 8** Solve each of the following, **showing all steps of working:** **a.** [*x*(*x*+3) = 0 ]{.math.inline} **b.** [   2*x*^2^ + 14*x*  − 12 = 0]{.math.inline} \ [c. 4(*x*−1)^2^ = 64]{.math.display}\ (2 + 3 + 3 = 8 marks) **Question 9** For the quadratic equation [*y* = *x*^2^ − 4*x*+ 3]{.math.inline}. (Show all working) a. Find the [y ]{.math.inline}intercept. b. Find the [x ]{.math.inline}intercepts. c. Find the turning point. **Question 10** Mr Abrahall and Mr Pomasan have a basketball free-throw competition to see who can score the greatest number of baskets in 5 minutes, over the space of multiple lunch times whilst at school. The results are summarised in these boxplots. Chart, box and whisker chart Description automatically generated a. State the 5-figure summary for both sets of results in the space provided. Mr Abrahall: Mr Pomasan: b. What percentage of baskets have a score less than 20 points for: Mr Abrahall: Mr Pomasan: c. What conclusion can you arrive at by comparing the median results? (2 + 2 + 1 = 5 marks) **End of Section B** Section C: Extended Response (11 marks) **Question 1** A golf ball's path is given by the rule [*h* =  − 0.014*d*^2^ + 1.5*d*]{.math.inline} where [*h*]{.math.inline} is the height in metres above the ground and [*d*]{.math.inline} is the horizontal distance in metres. Express all answers to three decimal places. **a.** If the ball is uninterrupted in flight, how far does the ball travel horizontally? **b.** What is the maximum height the ball will reach and how far from the tee does this occur? **c.** With assistance from your CAS calculator, sketch a graph of the path of the ball for an appropriate domain, labelling your axes, all axial intercepts and turning points accurately.  Mr Power has hit this ball whilst playing one Sunday morning. 100m from where the ball was hit, directly in line with the path of the ball, is a 12m tall tree. d. Will Mr Power's ball hit or miss the tree? Show calculations to prove your result. (1 + 2 + 2 + 2 = 7 marks) **Question 2** Given the right-angle triangle below, answer the following questions. MFV9%20WS%20111 a. Write an equation that could be used to solve for [*x*]{.math.inline}. a. Using your answer from part a, write your equation in expanded form. b. Hence, solve to find [*x*]{.math.inline}. c. Assuming the sides are in metres, what is the perimeter of this triangle? (1 + 1 + 1 + 1 = 4 marks) **END OF EXAMINATION** **THIS PAGE IS INTENTIONALLY BLANK**