Mathematics Department Grade 9 Placement Test Name This assessment will help the maths department to make a provisional placement. The final placement will be determined after a suitable period of in-class assessments by the classroom teacher. Instructions: Answer all the questions in the spaces provided. Show all your working. Calculators allowed Formulas - quadratic formula: x =!!±!!!!!"!! sin α =!""!#$%&!!"#$%&'(% cos α =!"#!$%&'!!"#$%&'(% tan α =!""!#$%&!"#!$%&' sin rule:!"#!! =!"#!! =!"#!! cos rule: a! = b! + c! 2bc cos A or cos A =!!!!!!!!!!"
1) a) Simplify: y + ( 3y) ( 4y) 8y b) What is the value of 3 + y when y = 6 c) Expand: 2(4x + 1) 2) The same type of training shoes is advertised in three different shops. Work out the cost of the training shoes in each of the three shops. Round to 2 decimal places if necessary. Tom s ; Pete s ; City Shoes
3) Factorise a) 2x + x! b) x! + 4x 12 4) Expand: a) (3x 2)! b) 2x + 1 3 5x (4x 3)(x + 2) 5) Make Q the subject of the formula A = Q! 2a.
6) The area, A cm 2, of a trapezium is given by: A =!(!!!) a) Change the subject of this formula to h.! b) Hence, calculate h for a trapezium with area 70 cm!, a = 13 cm and b = 22 cm. 7) A line passes through (5, 2) and is parallel to y = 3x. Find the equation of the line.
8) The circle has a diameter of 12 centimetres. a) Work out the circumference, in cm. Give your answer correct to 1 decimal place. cm The area of the circle increases by 30%. b) Work out the new area, in cm 2. Round to the nearest whole number. 9) In the right-angled triangle x = 3y. a) Write down another equation involving x and y. cm 2 b) Solve the equations and calculate x and y.
10) Work out the value of x. Round to 3 significant figures. a) b)
11) The scatter graph shows some information about seven children. It shows the age of each child and the number of hours sleep each child had last night. The table shows the ages of four more children and the number of hours sleep each of them had last night. Age (years) 1 2 3 4 5 6 7 10 11 12 13 Number of hours sleep 15 14 14 13 12 12.5 12 11 10 10.5 9.6 a) On the scatter graph, plot the remaining information from the table. b) Draw in a line of best fit. Use your line to estimate the number of hours sleep for an 8 year old child.
12) A random sample of 200 females measured the length of their hair in cm. The results are displayed in the cumulative frequency curve below. 200 175 Cumulative frequency 150 125 100 75 50 25 0 0 5 10 15 20 25 30 35 length (cm) 40 45 50 a) Write down the median length of hair in the sample. b) Find the interquartile range for the length of hair in the sample 13) Calculate the length of the altitude (height) of an equilateral triangle with side 25 cm. Round to 1 decimal place.
14) The diagram shows a rectangle with length 3x + 2 and width 2x. All measurements are given in centimetres. The perimeter of the rectangle is P centimetres. The area of the rectangle is A square centimetres. a) Write down an expression in its simplest form, without brackets, in terms of x, for i) P. ii) A. P = 44 b) Work out the value of A.
15) A and B are points on the circumference of a circle, centre O. TA and TB are tangents to the circle. Calculate the size of the angle ATO when angle AOT = 56 16) Solve the simultaneous equations y = x + 5 x + y = 1 x = y =
17) Using the quadratic formula, calculate the solutions of 5x! 9x 1 = 0. Round to 2 decimal places. x = or x =
18) Solve the simultaneous equations 2x + 6y = 17 3x 2y = 20 x = y = 19) Simplify by first factorizing: a)!!!!!!!!!!! b)!!!!!!!!!!!!!
20) Make the following into a single fraction:!!!! +!!!! 21) Solve the following equation:! +! =!!!!!!!!!!! x =
22) An extension is being built onto a golf clubhouse so that people in the clubhouse can get a good view of the 18th green. The floor plan is shown here. a) Calculate the area of the extension. Round to one decimal place. Extension m 2 b) Calculate the cost of carpeting this extension with carpet that costs 11.99 per square metre. Round to two decimal places.
23) y varies inversely with x. When x = 4, y = 14. a) Find a formula for y in terms of x. b) Calculate x when y = 10.
24) Δ ABC is right-angled at B. a) Calculate the perimeter of ABC. cm b) By how much is ACB smaller than BAC? Round to a whole number.
25) A toy maker has two similar soft toys in stock. a) Calculate the reduction factor from the large to the small toy. b) The larger toy requires 6 litres of stuffing. What volume of stuffing is needed for the smaller toy? Round to 2 decimal places. c) The smaller toy needs an area of 1000 cm 2 of material to make it. What area of material is required to make the larger toy?
26) Work out the value of x. Round to 2 decimal places. a) x = b) x = c) x =
27) Work out the area of the following shape. Round to a whole number. 28) Work out the shaded area, in terms of x. Write your answer as a single fraction. cm 2
29) The diagram represents the back section of a greenhouse. It is circular with a horizontal floor PQ = 1.8 m wide. The radius OP of the cross-section is 1.4 m. a) Calculate the height of the greenhouse, h m. Round to 2 decimal places. b) Calculate the angle of elevation from P to the top of the greenhouse, A. Round to a whole number.
30) The diagram shows the shape PQRST. RST is a circular arc with centre P and radius 18 cm. Angle RPT = 40. a) Calculate the length of the circular arc RST. Give your answer correct to 3 significant figures. cm PQR is a semicircle with centre O. b) Calculate the total area of the shape PQRST. Give your answer correct to 3 significant figures. cm 2